International Journal of Operational Research (121 papers in press)

Regular Issues

• Metaheuristics for Time-Dependent Vehicle Routing Problem with Time Windows  
  by Yun-Chia Liang, Vanny Minanda, Aldy Gunawan, Hsiang-Ling Chen 
  Abstract: Vehicle routing problem (VRP), a combinatorial problem, deals with the vehicle’s capacity visiting a particular set of nodes while its variants attempt to fit real-world scenarios. Our study aims to minimise total travelling time, total distance, and the number of vehicles under time-dependent and time windows constraints (TDVRPTW). The harmony search algorithm (HSA) focuses on the harmony memory and pitch adjustment mechanism for new solution construction. Several local search operators and a roulette wheel for the performance improvement were verified via 56 Solomon’s VRP instances by adding a speed matrix. The performance comparison with a genetic algorithm (GA) was completed with the same number of parameters and ran in the same computer specification to justify its performance. The results show that HSA can outperform the GA in some instances. The research outcomes suggest that HSA can solve TDVRPTW with comparable results to other commonly used metaheuristic approaches.
  Keywords: vehicle routing problem; VRP; time window; harmony search algorithm; HSA; genetic algorithm; metaheuristic.
  DOI: 10.1504/IJOR.2022.10045858
   
  
• A Conditional Value-at-Risk (CVaR) approach to studying the Sustainable Crude Oil Supply Chains (SCOSCs) evolved due to change in government policies  
  by Davoud Ghahremanlou, Wieslaw Kubiak 
  Abstract: Recently US oil and bioethanol industries have faced drastic economic damage due to the 2020 Saudi Arabia-Russia oil price war and coronavirus disease (COVID-19), resulting in many bankruptcies. Government policies have brought these two main industries together to ensure sustainable crude oil supply chains, to combat global warming and energy insecurity. This motivated us to extend the study of Ghahremanlou and Kubiak (2021a) to protect the current and new SCOSCs against financial risks during economic crises by providing insights for the government and the investors, working to rescue the industries. We employ conditional value-at-risk, and develop a two-stage stochastic programming model. We perform a case study of the State of Nebraska by carrying out a computational experiment with 10,710 different policy scenarios. We recommend robust strategic investment decisions to businesses during policy changes within economic crises. We also identify resilient strategic investment decisions.
  Keywords: COVID-19; conditional value-at-risk; CVaR; government policies; economic crises; sustainable crude oil supply chain; two-stage stochastic programming.
  DOI: 10.1504/IJOR.2022.10046294
   
  
• A Fuzzy Economic Order Quantity Model for Multiple Stage Supply Chain with Fully Backlogged Shortages Derived without Derivatives under the Effect of Human Learning  
  by Richi Singh, Ashok Kumar, Dharmendra Yadav 
  Abstract: In industries, inventory managers face major difficulties in inventory planning when the available information fluctuates abruptly or is unclear. This ambiguity can be treated appropriately by using fuzzy sets. Moreover, human learning is effective in reducing the level of fuzziness over the infinite horizon. In the present study, a fuzzy three-stage (buyer-distributor-vendor) EOQ model is developed. In this model, all the cost parameters are taken as fuzzy parameters. Shortages are allowed but fully backlogged at the buyer end. The novelty of the paper lies in deriving the fuzzy model by using the arithmetic-geometric inequality method and proposing four theorems based on optimal frequency for vendor and distributor, along with incorporating the concept of learning in fuzziness. Some numerical examples are taken to demonstrate the model in a better way. Also, a comparison among the results of this paper, and other papers are done with the help of an example, which shows that the present model better represents the practical financial situations. At last, sensitivity analysis concerning all parameters and managerial insights are presented to justify the significance of the model.
  Keywords: supply chain; arithmetic geometric inequality; fuzzy costs; learning; backlogging.
  DOI: 10.1504/IJOR.2022.10046637
   
  
• Comparative Study of Maximization Assignment Model by Existing Method and Newly Proposed Methods  
  by Agnivesh Tiwari, Kabir Chaudhary, Rahul Boadh, Yogendra Rajoria 
  Abstract: One of the simplest uses of linear programming is known as the assignment problem, which is a special case of the transportation problem. The assignment problem manages the inquiry about to dole out n-items to m-different items in the most ideal way for production planning, telecommunication, VLSI design, economics, etc. Many researchers developed newly proposed methods for solving assignment problems and others modified the Hungarian method. Therefore, in the present study, an effort has been made to solve the real-life balance and unbalance type profit maximisation assignment problem used by ten newly proposed methods such as MAP, MSEI, ATOC, NAZs and six others methods, and compared results with Hungarian method. This study found that Method 8 takes the least time for computation of both type problems as compared with other methods. This paper advocates that new researchers and scientists may use the newly proposed Method 8 in place of the existing method.
  Keywords: assignment problem; Hungarian method; optimal solution; profit maximisation.
  DOI: 10.1504/IJOR.2022.10046644
   
  
• A NEW GENERALIZED MEDIAN BASED ESTIMATOR OF THE FINITE POPULATION MEAN  
  by Dharmendra Yadav, Dinesh K. Sharma, S.K. Yadav 
  Abstract: To enhance the performance of an estimator, the use of additional information on study variables instead of the auxiliary variables may be a good alternative in survey sampling as it does not increase the survey cost. One of the examples of such additional information is the use of the median of the main variable. As there is no need for full information on units of the population under consideration for the median, so many times it is known to us. In the present article, we have developed an extended ratio estimator for the population mean utilising a given population median of the study variable. We have driven out the expressions for Bias of suggested estimator along with its MSE up to the approximation of degree one. The optimal value of the characterising scalar has also been derived using the method of maxima and minima. The conditions under which the suggested estimator is more efficient than previous estimators are also obtained. Our findings, in theory, are supported by the numerical illustration consisting of three different natural populations. The efficiency of the suggested estimator over competing estimators is also presented in the form of graphical representation.
  Keywords: median; ratio estimator; bias; MSE; efficiency.
  DOI: 10.1504/IJOR.2021.10046753
   
  
• Solution of a mining equipment maintenance system model in imprecise environment  
  by Ashok Kumar Shaw, Mostafijur Rahman, Sankar Prasad Mondal, Banashree Chatterjee, Shariful Alam 
  Abstract: In this paper, a mining equipment maintenance system is depicted by a mathematical model described in terms of a pair of differential equations. The impreciseness involved in a real-life situation is accounted in this paper letting the initial condition and associated parameters to be imprecise in nature. Two most popular mathematical knowledge dealing with the sense of uncertainty, namely the fuzzy and interval environments are utilised here to analyse and solve the proposed model under uncertainty. The solutions of the uncertain differential equations (both interval and fuzzy) corresponding to the model are getting inspired by the generalised Hukuhara derivative of a set valued function. Different crispification techniques of converting the fuzzy and interval solutions into their crisp representatives are manifested to compute and compare the score of feasible decisions under uncertainty.
  Keywords: mining equipment maintenance problem; generalised Hukuhara derivative; fuzzy differential equation; FDE; interval differential equation; removal area method; mean of centre method.
  DOI: 10.1504/IJOR.2022.10047628
   
  
• MSTL: A Seasonal-Trend Decomposition Algorithm for Time Series with Multiple Seasonal Patterns  
  by Kasun Bandara, Rob Hyndman, Christoph Bergmeir 
  Abstract: The decomposition of time series into components is an important task that helps to understand time series and can enable better forecasting. Nowadays, with high sampling rates leading to high-frequency data (such as daily, hourly, or minutely data), many datasets contain time series data that can exhibit multiple seasonal patterns. Although several methods have been proposed to decompose time series better under these circumstances, they are often computationally inefficient or inaccurate. We propose a procedure to decompose time series with multiple seasonal patterns that is suited to a wide range of high-frequency data. The procedure for multiple seasonal trend decomposition (MSTL) introduced in this paper extends the traditional seasonal-trend decomposition using Loess (STL) algorithm, allowing the decomposition of time series with multiple seasonal patterns. In our evaluation on synthetic and a perturbed real-world time series dataset, compared to other decomposition benchmarks, MSTL demonstrates competitive results with lower computational cost. The implementation of MSTL is available in the R package forecast.
  Keywords: time series decomposition; multiple seasonality; MSTL; TBATS; STR.
  DOI: 10.1504/IJOR.2022.10048281
   
  
• Analysis of (MAP, PH)/(PH, PH)/1 Retrial Queueing Model with Standby Server, Collision of Orbital Customers, Breakdowns, Two-way communication, Phase Type Repairs, Constant Retrial Rate and Impatient Behaviour of Customers  
  by AYYAPPAN Govindan, Thilagavathy Karthikeyan 
  Abstract: Having modelled our system using standby server whenever the main server unavailable due to breakdowns and analysed the constant retrial policy for the orbital customers. The incoming arrival (IA) of customers follows the Markovian arrival process (MAP). The outgoing arrival (OA) of customers, service for both incoming and outgoing arrival of customers, repairs are all based on the phase-type (PH) distributions. Using Matrix analytic method, we investigate the steady state probability vector of the system. We described the busy period, cost analysis of the system and some characteristics of the system measures. We evaluate some numerical and graphical representation for the elucidation of our proposed model.
  Keywords: PH Distribution; MAP; Standby Server; Impatient Behaviour; Constant retrial rate; Two-way Communication.
  DOI: 10.1504/IJOR.2022.10048364
   
  
• A Novel Technique for Solving Bi-Level Linear Fractional Programming Problems with Fuzzy Interval Coefficients  
  by Nejmaddin Sulaiman, Gulnar Wasim, Basiya Kakawla 
  Abstract: In this paper, a bi-level linear fractional programming problem (BILLFPP) with fuzzy interval coefficient (FIC) is contemplate where really all of it is coefficients in the goal function and constraints are fuzzy intervals (FIs). Firstly, to resolve this issue, we are going to construct two LFPP with fuzzy coefficients. Before all else, of these issues is a LFPP where all of coefficients are upper approximations of FIs and the other is a LFPP where all of coefficients are lower approximations of FIs. Secondly, the BILLFPP is transformed to the form of single goal LFPP and QFPP. We address problems with a factorised or non-factorised optimisation problem and homogeneous or non-homogeneous constraints. Our proposed technique is based on a mathematical model that converts the QFPP to a LPP by solving the problem in an algebraic expression with a Taylor series. This technique, which is based on the LPP solution, can be applied to specific problems. NLFPP containing nonlinear constraints, on iterative processes, it decreases the overall processing time. To explain, the novel technique for solving BILLFPP by taking numerical examples and compare with Jayalakshmi (2015) and Syaripuddin et al. (2017).
  Keywords: LFPP; bi-level linear fractional programming problem; BILLFPP; FBILLFPP; BILLFPP with fuzzy interval; FBILLFPP with FIC; QFPP; Taylor series; a novel technique.
  DOI: 10.1504/IJOR.2022.10049559
   
  
• An integrated Systematic Layout Planning (SLP), Analytical Hierarchy Process (AHP) and Non-Linear Programming (NLP) approach to facility layout design  
  by Vikas Singla 
  Abstract: This study has three aims: 1) finding alternative layout designs through procedural approach of SLP of a large-scale auto component manufacturer; 2) examine optimality of identified alternatives by using both qualitative and quantitative criteria and ranking them by using AHP method by collecting data from decision-makers of similar 132 manufacturers; 3) identifying most optimal design by using mathematical optimisation model of NLP. Results of SLP provided three prominent quantitative criteria by comparing key performance indicators of four alternative designs with those of existing layout. Informal discussions extracted major qualitative criteria. Rating of all six criteria indicated distance and cost of change being primary influencers. Results of NLP were able to identify one most optimal alternative from feasible four derived from SLP. The study derives its originality by dealing with shortcoming of SLP approach of over emphasis on subjective criteria and of metaheuristic methods of assigning excessive importance to metaheuristic methods.
  Keywords: facility layout; systematic layout planning; SLP; analytic hierarchy process; AHP; nonlinear programming; NLP; quadratic assignment problem; QAP.
  DOI: 10.1504/IJOR.2022.10049593
   
  
• PROPOSAL OF A NUMERICAL APPROXIMATION THEORY TO SOLVE THE ROBUST CONVEX PROBLEM OF PRODUCTION PLANNING  
  by Marcelo Gonçalves, Rafael Wollmann, Raimundo Sampaio 
  Abstract: his research seeks to solve the production planning problem modelled as a queuing system to propose to managers a production planning model that uses efficient, simple and robust methods. First, a robust mathematical model of nonlinear programming was proposed considering the concepts of queuing systems to estimate production capacity. Next, this model was approximated by a family of affine functions using the strategy of approximating a convex set by a polyhedral set. Finally, a theorem was proposed to demonstrate that a robust nonlinear programming model can be approximated by a robust linear programming model. From a numerical experiment with data from an electronic equipment company, it was possible to observe the effectiveness of the approximation method.
  Keywords: robust optimisation; linear programming; convex programming; queuing systems.
  DOI: 10.1504/IJOR.2022.10049618
   
  
• Optimal Location Prediction for Emergency Stations using Machine Learning  
  by Prasham Sheth, Praxal Patel, Priyank Thakkar 
  Abstract: Time is a critical aspect in emergency circumstances like medical crises, natural disasters, breaking out of a fire, etc. The average response time of emergency services is on the rise in recent times owing to the growing traffic. This has raised some serious concerns for people’s safety. It is easy to perceive that optimally located emergency stations (e.g., ambulance, fire station) can help in these situations by minimising travel time to reach the location of casualty. With this motivation, we propose an approach which employs K-medoids driven by extreme gradient boosting (XGBoost) for predicting optimal locations of emergency stations. The proposed approach is validated on real datasets, namely: New York City, USA 100-metre Grid Coordinates, NYC Taxi Trip Duration, KNYC Metars 2016 and FDNY Firehouse Listing dataset and the results demonstrate that the proposed method reduces normal average response time and allows serving more locations.
  Keywords: emergency station; optimal location prediction; OLP; machine learning; XGBoost; K-medoids; average response time.
  DOI: 10.1504/IJOR.2022.10049826
   
  
• An EOQ Model for Deteriorating Item with Ramp type Linear Time Dependent Demand and Time Dependent Partial Backorder  
  by Prokash Mondal, Asim K. Das, Tapan Kumar Roy, Surajit Naskar 
  Abstract: In this present article we have developed an economic order quantity (EOQ) model over a finite time horizon for an item with a liner time dependent demand rate with constant rate of deterioration in consideration of shortages (SFI policy) in inventory under permissible delay in payments and partial backlogging. Studied witnessed that the demand always play a pivot role in the inventory model, due to COVID crisis there is a shift in the paradigm on the demand characteristics. This model studied the shifting demand rate after stock out period. Mathematical models are also developed under two distinct circumstances, i.e., case 1: the trade credit is before the stock out period and case 2: the trade credit scheduled after stock out period. The results are illustrated with numerically and graphically. The sensitivity analysis of key parameters of the optimal solution has also been conducted to study the effect of the parameter.
  Keywords: inventory; economic order quantity; EOQ; deterioration; delay in payment; trade credit; backlog dependent.
  DOI: 10.1504/IJOR.2022.10049855
   
  
• Linearization of Non-Linear Programs using the Essence of Calculus and Integer Programming  
  by Matthew Zilvar 
  Abstract: This paper contains an approach to solve nonlinear programming (NLP) problems using a linearisation approach based on theorems of calculus. The solution method relies upon dividing functions with finite domains into a series of domains and coefficients used to model linear and nonlinear functions within a mixed integer linear program (MILP). Nonlinear terms are solved for in the objective function and constraints while achieving global optimality at a specified resolution using the international system of units (SI). An efficient solution method is provided by creating a set of MILPs that represent the same problem with different complexities and using the solutions to achieve global optimality. Numerical results and a comparison are provided. From the results an argument in the P versus NP problem is formed.
  Keywords: linearisation; nonlinear programming; integer programming; P vs. NP; calculus; logarithmic programming; transportation problem; set forming; complexity theory; global optimality.
  DOI: 10.1504/IJOR.2022.10050354
   
  
• A Comparison of a novel single reference point Multi-Attribute Decision Making Method with EDAS method  
  by Sirine Boujelben, Mohamed Souissi 
  Abstract: The present work aims to introduce a new method called the evaluation based on deviation from median attribute values (EDMAV) to solve the multi-attribute decision problems. This method is based on the deviation of each alternative from to the reference median solution with respect to each criterion. However, the proposed method combines the results of two different models to get the global score of each alternative, namely weighted arithmetic mean (WAM) and weighted median model (WMed). A ranking of alternatives is performed based on the value of a joint generalised criteria computed according to the results of these models. The proposed method is applied on illustrative example in order to illustrate its applicability, usefulness, and effectiveness and it has been compared with the evaluation based on distance from average solution (EDAS) method.
  Keywords: multi-attribute decision; operational research; weighted median; average; single reference point.
  DOI: 10.1504/IJOR.2022.10050398
   
  
• A Double-Pivot Degenerate-Robust Simplex Algorithm for Linear Programming  
  by Yaguang Yang, Fabio Vitor 
  Abstract: A double pivot simplex algorithm that combines features of two recently published papers by these authors is proposed. The proposed algorithm is implemented in MATLAB. The MATLAB implementation is tested, along with a MATLAB implemention of Dantzig’s algorithm, for several test sets, including a set of cycling linear programming problems, Klee-Minty’s problems, randomly generated linear programs, and Netlib benchmark problems. The test results show that the proposed algorithm, with a careful implementation is: 1) degenerate-robust as expected; 2) more efficient than Dantzig’s algorithm for large size randomly generated linear programming problems, but less efficient for Netlib benchmark problems and small size randomly generated problems in terms of CPU time.
  Keywords: double pivots; degenerate-robust; simplex method; linear programming; Klee-Minty cube.
  DOI: 10.1504/IJOR.2022.10050447
   
  
• General finite approximation of noncooperative games played in staircase-function continuous spaces  
  by Vadim Romanuke 
  Abstract: A method of general finite approximation of N-person games played with staircase-function strategies is presented. A continuous staircase N-person game is approximated to a staircase N-dimensional-matrix game by sampling the player’s pure strategy value set. The method consists in irregularly sampling the player’s pure strategy value set, finding the best equilibria in
  Keywords: game theory; payoff functional; staircase-function strategy; multidimensional-matrix game; approximate equilibrium consistency; equilibrium stacking.
  DOI: 10.1504/IJOR.2022.10050526
   
  
• DEVELOPMENT AND VALIDATION OF A HYBRIDIZED ALGORITHM INVOLVING AHP AND MACHINE LEARNING FOR AUTOMOBILE VEHICLE SELECTION  
  by Sanjeev Kumar, Ashirbad Sarangi, Rakesh P. Badoni, R.P. Mohanty 
  Abstract: The problem of selecting an automobile has always been one of the most complex decisions to make, given a person’s social and economic life. It is often resolved either through a qualitative judgement of vehicles or through multiple criteria decision-making (MCDM) methods in an algorithmic way. However, the modern machine learning (ML) procedures have surfaced themselves as efficient techniques in the field of recommendation engines (REs) to predict the items that may be useful to the customers according to their preferences. In this paper, an attempt has been made to study the automobile vehicle selection (AVS) problem in an innovative manner by hybridising the analytic hierarchical process (AHP) with the collaborative filtering (CF) technique to construct a selector to recommend the customers precisely one pair of cars that would suit best to their preference. The proposed algorithm provides an efficient way to map the satisfaction level of the customers by eliminating the vagueness and complexity in the selection process. We have validated the algorithm using real-life datasets collected by administering an exploratory survey across geographies, including India.
  Keywords: multiple criteria decision-making; MCDM; analytic hierarchical process; AHP; automobile vehicle selection; AVS; collaborative filtering; CF; recommendation engine.
  DOI: 10.1504/IJOR.2022.10050616
   
  
• Modelling MX/G/1 queuing system with optional second service under disaster and repairs with multiple adapted vacation policy  
  by S. Jeyakumar, B. Logapriya 
  Abstract: In this article, the queuing system with disaster is considered in which every customer will receive the essential service and demanded customer alone will receive second optional service. When the system is affected by any of the disaster, the server initiates the repair period and operates under multiple adapted vacation (MAV) policy causing all waiting and served customer to leave the system. Using supplementary variable technique, we procure the queue size distribution with few measures of performance. Expected queue length, expected waiting times and certain special cases are discussed. In addition, the effect of parameters is studied with a numerical illustration.
  Keywords: supplementary variable technique; second optional service; disaster; multiple adapted vacation policy.
  DOI: 10.1504/IJOR.2022.10050810
   
  
• A systematic literature review to measure lean, green and agile in manufacturing organisations  
  by Fadwa Bouhannana, Akram Elkorchi 
  Abstract: Most manufacturing companies are mainly interested in strengthening competiveness by concentrating on competitive priorities. The majority of companies have started implementing lean, green and agile paradigms in order to become more efficient and highly productive. To achieve those objectives, researchers around the world have been increasingly interested in developing tools to control the process of implementing these three paradigms in organisations. In this context, various approaches have previously been proposed in the literature. Consequently, a systematic review of measurement methods, such as leanness, greenness and agility, in manufacturing organisations was performed for the purpose of defining some guidance for managers and practitioners who are interested in measuring these three concepts. Therefore, 121 methods have been selected and analysed based on a set of comparative dimensions. The main strengths and weaknesses of the selected approaches are mentioned. Some literature gaps are highlighted, and a number of directions are provided for future research.
  Keywords: manufacturing; leanness; greenness; agility; literature review; score.
  DOI: 10.1504/IJOR.2022.10050966
   
  
• A multi-objective portfolio selection problem with parameters as interval type fuzzy set.  
  by Jayanti Nath, Sanjoy Chhatri, Debasish Bhattacharya 
  Abstract: A multi-objective portfolio selection problem with fuzzy parameters is studied here based on the possibility concept of fuzzy set theory. Here, for a given degree of membership ? of the fuzzy parameters, the problem has been reduced to an equivalent crisp problem. This reduced problem is then solved by the min-max goal programming (GP) method in one step. This approach gives the decision maker the flexibility to choose the solution of the problem for an assigned degree of satisfaction ? and concomitant risk (1
  Keywords: portfolio optimisation; fuzzy multi-objective linear programming; capital growth; return; risk; liquidity; dividend; min-max GP.
  DOI: 10.1504/IJOR.2022.10051487
   
  
• Applying Mathematical Modeling to the Factor Analyses of Obtaining GASR Funds for Universities in Japan  
  by Masashi Miyagawa, Takuro Matsumoto, Atsushi Inoue, Tatsuo Oyama 
  Abstract: First, we briefly explain the historical trend of the Japanese competitive research funding system, focusing on the grants-in-aid for scientific research (GASR). We provide mathematical models, such as logistic curves and Zipf’s model, to explain the trend of budgets for research promotion funds and their allocation to Japanese universities and research institutions. Subsequently, we evaluate the performance of Japanese universities from the perspective of obtaining GASR funds using Gini coefficients. We then build multiple regression models to quantitatively investigate the factors that determine and affect the dependent variables, such as the number of accepted GASR projects and number of distributed funds of the GASF projects, in which independent variables including the number of undergraduate students, external funds, operating expenses grants, and operating expenses grants to all university-specific project expenses, or the ratio of external funds per faculty member, may also be considered as influential factors. We apply multivariate analysis techniques such as cluster analysis and principal component analysis to determine the key factors for obtaining GASR, to classify Japanese universities with respect to their recent scenario for obtaining GASR funds and reveal the determining factors underlying these results.
  Keywords: competitive research fund; scientific research fund; mathematical model; logistic curve; Zipf’s model; multiple regression model; cluster analysis; principal component analysis.
  DOI: 10.1504/IJOR.2022.10051636
   
  
• Priority Study on Commodity Market Operation and Performance for Indian Investors  
  by Sanat Rout, Sadananda Sahoo, Rabindra Kumar Mishra 
  Abstract: The present research explores the investors’ behavioural intention towards the commodity market in an emerging economy. Drawing cues from the extant literature, this research identifies and empirically prioritises the dimensions of investor intention regarding commodity trading. Based on the RIDIT analysis, the findings indicate that a lower degree of risk, geopolitical changes, and a higher rate of return are the most important dimensions based on the respondent perceptions. These findings offer newer insights on this under-explored domain to facilitate conceptual development and policy formulation. The portfolio managers, market regulators, and financial institutions can take cues from the study findings to redesign their strategies for attracting investors to commodity exchanges.
  Keywords: commodities; investor; behavioural intention; emerging economy; RIDIT.
  DOI: 10.1504/IJOR.2022.10051839
   
  
• On state dependent batch service queue with single and multiple vacation under Markovian arrival process  
  by Gagan Kumar Tamrakar, Anuradha Banerjee 
  Abstract: : An infinite buffer batch service vacation queue has been studied where service rate of the batch is dependent on the size of the batch and vacation rate is dependent on the queue size at vacation initiation epoch. The arrivals follow the Markovian arrival process (MAP). For service rule, general bulk service (GBS) rule is considered. The service time and vacation time both are considered to be generally distributed. Several joint distributions of interest are obtained using the bivariate vector generating function method and the supplementary variable technique (SVT). Numerical results are presented to show the behaviour of the system performance to validate the analytical results.
  Keywords: Markovian arrival process; infinite buffer; GBS rule; bivariate VGF; supplementary variable technique.
  DOI: 10.1504/IJOR.2022.10052122
   
  
• On Solving Game Problem using Octagonal Neutrosophic Fuzzy Number  
  by R. Narmada Devi, S. Sowmiya 
  Abstract: Game theory deals with competitive situation where there are two or more opposing parties with conflicting interests are involved. A competitive situation will be called a game. In this paper, a new approach for selecting a best strategy for increasing the shares for two companies using octagonal neutrosophic fuzzy number is proposed. Further, convert a octagonal neutrosophic fuzzy number to neutrosophic fuzzy number by using deneutrosophication and finally get the fuzzy number by using fuzzification method. The obtained matrix represents fuzzy game matrix. This matrix is solved using game theory to obtain the best strategy for these companies.
  Keywords: octagonal neutrosophic fuzzy number; ONFN; DTNON: de-neutrosophication of trueness; DINON: de-neutrosophication of indeterminacy; DFNON: de-neutrosophication of falsity.
  DOI: 10.1504/IJOR.2022.10056357
   
  
• Multi-Echelon Reverse Supply Chain Network Design using New Ant Colony Optimization Algorithms  
  by Mostafa Ashour, Raafat Elshaer 
  Abstract: Reverse logistics (RL) is becoming more important in the general area of the industry due to environmental and business factors. Planning and implementing a suitable RL network can lead to more benefits, customer satisfaction, and a nice social image for businesses. Since such network design challenges belong to the NP-hard problem class, three proposed ant colony algorithms that differ in the heuristic information, and artificial pheromone trail calculation rules were developed to solve a designed distribution-allocation problem in multi-stage RL network with a fixed transportation cost in distribution network as well as variable cost of the route. Five network characteristics with different sizes are designed, and thirty instances are randomly generated for each network characteristic to evaluate the performance of the three developed ant colony optimisation (ACO) algorithms. Computational analysis of the results reveals the high quality and validity of the developed ACO algorithms when compared with the exact results.
  Keywords: logistics network; forward/reverse supply chain; single-objective; ant colony optimisation; ACO.
  DOI: 10.1504/IJOR.2022.10052168
   
  
• A LINMAP Approach for Determining Subjective Attribute Weights for Neutrosophic Multi Attribute Decision Making Models  
  by S. Paulraj, G. Tamilarasi 
  Abstract: The linear programming technique for multidimensional analysis of preference (LINMAP) is one of the well-known methods involved to solve multi-attribute decision-making (MADM) problems. Many authors developed LINMAP method based on fuzzy and intuitionistic fuzzy environment. In this paper, we develop a new method called neutrosophic Linear programming technique for multidimensional analysis of preference (LINMAP), which combines the single valued neutrosophic sets with LINMAP method. This paper establish the conventional LINMAP method to a neutrosophic MADM framework using single valued trapezoidal neutrosophic numbers and we obtain the attributes weight and ideal solution. A practical example is provided to show that our method is very effective for solving MADM problems with single valued trapezoidal neutrosophic number information. Comparative analyses with existing method are also furnished to shows the advantage of our proposed method.
  Keywords: single valued trapezoidal neutrosophic number; LINMAP; consistency and inconsistency measures; multi-attribute decision making; MADM.
  DOI: 10.1504/IJOR.2022.10052436
   
  
• Parallelization of multiple traveling salesman problem without returning to the starting node  
  by Vadim Romanuke 
  Abstract: A method of heuristically solving the non-classic multiple travelling salesman problem is suggested, where a dramatic computational speedup is guaranteed. The salesmen covering the route must not return to the starting node in this problem. A specific genetic algorithm is the solver. To get the speedup, the nodes should be separable so that they could be divided into two or more groups. Every two adjacent groups are connected by a node called the isthmus. The respective subproblems are solved independently, in parallel, whereupon their subroutes are aggregated through the isthmuses. This shortens the aggregated route on average, although it may be slightly longer in specific cases. Such an accuracy loss is 1% to 2% in the worst case for a few hundred thousands to millions of nodes, but instead the saved computational time is counted in days, weeks, and months. The efficiency of such a parallelisation dramatically grows as more isthmuses as distinct node group separators are found. If two successive subroutes are covered by the same number of salesmen, the constraint of that every node can be visited only by one salesman is easily satisfied by correcting the subroutes at the isthmus.
  Keywords: multiple travelling salesman problem; route length; genetic algorithm; parallelisation; isthmus; node group separability.
  DOI: 10.1504/IJOR.2022.10052526
   
  
• Effect of Quadratic Price-Dependent demand with Quadratic Time-Dependent Demand in EOQ Inventory Models for Deteriorative items  
  by Selvaraju P, Sivashankari C.K. 
  Abstract: This research focuses on impact of quadratic price-dependent and time-dependent demand in EOQ inventory models for deteriorative products in higher-order equations is examined in this article. Linear, constant, exponential, quadratic, stock dependent, price dependent, and other demand models have been discovered in the literature. In real practice, the price of the item and the time it takes to sell has a significant impact on the demand rate. Three models are developed: Quadratic time-dependent and price-dependent demands are used in the first model. In second model quadratic-time dependent and in the third model quadratic price dependent demands are used. The aim of this study is to identify the optimum cycle time and the optimum quantity that minimises the total cost. Each model has its own set of mathematical models. A sensitivity analysis is performed after solving and studying many numerical examples. Visual Basic 6.0 was used to create the required data.
  Keywords: EOQ inventory; quadratic price-dependent demand; quadratic time-dependent demand; integrate; optimality; sensibility analysis.
  DOI: 10.1504/IJOR.2022.10053350
   
  
• A Vendor-Managed Inventory Model for Deteriorating Products  
  by Anyarin Sakrujiratham, Huynh Trung Luong 
  Abstract: This paper develops a vendor-managed inventory model for deteriorating products in a two-level supply chain which is comprised of one vendor and one retailer in the case when the time to deterioration of the product follows Weibull distribution. It is assumed that the market demand is price-sensitive and shortages are fully backlogged. The proposed inventory model helps to determine the replenishment cycle length and the optimal replenishment quantity to help minimise the total cost of the entire supply chain. Numerical experiments and sensitivity analyses are conducted to illustrate the applicability of the proposed model. Some future research directions are also discussed.
  Keywords: vendor-managed inventory; VMI; inventory control; deteriorating products; supply chain management.
  DOI: 10.1504/IJOR.2022.10053513
   
  
• A novel hybrid BSC-DEA model for performance assessment in knowledge enterprises using balanced scorecard and data envelopment analysis approach  
  by Bakhtiar Ostadi, Masoud Sadri, Ehsan Nikbakhsh 
  Abstract: The importance of knowledge enterprises (knowledge-based companies) in countries’ economies and their role in GDP has recently increased, and many efforts have been made to achieve a comprehensive and consistent benchmark and model for evaluating these companies. Therefore, the purpose of this paper is to provide a hybrid model for performance assessment in knowledge enterprises. So, the primary indicators have been extracted by reviewing the literature and structure of knowledge enterprises. After collecting data from knowledge enterprises and combining the balanced scorecard (BSC) and data envelopment analysis (DEA) approach, a hybrid BSC-DEA model developed to assess the partial efficiency of each unit and the total efficiency of each knowledge enterprises. Finding mentioned that the ability of start-ups and knowledge enterprises to be compared with large and old ones. Also, there will be no significant difference in the performance of companies with respect to their type.
  Keywords: performance assessment; knowledge enterprises (knowledge-based companies); data envelopment analysis; DEA; balanced scorecard; BSC.
  DOI: 10.1504/IJOR.2023.10053850
   
  
• Optimizing Production and Operational Cost in a Limestone Mine by MINLP Approach: An End-to-End Case Study  
  by Anindita Desarkar, Aaditya Umasankar, Viswa Janith Paidisetty, Abhishek Sarma, Santosh Kumar Annabattula Venkata Varaha, Vishwanathan Raman, Mahesh Mahajan 
  Abstract: Prediction is always a challenging task; it gets harder especially in mining where lots of complexities and uncertainties are present in the system. Optimizing the production output by adhering to the ore quality, minimizing fuel consumption towards operational cost reduction, maximizing utilization and minimizing the idle time of the fleets are a few major goals in the mining industry. However, all these things depend upon the optimal distribution of resources and equipment in appropriate places. Though manual allocation can be one solution, but optimal result is not always achieved because it's quite difficult to optimize so many parameters on a day-to-day basis. The present research proposes a multistage and multi-objective optimization approach based on mixed integer non-linear programming to achieve the aforesaid goals. The experimental results show the efficacy of the method, and it is also implemented in one real mine scenario where all the above-mentioned goals are achieved.
  Keywords: Optimization; Mixed-Integer Non-linear programming; Production maximization; Fuel minimization; Resource allocation; Utilization; Productivity; Truck dispatching.
  DOI: 10.1504/IJOR.2023.10053952
   
  
• Waste Management by Bilevel Optimisation: A Survey  
  by Massimiliano Caramia, Emanuele Pizzari 
  Abstract: Waste Management is a complex and broad field of research. In problems falling under this category, several decision-makers have conflicting objectives and hierarchies. Therefore, the common approaches of single-objective optimisation or multiobjective optimisation may fail to capture the nuances of the situation. Hierarchical problems are best handled from a mathematical optimisation point of view via bilevel programming. In this paper, we survey contributions modelling waste management issues employing bilevel optimisation, a relatively new yet promising field of research. We start by providing a general analysis of these contributions and then describe the latter in macro-subjects. Finally, we draw some conclusions by providing open problems and follow-ups.
  Keywords: Bilevel optimisation ; Waste management ; Literature review.
  DOI: 10.1504/IJOR.2022.10054097
   
  
• A Production Model for Deteriorative items with Time Dependent Demand and Possible Adjustment of the Production Rate  
  by Sivashankari C.K., Valarmathi R. 
  Abstract: In this paper, two different rates of production problem of production inventory system for deteriorative items having constant demand, linear demand as well as quadratic demand is considered and in order to cut costs, it is preferable to begin production at a low rate (X1) and gradually increase to a higher rate (X2) over time. This is because starting with a low rate of production prevents an excessive quantity of manufactured goods from being stored at the outset. The variability in production rate offers a means both of resulting in the happiness of customers and of generating possible profit. There will be three models created. There is a consideration of demand that is constant demand in the first model, demand that is linear demand in the second model, along with quadratic demand in the third model. In all models, triangular inequality is used for evaluating production time and Bernoulli’s integration is used for integration in all three models.
  Keywords: Constant; Linear and Quadratic Demands; Two Rates of Productions; Optimality and comparative study.
  DOI: 10.1504/IJOR.2023.10054233
   
  
• Multi-objective optimization of surplus food recovery and redistribution units in India  
  by Nistha Dubey, Ajinkya N. Tanksale 
  Abstract: Food banks are not-for-profit organizations that collects surplus and leftover food and distribute it to unfortunate people of society with an aim to alleviate hunger. The problem can be modeled as multi depot-VRP. We endeavour three primary objectives of food banks - efficiency, effectiveness, and equity. The measure for efficiency is minimum total transportation cost, minimum total shortage for effectiveness, and minimum of the maximum shortage of network is taken for equity. This paper proposes a MILP model for multi-objective optimization of surplus food recovery and redistribution in India. Our study is the first to evaluate Indian food banks from a multi-objective perspective. To solve the proposed problem, state-of-the-art-solver Gurobi is used for weighted sum method, augmented ?-constraint method, and augmented weighted Tchebycheff methods. Non-Sorted Genetic Algorithm is developed to solve the larger network problems. The results of the computational experiments show significant trade-off behavior between efficiency and effectiveness.
  Keywords: Food banks; VRP; Multi-depot; NSGA-II; Multi-objective; Split loads.
  DOI: 10.1504/IJOR.2023.10055079
   
  
• Interaction Model Development in Determining House Prices by Using Goal Programming  
  by Nerda Zura Zaibidi, Nor Syuhaddah Saiddin, Adyda Ibrahim, Siti Aisyah Saupi 
  Abstract: The buyer, the real estate developer, and the government are typically the three main parties engaged in housing projects. The interaction between these parties affects the housing market, particularly the prices of homes. The interaction has become more difficult because of the disparities in preferences between the parties. The ideal strategy for creating a fruitful partnership between these parties is still a mystery. As a result, this study has established a decision maker interaction model for getting mutual understanding on a housing project. Goal programming and a simulation method were used in this work to develop a successful interaction model. The average dwelling price that all the parties had mutually agreed upon was represented by the mean value of RM 169,878 and it is skewed between RM 85,000 and RM 350,000. The results of this study can be used by developers in Malaysia to design homes that are affordable and appealing to buyers, preventing problems with long-term unsold homes.
  Keywords: interaction model; house prices; multi-objective optimisation; goal programming.
  DOI: 10.1504/IJOR.2023.10055108
   
  
• Genetic and Hybrid algorithms to solve the container stacking problem at Tripoli-Lebanon seaport.  
  by Nobar Kassabian, Zakaria Hammoudan, Olivier Grunder, Lhassane Idoumghar 
  Abstract: Several factors determined the survival of the seaport: logistics, storage and distribution. A storage strategy dependent on container stacking rules is an important factor in the competence of the container terminal. This article focuses on solving the problem of stacking incoming containers in the storage yard, taking into account several criteria regarding the port of Tripoli-Lebanon. A mathematical model with a mixed integer linear program for the container stacking problem is considered in this paper. As this problem is NP-hard, large instances cannot be solved by optimisation solvers as Gurobi. We develop four algorithms to tackle this problem: a genetic algorithm (GA), a randomised greedy algorithm (RGA), an iterated local search (ILS) and a hybridisation approach between RGA and ILS. Finally, numerical simulations prove the efficiency of the GA which produces results close to the optimal solution on real instances taken from the containers terminal for small and medium sizes.
  Keywords: container stacking problem; CSP; mathematical modelling; optimisation; Gurobi optimiser; genetic algorithm; GA; randomise greedy algorithm; RGA.
  DOI: 10.1504/IJOR.2023.10055823
   
  
• Metaheuristic-based approaches for the multi-centre open home healthcare routing problem  
  by Bilal Kanso, Ali Kansou, Adnan Yassine 
  Abstract: This paper presents the multi-centre open home healthcare (MC-OHHC) problem with time windows and synchronisation constraints. The MC-OHHC can be described as the problem of designing least cost routes from several centres to a set of visits, without forcing them to return to the centres. Some services require simultaneous visits by using different routes to be accomplished. The contribution of the paper is three-fold: 1) it presents the corresponding mathematical linear model; 2) it gives the results related to the CPLEX resolution and an adapted constructive heuristic solution of such a problem; 3) it provides the results related to a variable neighborhood descent algorithm, a simulating annealing algorithm and a hybrid genetic algorithm. Computational results on adapted set of benchmark instances from the literature are reported and show that our proposed approaches are fast, efficient and competitive compared to the solutions provided by the CPLEX software. Some optimal solutions are provided in short computational times, and greatly improve the initial solutions obtained by the proposed efficient constructive method.
  Keywords: home healthcare problem with multi-centres; window time; synchronisation; constructive heuristic; variable neighbourhood descent metaheuristic; simulating annealing metaheuristic.
  DOI: 10.1504/IJOR.2023.10056210
   
  
• Energy Demand Forecasting Using A Novel Optimised Fourier Grey Markov Based Approach  
  by Noorshanaaz Khodabaccus, Aslam A. E. F. Saib 
  Abstract: Energy supply affects the sustainable development of an economy, hence making its modelling and forecasting crucial to policymakers. Conventional statistical models often require either prior assumptions on the distribution of the data or large historical datasets. This paper proposes the optimised Fourier-Markov grey model (OFGM), which alleviates the former two assumptions. Two test scenarios are proposed for assessing the model's performance: data prior to the COVID-19 pandemic (20102019) and data extending over the pandemic period (20102020). Numerical experiments demonstrate that the proposed algorithm very well models both scenarios and a significant improvement in the prediction accuracy is achieved.
  Keywords: grey prediction model; Fourier; Markov; metaheuristic algorithm; energy forecasting.
  DOI: 10.1504/IJOR.2023.10056840
   
  
• The Reduction of Realized Variance in Deductible Insurance  
  by Christopher Gaffney 
  Abstract: We derive a series of mathematical identities that connect insurance purchasers with insurance companies. In particular, we focus on the way in which variance is shared between the parties. We argue that, from the perspective of governmental oversight, a desirable property of insurance is that the total amount of variance experienced by the involved parties is smaller under an insurance contract than in the uninsured case. It is shown that this always holds in the case of a single insurer and a single insured, while for the case of a single insurer and multiple insured, we derive a condition which guarantees the relationship.
  Keywords: deductible insurance; Affordable Care Act; ACA; insurance coverage; mean-variance analysis; variance reduction.
  DOI: 10.1504/IJOR.2023.10056842
   
  
• A State Dependent Arrival Analysis In a Non-Markovian Bulk Queue with Server Failures  
  by Palaniammal S, Pradeep S 
  Abstract: Breakdown brings a huge impact in the queueing system which causes complicated consequences. This paper comprises the results of functioning and malfunctioning of the queueing system due to continuous server breakdown. This work examines the failure of the server without interruption in state-dependent arrivals and numerous vacations. Even if a failure happens, the Server is not stopped for maintenance before finishing a batch of service. The queue size PGF at an irrational time period, as well as the probability generating functions of vacation, service, and renovation completion epochs, are derived using the additional variable technique. The queueing system's unique qualities and key features are provided, along with a cost model. An extensive numerical research is done using real-world examples.
  Keywords: state dependent arrivals; server breakdown; supplementary variable method; queue; bulk service; multiple vacations; cost model.
  DOI: 10.1504/IJOR.2023.10056844
   
  
• Performance analysis for F-policy machine repair problem with unreliable server balking, working breakdown and retention  
  by Sreekanth Kolledath, Kamlesh Kumar 
  Abstract: In this paper we study the controlled arrival of machine repair problem with balking, working breakdowns, reneging, and retention of failed machines. Failure times and service times of operating machines are assumed to follow the exponential distribution. When the service station works in normal mode, it is subject to breakdowns; while a breakdown occurs, the service station requires repair by the repairing facility. The service station’s breakdown and repair times are also presumptively exponentially distributed. Additionally, it is assumed that during a breakdown period of the service station, the service station may allow to provide service to the failed machines with slower service rate. The Runge-Kutta method (4, 5) has been employed to obtain the transient behaviour of the machine repair model. Several system governing performance measures are calculated. A cost function is constructed and also the sensitivity analysis is performed to explore the effect of different parameters.
  Keywords: unreliable server; F-policy; working breakdown; balking; retention.
  DOI: 10.1504/IJOR.2023.10057145
   
  
• Impact of Time-Dependent Environmental Factor on Software Release Planning  
  by Vibha Verma, Sameer Anand, Hoang Pham, Anu G. Aggarwal 
  Abstract: Reliability assessment of software during operational phase is critical for release and warranty decisions because users are concerned about software performance during usage period. To characterise the distinctions in the settings during the testing and operational phase an environmental factor is introduced in release planning problem. It represents the impact of the usage frequency on software performance and the relative severity of the phases. In this paper, the effect of a constant environmental factor (during the warranty phase) and a time-dependent environmental factor (during the post-warranty phase) on reliability and release decisions have been analysed. A software cost model has been formulated that minimises the development cost and determines optimal variable values (testing and warranty time) while achieving reliability requirements incorporating environmental factor in the release model. The impact of changes in reliability requirements cost components, and environmental factor on the release schedule has been studied using real-life fault datasets.
  Keywords: software release decisions; time-dependent environmental factor; warranty phase; testing phase; operational phase; development cost.
  DOI: 10.1504/IJOR.2023.10057646
   
  
• An approach for solving fully fuzzy linear fractional transportation problem with the using of splitting technique  
  by Sapan Das, Rajeev Prasad, Tarni Mandal, S.A. Edalatpanah 
  Abstract: This paper deals with an application of splitting technique to LFP problem including fuzzy coefficients (FC). This article mainly establishes and applies a modified form of splitting technique and ranking function for solving fully fuzzy linear fractional programming (FFLFP) problem. Here, we propose a method for solving for solving FFLFP problem with the help of splitting technique. After utilising the splitting technique, the problem is converted into equivalent fully fuzzy non-linear fractional programming (FFNLFP) problem and solved the problem with the help of ranking function. The proposed algorithm is tested with three types of problems. A real life diet example (data was collected from TATA-Main Hospital, Jamshedpur, India) is first used. Then, random problem instances are generated and finally, the benchmark problems addressed in literature are also considered. In all the three cases, the results are compared with earlier reported algorithms in the literature and the computational results reveal that the proposed algorithm is competent.
  Keywords: fully fuzzy linear fractional programming; FFLFP; crisp non-linear programming; fuzzy arithmetical; ranking function.
  DOI: 10.1504/IJOR.2023.10057875
   
  
• Optimal Inventory and Pricing for EOQ Inventory Models with Price-Dependent Demand and Exponential Demand  
  by Sivashankari C.K., Nithya T 
  Abstract: In the present work, an optimal lot size and optimal pricing with price-dependent and exponential demand for deteriorative items in third order equations is developed and also a special case for predetermined price is also considered. Optimal lot size and price are two decision variables in this paper and optimal cycle time is a decision variable in special case of this paper. The breakeven price is considered and the law of demand is proved. There are two models designed: the first model utilises an inventory model with optimum output and price in third order equation and the second model uses optimal cycle time of an inventory model for determining the price-breakeven point. But to my knowledge, no authors developed models for optimal pricing, and optimal lot size policies in price dependent and exponential demand in a third-order equation. This aims to obtain optimal lot size as well as pricing for overall maximum profits. The essential, as well as sufficient mathematical models are developed. Several examples, numerical in nature, are offered to achieve model validation. Additionally, a sensitivity analysis is carried out in conjunction with the representation's building blocks. Microsoft Visual Basic 6.0 was used to program the model's outcome validation.
  Keywords: EOQ; optimality; price-dependent demand; exponential time-dependent demand; sensitivity analysis; cycle time.
  DOI: 10.1504/IJOR.2023.10058103
   
  
• Inventory Control Optimisation: the Dynamics of Deterministic Request Model of Pharmaceutical Appropriation and Storage  
  by Adedugba Adebayo, Daniel Inegbedion 
  Abstract: The paper presents a stock control constraint at a drug manufacturing facility in Lagos State, Nigeria. The echelon of the organisational inventory chain was evaluated. The study developed a two-situation deterministic stock model that is based on realistic assumptions and necessities within the inventory network in order to conceptualise the situation within the model. A single medicine item, build lead time, and a definite request are taken into account in the formulation. The contingent request is handled as a forecast for the item’s sales and the optimisation between the recognised stock, the scheduled average stock level, and the reduction of stock-out situations are two mathematical functions. This was done in order to conclude the suggested mathematical formulation, which depends on a particular approach for selecting how to arrange the echelon. This is based on the paradigm of inventory and request. Therefore, optimality is achieved as a control mechanism.
  Keywords: control; inventory chain; request; optimality; pharmaceutical organisation; models.
  DOI: 10.1504/IJOR.2023.10058197
   
  
• Data Mining Techniques and Mathematical Models for the Optimal Problem at a State Public University  
  by Lijian Xiao, Shuai Wang, Xinhui Zhang 
  Abstract: This paper studies the optimal allocation problem of financial aid: the allocation of the appropriate levels of scholarships to the correct students, as observed in a state university. This research applies data mining techniques and mathematical models to solve the optimal financial aid allocation problems in three steps. First, data mining techniques, such as logistic regression, are used to determine the matriculation and graduation probabilities associated with students from various socioeconomic backgrounds and given levels of scholarship. Second, based on the responses to the different scholarship levels, an integer programming model is developed to maximise revenue over the students’ course of study. Third, decision tree and piecewise linear regression methods are employed to transform the results from the optimisation model into effective policies for implementation. This research has led to a scholarship redesign, and a straightforward scholarship award policy, based on a composite GPA and ACT score, has been implemented.
  Keywords: financial aid allocation; optimisation; data mining; logistic regression; integer programming; decision tree.
  DOI: 10.1504/IJOR.2023.10058404
   
  
• Data-Driven Approaches for Decision-Making in Advanced Manufacturing Systems: A Systematic Literature Review  
  by Vimlesh Kumar Ojha, Sanjeev Goyal, Mahesh Chand 
  Abstract: Rapid automation in advanced manufacturing systems enable them to capture, store and analyse data and adopt data-driven decision-making techniques. This study investigates the applications of data-driven techniques like big data analytics, AI, and ML in advanced manufacturing systems for decision-making. The paper identifies the various factors that affect the adoption of data-driven manufacturing techniques and reviews the framework strategies for their adoption. Applications of data-driven techniques in manufacturing, such as predictive maintenance, fault analysis, forecasting, and quality improvement, are discussed in detail. The authors also highlight the challenges associated with implementing data-driven decision-making (DDDM) in the manufacturing industry, such as data quality, privacy concerns and skilled workforce requirements. The study concludes that DDDM in AMS increases productivity, reduces operational costs, improves manufacturing operations and increases competitiveness. However, further research is needed to address the identified challenges and develop effective DDDM implementation strategies in AMS.
  Keywords: big data; IoT; decision-making; manufacturing; data analysis; automation; industrialisation; systematic review; data-driven decision-making; DDDM.
  DOI: 10.1504/IJOR.2023.10058496
   
  
• Analysis of Copula Based Variable Clustering Techniques and Application of Mortality Estimation  
  by Zeynep Ilhan Taskin, Veysel Y?lmaz, Kasirga Yildirak 
  Abstract: This paper aims at developing different mortality estimation models in MIMIC-III data set. One of the aims of the study is to bring an efficient technical proposal to determine the dependency structures between the variables. The study is conducted with 38015 adult intensive care patients in the MIMIC-III database. The dependency structure between the variables is determined and divided into clusters with CoClust and tail dependency. With Logistic Regression Analysis applied through clusters, the number of significant and appropriate models for death variable within 24 hours was four while there were five for death variable in the hospital. When the obtained models were analysed with error matrix, cross validity criterion and ROC curve, three valid models were obtained for the death variable within 24 hours and two for the death variable in the hospital.
  Keywords: Copula; CoClust; Clustering with Tail Dependency; Logistic Regression Analysis; Mortality Estimation.
  DOI: 10.1504/IJOR.2023.10058499
   
  
• A MODEL ON AN OPTIMAL ORDERING POLICY FOR DETERIORATING ITEMS WITH EXPONENTIAL DECLINING RAMP-TYPE DEMAND, VARIABLE DETERIORATION AND SHORTAGES  
  by Sephali Mohanty, Trailokyanath Singh 
  Abstract: The main objective of the proposed paper is to extend Sanni and Chukwu’s (2013) model with the incorporation of the following characteristics: 1) inventory system deals with a single type of item; 2) demand is a generalized demand pattern and is an exponential declining ramp-type function of time; 3) deteriorating items follow a variable deterioration rate where deterioration rate is a linear increasing function of time; 4) shortages in the developed system are assumed to be a natural phenomenon; 5) only complete backlogging case has been taken into consideration. The demand rate is deterministic: it varies with respect to time up to a certain fixed point, becomes steady and then, it is fully backlogged. A couple of numerical examples are used to study the effectiveness of decision variables in the model. Finally, sensitivity analysis of the optimal solution with respect to several system parameters of the model is examined.
  Keywords: completely backlogged; deteriorating items; EOQ; exponential declining ramp-type demand; shortages; variable deterioration.
  DOI: 10.1504/IJOR.2023.10058544
   
  
• Optimizing End-of-Life Laptop Remanufacturing Decisions Using Meta-Heuristics  
  by Gurunathan Anandh, Shanmugam Prasanna Venkatesan, Mark Goh, Gyan Chandra Kushwaha 
  Abstract: As the lifecycle of a laptop gets shorter, the world should expect more end-of-life (EOL) laptops. Remanufacturing of laptops is viewed as the best EOL alternative for environmental and societal reasons. This research uses a multi-period nonlinear integer programming model to decide the best EOL options for the remanufactured laptop parts based on their quality. Discrete particle swarm optimisation (DPSO) and genetic algorithm (GA) are implemented as a decision support tool in Microsoft Excel to yield the near-optimal solution. Numerical tests are conducted to compare the effectiveness of the two algorithms. For small-sized problems, the solution of the algorithms is compared with the global optimal solution obtained by the full enumeration method. For large problem instances, the solution obtained using the algorithms is compared with each other. A sensitivity analysis is performed to study the impact of the shortage and repair costs and demand on profit.
  Keywords: WEEE; end of life laptop; remanufacturing; discrete particle swarm optimisation; DPSO; genetic algorithm; GA; nonlinear integer programming.
  DOI: 10.1504/IJOR.2023.10058823
   
  
• Comparing classical time-series models and machine learning for demand forecast on the beverage industry in COVID-19 pandemic.  
  by Ana Camilla Macedo, Caio B. S. Maior 
  Abstract: Due to the growth of competitiveness in the market, demand forecasting has become a fundamental tool to manage production and identify new opportunities for the company. The fundamental goal of a series analysis is to make predictions from historical data to support decisions accurately. During the COVID-19 pandemic, the market has undergone numerous changes, and consumer needs have changed, directly affecting beverage sales. In this work, classic models of time series Holt-Winters and ARIMA and machine learning support vector machines and random forests were used to perform demand forecasts from several historical data series of a real beverage direct distribution centre located in Brazil. The data used were stratified into nine data series: 1) the total volume of beverages sold by the operation; 2) separated by type of beverage (beer and non-alcoholic beverage); 3) in six sales channels. Indeed, as the comparison considers demands before and after the pandemic (including pre-and post-vaccination), the predictions were challenging. The comparison of models considers predictions up to 15 steps (months) ahead using the RMSE and MAPE error metrics. Here, the models with the best-aggregated performances were ARIMA and SVM; however, no model was strictly better than the others.
  Keywords: time series; demand forecast; beverage industry; Holt-Winters; ARIMA; support vector machine; SVM; random forest.
  DOI: 10.1504/IJOR.2023.10059084
   
  
• A Two-Phase Extended Warranty Strategy for New and Reman Products  
  by Jalapathy P, Mubashir Unnissa Munavar 
  Abstract: In recent decades, waste management has attracted the attention of a substantial number of scientific and industrial firms, which paved the way for reman products. Also, reman product reliability increases significantly in the product market, and offering a warranty is the most efficient way to identify the product's quality and dependability through market sales. In this paper, a two-phase extended warranty model is offered for a new and reman product to analyse the pricing strategy of the monopolistic manufacturer. The paper develops a model framework to examine optimal prices, demands, and profits of new and reman products with an extended warranty by using the Karush-Kuhn-Tucker (KKT) condition. Further, to highlight the impact of the extended warranty, failure rates, and customer willingness on new and reman products, a numerical analysis is performed. The results reveal an insight on providing an extended warranty increases the manufacturer's profit.
  Keywords: re-manufacturing; pricing strategy; extended warranty; customer utility; profit analysis.
  DOI: 10.1504/IJOR.2023.10059156
   
  
• Analysis of MMAP/PH(1), PH(2)/1 Non-Preemptive Priority Queueing Model with Phase-Type Vacation and Repair, Feedback, Breakdown, Closedown and Reneging  
  by Ayyappan G, Meena S 
  Abstract: We consider a single server non-preemptive priority queue with phase-type vacation and repair, feedback, breakdown, close-down, and reneging. Customers arrive according to the marked Markovian arrival process and their service time according to phase-type distribution. If the high priority customers need feedback, they lose their priority and join the low priority queue. At any instant, if the server is broken down, it will immediately go into a repair process. When there are no customers present in both the queues, the server close-down the system and then goes on vacation. During the close-down and vacation period, high priority customers may renege. The matrix analytic method is used to look into the number of consumers that are currently in the system. Analysis of the steady-state, the server active period, and the total cost are all discussed. Finally, some significant performance measures and numerical examples are given.
  Keywords: marked Markovian arrival process; phase-type distribution; server vacation; breakdown; repair; feedback; close-down; reneging; non-preemptive priority; matrix-analytic method.
  DOI: 10.1504/IJOR.2023.10059338
   
  
• Fluid approximation for a Markovian queue under disaster and reboot  
  by Mayank Singh, Madhu Jain 
  Abstract: A fluid approximation for the performance analysis of a Markovian disaster queue with reboot and repair is presented. During normal operation, the system may suffer disaster failure, in which case all jobs in the system will be lost. If the fault is successfully covered, the system recovers from the failure by rebooting; otherwise, the system enters a repair state, where a specialised repairman removes the fault. An analytical methods of continued fractions (CFs) and probability generating function (PGF) are used to get the probability distribution of buffer content. To analyse the fluctuation in buffer content with regard to buffer content probabilities, the numerical data is computed and displayed in the form of graphs and tables. Furthermore, numerical results obtained using analytical formulae are compared with the results obtained by adaptive neuro-fuzzy inference system (ANFIS).
  Keywords: Markov fluid queue; disaster; reboot; continued fractions; ANFIS; probability generation functions.
  DOI: 10.1504/IJOR.2023.10059527
   
  
• MADEA: Multiobjective Amended Differential Evolution Algorithm  
  by Ishan Gawai, D.I. Lalwani 
  Abstract: The aim of the current work is to modify the amended differential evolution algorithm (ADEA) to solve multiobjective optimisation problems. The modified ADEA algorithm is named MADEA. The single objective ADEA algorithm is employed with an efficient non-dominated search (ENS) method for finding the non-dominated solutions, a crowding distance technique for comparing the non-dominated solutions, and an archive that stores the non-dominated solutions. The above-mentioned modifications in ADEA resulted in an algorithm capable of solving benchmark functions given in CEC 2009 with competitive results. The performance of the MADEA is measured using inverted generational distance (IGD) and hypervolume (HV). The outcomes of performance measures are compared against MWDEO, MOEA/D, MOPSO, SMPSO, NSGA-II, SHAMODEWO, MOEADSTM and NSGA-III. The results show that MADEA has outperformed 60% of the problems in the test suite in IGD values and the results were found to be significantly similar to 20% of the competition.
  Keywords: meta-heuristics; evolutionary algorithm; differential evolution; archives; multiobjective optimisation problems; amended differential evolution algorithm; ADEA; efficient non-dominated search; ENS.
  DOI: 10.1504/IJOR.2023.10059547
   
  
• Permutation flow shop scheduling with early and late penalty costs using the Jaya algorithm  
  by Raunaque Paraveen, M.K. Khurana 
  Abstract: Purpose of this study is to use the most efficient meta-heuristic methodologies in permutation flow shop to identify the ideal sequence of jobs with the least amount of penalties for being early and late. The permutation flow shop is a common job shop problem in which all jobs must pass through all machines in a predefined order. Numerous meta-heuristic algorithms have been developed to tackle this problem. However, users often struggle with selecting appropriate algorithm parameters due to the problem’s complexity. To address these challenges, this research adopts the recently developed Jaya algorithm, which stands out for being a parameter-less approach that aims to achieve success while avoiding failure. The Jaya algorithm was tested alongside a genetic algorithm using a simulated industry dataset. This dataset contained different scenarios with varying numbers of jobs and machines. The Jaya algorithm consistently outperformed the Genetic algorithm, providing superior results for the given problem.
  Keywords: permutation flow-shop scheduling; Jaya algorithm; tardiness penalties; earliness penalties.
  DOI: 10.1504/IJOR.2023.10059626
   
  
• Solving the multi depot vehicle routing problem with limited supply capacity at the depots with a multi phase methodology  
  by Javier De Prado, Sandro Moscatelli, Pedro Piñeyro, Libertad Tansini, Omar Viera 
  Abstract: We consider an extension of the multi-depot vehicle routing problem (MDVRP), in which the supply capacity of the depots is limited. To solve this problem, we propose a multi-phase methodology, that extends the
  Keywords: multi-depot vehicle routing problem; MDVRP; heuristics; limited supply capacity at depots; capacitated vehicles; clustering; assignment; routing; multi-phase methodology; MPM.
  DOI: 10.1504/IJOR.2023.10059627
   
  
• Threshold neutrosophic set and its application to decision making in planning and construction industry  
  by Tuhin Bera, N.K. Mahapatra 
  Abstract: The basic motivation of the present study is to furnish a decision making approach in soft and neutrosophic environment. The methodology is based on the notion of neutrosophic cut set. Different kind of threshold neutrosophic set and their level soft set are innovated here. Then their inter relations are also investigated. The approach is further extended over soft and weighted neutrosophic set. Suitable solution algorithms are developed in both attempts and these are demonstrated to make a decision in planning and construction industry. The outcomes are analysed and the potentiality of the proposed method is claimed after comparing the results from existing study.
  Keywords: neutrosophic soft set; threshold neutrosophic set; level soft set; decision making approach.
  DOI: 10.1504/IJOR.2023.10059650
   
  
• Uncertainty Quantification and Global Sensitivity Analysis of an M/G/1 Retrial Queue with Bernoulli Schedule  
  by Khedidja Boughafene, Karim Abbas 
  Abstract: In this paper, we are interested in studying uncertainty quantification and global sensitivity analysis in retrial queueing models. Specifically, we investigate the M/G/1 retrial queue with priority customers, Bernoulli schedule and general retrial times. We develop a new methodology for integrating epistemic uncertainties into the computation of performance measures of retrial queueing models, where these measures are considered as functions of the input random parameters and approximated with polynomial chaos expansions. In order to perform global sensitivity analysis, we use Sobol’ indices which allow us to make an importance ranking of parameters. In addition, we characterise statistically several performance measures, given that distribution of the model parameter expressing the uncertainty about the exact parameter value is known. Furthermore, we use the Markov inequality to assess the risk induced by working with uncertain performance measures instead of that evaluated at fixed parameters. Several numerical results are provided and compared to Monte Carlo simulations ones.
  Keywords: Sobol’ indices; polynomial chaos expansions; epistemic uncertainty; uncertainty quantification; risk analysis; Monte Carlo simulation; retrial queueing model.
  DOI: 10.1504/IJOR.2023.10059728
   
  
• Optimizing inventory management: addressing constant deterioration and imperfect items with screening, time-dependent demand, and two-layer trade credit  
  by Chirag Trivedi, Mrudul Jani, .Dilip C. Joshi, Manish Betheja, Nakul Kumar Rawal 
  Abstract: Inventory models are frequently developed with products produced are of perfect quality The purpose is to create a model with uncertain supply may have a random proportion of defective items As a result, item inspection becomes critical in all situations, when products are vanishing current companies may use promotional tools to boost sales trade credit is a strategy that benefits both suppliers and retailers Hence, a two-level trade credit scheme in which the supplier offers a credit period to retailer and retailer provides to customers Inflation is the rate at which the prices for goods often affects the buying capacity of consumers and recent time value of money is calculated The primary purpose is to enhance the retailer's overall profit with respect to cycle time and is numerically solved using a devised algorithm Finally, sensitivity analysis is done on key parameters, and some managerial implications for the retailer are emphasised.
  Keywords: deterioration; imperfect items; screening; time-dependent demand; two-layer trade credit.
  DOI: 10.1504/IJOR.2023.10059878
   
  
• Solving a Practical Examination Timetabling Problem via Abductive Reasoning and Integer Programming  
  by Daniel Morillo, Nicol Solarte-Herrera, Maicol Narváez-Rincón, Rafael Rojas-Millan, Gustavo Gatica, Jesus Gonzalez-Feliu 
  Abstract: Scheduling of examination dates is a complex process that affects student satisfaction at higher education institutions. The literature refers to this as the timetabling problem. Formally, it consists in assigning a series of events to certain timetable blocks within a given time interval, limited by a set of constraints, some of which must be strictly adhered to (hard), while others are only desirable (soft). This paper proposes and validates a mathematical model for scheduling at a university in Colombia. The main paper’s contribution is that the model is aimed at improving student satisfaction compared to the scheduling performed previously by the university. The methodology is based on an abductive vision of operations research with five stages where a mixed-integer linear programming model was proposed, and it was validated in a real-life instance. The results show a 38.9% average reduction in contiguous exams.
  Keywords: abductive methodology; integer programming; timetable problem; exam scheduling problem; applied case.
  DOI: 10.1504/IJOR.2023.10059881
   
  
• Evaluation of Power Generation Units of a Thermal Power Plant Focusing on Sustainability and Technical Attributes  
  by Taquiuddin Quazi, Vivek Sunnapwar 
  Abstract: Coal is the primary source for generating power across the world and it is expected that this fuel's domination would last for a few more decades. Coal-fired power generation contributes substantially to pollution, negatively impacts the natural habitat, and hampers socioeconomic aspects of the economy. Hence, there is a need to investigate the performance of the power-generating units of thermal plants based on the evaluation criteria. In this study, the evaluation attributes related to technical, economic, social, and environmental aspects have been identified through the critical literature survey and interaction with the subject matter experts of the domain. Three power units of a coal-fired power plant have been evaluated using the hybrid MCDM framework. The results of the investigation highlighted that the social aspect is the most crucial and subfactors, namely risk related to safety, energy generation efficiency, and social acceptability are the significant ones. Also, the power unit C ranked first out of the three units under consideration. Finally, managerial, academic, and social implications are offered.
  Keywords: evaluation; coal-fired power generation; sustainability; coal technologies.
  DOI: 10.1504/IJOR.2023.10059961
   
  
• A novel inverse DEA-R model as for decision maker's preferences  
  by Javad Gerami, Mohammad Reza Mozaffari, Peter F. Wanke, Yong Tan 
  Abstract: In this paper, we present an innovative inverse data envelopment analysis (DEA) approach that incorporates ratio data. The proposed model simultaneously estimates the levels of inputs and outputs of decision-making units (DMUs) based on predetermined efficiency. Additionally, the model allows for assessing the levels of inputs and outputs according to the preferences of the decision maker (DM). The proposed model is nonlinear initially, but we transform it into a linear programming model. We demonstrate that the proposed model is always feasible. For the inverse DEA ratio-based (DEA-R) process, we adopt a two-step approach. Depending on the DM’s preferences, we can employ different models in the inverse DEA-R process when dealing with ratio data. To illustrate the effectiveness of our approach, we present two numerical examples in the paper.
  Keywords: data envelopment analysis; DEA; ratio data; DEA-R; inverse DEA-R; input/output estimation.
  DOI: 10.1504/IJOR.2023.10060052
   
  
• Aspiration Level based Multi-Objective Quasi Oppositional Jaya Algorithm to solve Multi-Objective Solid Travelling Salesman Problem with Carbon Emission  
  by Aaishwarya Bajaj, Jayesh Dhodiya 
  Abstract: This paper aims to analyse the steady-state behaviour of a bulk input general service queue with second optional service (SOS), balking, feedback, random system breakdowns, delay time, and repair time. After arriving at the queue, the customer has to decide whether to join or refuse to join the queue (balking). After completing the first essential service (FES), if a customer is not satisfied with it, he may choose to rejoin the system (feedback) or opt for SOS or depart from the system with a certain probability. From time to time, the server may face random breakdowns during FES and SOS, and we assume there is a delay time before the server starts the repair process. Moreover, the service times (FES and SOS), delay time, and repair time have a general distribution, while the breakdown time follows an exponential distribution. The steady-state probabilities are computed using the probability-generating function (PGF). Finally, numerical illustrations of performance measures are provided.
  Keywords: Multi-Objective Solid Travelling Salesman Problem; Aspiration Level; Carbon Emission; Multi-Objective Quasi Oppositional Jaya; CPLEX.
  DOI: 10.1504/IJOR.2023.10060053
   
  
• Role of time dependent Parabolic Demand for deteriorating items and Time Dependent Partial Back order in an EOQ model of seasonal fruits under intuitionistic fuzzy environment.  
  by Sriparna Chowdhury, Prokash Mondal, Sanat Kumar Mazumder, Pritha Das, Prof. Kajal De 
  Abstract: This study stimulates a major business factor for seasonal retailers and farmers that meet big goals by minimizing the total inventory cost of seasonal agro products. At the rising of every season, demands start with shortages, and it takes time to fully filed a prime time. After that, a fresh order is placed to meet demand and deterioration for the remaining time. So, the model designed here stands with its implementation in a manufacturing concern. Here, we introduced an economic order quantity (EOQ) model with a time-dependent parabolic demand and constant deterioration rates, shortages allowed with payment delays, and a partial backorder. For a more realistic feeling, the uncertainty occurs, the model is simultaneously constructed under a crisp and intuitionistic fuzzy environment; the trade credit policy up to stock-out time is planned for both cases. The numerical example and the sensitivity analysis have been done for both environments.
  Keywords: EOQ; Seasonal Agro product; Deterioration; Trade credit; Partial backorder; Intuitionistic fuzzy.
  DOI: 10.1504/IJOR.2023.10060190
   
  
• A novel fuzzy network ASBM approach based on DEA and DEA-R models for efficiency measurement in oil refineries  
  by Javad Gerami, Sahar Ostovan, Mohammad Reza Mozaffari, Peter F. Wanke, Yong Tan 
  Abstract: In this study, we develop fuzzy network data envelopment analysis (DEA) models based on the additive slacks-based measure (ASBM) model in the presence of undesirable output. In the real world, we encounter many cases where the data are inaccurate and ratios are involved simultaneously. In this regard, we propose two new models to evaluate the efficiency of Decision Making Units (DMUs) with a three-stage network structure in the presence of fuzzy inputs and outputs based on DEA and DEA-R models, by selecting two different strategies, external and internal. In the following, we apply the proposed approach to evaluate a set of oil refineries in Iran, and we present the results of the research.
  Keywords: Data envelopment analysis; Efficiency; DEA-R; Fuzzy network DEA; three-stage network.
  DOI: 10.1504/IJOR.2023.10060303
   
  
• Non-Convex Queue Time-bound Optimal Load Balancing  
  by Najeeb Al-Matar 
  Abstract: Cloud computing offers numerous advantages and flexibility, but also presents challenges in scheduling and load balancing. These challenges are particularly significant in distributed computing paradigms, and the addition of cloud technology on top of distributed systems further complicates the problem. The performance of cloud computing is significantly influenced by these factors. To optimise scheduling and load balancing, the proposed work introduces non-convex queue time-bound optimal load balancing, a set of nonlinear metrics that can be applied to both convex and non-convex surfaces. The work involves mathematical modelling an objective function with bounded constraints using queuing theory, applying non-convex optimisation techniques to minimise metrics like cost, error, and bandwidth. The results are evaluated using cloudsim metrics and analysed to improve performance. This mathematically modelled system provides a reliable and cognitive approach to optimising the cloud environment.
  Keywords: non-convex cloud; nonlinear cloud; cloud optimisation; cloud load balancing; cloud resource management; cloud non-Markovian; cloud queue.
  DOI: 10.1504/IJOR.2023.10060407
   
  
• Queueing Models of Machine Repair Problems with Control Policies: A Survey and Analysis  
  by Parmeet Kaur Chahal, Kamlesh Kumar 
  Abstract: : This article offers a thorough review and analysis of the studies done on queueing models of machine repair problems (MRP) with various control policies. These policies govern the arrival of failed machines and the service mechanism in the queueing systems. Due to their many practical applications, queueing models of machine repair problems have drawn significant interest from researchers across the globe. Considerable efforts have been dedicated to investigating this area of research and the present article provides a mathematical framework for queueing models of machining systems, which incorporates various control policies. Furthermore, we explore the potential applications of machine repair queueing models that apply control policies and give a tabular summary of the research works listed while taking into account the models attributes and methodology used in particular investigations.
  Keywords: Machine Repair Problem; standbys; N-policy; F-policy; Threshold recovery policy; Bi-level control policy; Triadic control policy.
  DOI: 10.1504/IJOR.2023.10060548
   
  
• Selection of Suppliers for Supplier Development : An Integrated FD-FIS Approach  
  by Dalvi Manojkumar, Vishal Bhosale, Anjali More 
  Abstract: The objective of this study is to evaluate and rank a group of suppliers for the execution of supplier development activities (SDAs) based on identified supplier development (SD) criteria. An exhaustive literature analysis revealed a total of 14 SD criteria, which were then divided into five major criteria in consultation with decision-making authorities (DMAs). Fuzzy Delphi (FD) is used to determine the weights of significant SD criteria, and the fuzzy inference system (FIS) is used for the evaluation and ranking of suppliers. Based on the opinions of DMAs, the significance of SD criteria and sub-criteria is finalised. This study unveils that suppliers past performance and strategic benefits emerged as the foremost major criteria when evaluating and selecting suppliers for the implementation of SDAs. For the first time, an integrated FD-FIS approach is proposed to rank a set of suppliers based on the weights of SD criteria and sub-criteria.
  Keywords: supplier development; SD activities; fuzzy Delphi; fuzzy inference system; FIS; supplier development activities; SDAs; decision-making authorities; DMAs.
  DOI: 10.1504/IJOR.2023.10060727
   
  
• A first augmented Lagrangian method for binary QCQP problems based on a class of continuous functions  
  by Nirakar Sahoo, Rupaj K. Nayak 
  Abstract: This paper addresses the solution of a nonconvex 0-1 QCQP using two faster convergent augmented Lagrangian methods (ALM) based on a class of continuous functions and a parameter free convexification method. The binary constraints are converted into a class of continuous functions and the nonconvex constraints are convexified by a parameter free method. The proposed algorithm is then tested on a set of QCQP problems available in the research of Zheng and co-workers. We also present the comparison results among relaxed versions of SDPs and some state-of-the-art ALMs and obtained an advantage over their counterparts.
  Keywords: Augmented Lagrangian method; QCQP; semidefinite relaxation; global optimal solution; SDPNAL.
  DOI: 10.1504/IJOR.2023.10060840
   
  
• A non linear mathematical model for optimal discount pricing strategies to maximize the stakeholders-perceived value: Mapping in Tagouchi loss function concept  
  by Bakhtiar Ostadi, Ali Abdollahi, Ali Husseinzadeh Kashan 
  Abstract: Customer-perceived value (CPV) is the difference between the prospective customer’s evaluation of all the benefits and costs of an offering and the perceived alternatives. In this paper, we introduce a new non-linear mathematical model for developing optimal discount pricing strategies using the Taguchi loss function and the concept of customer lifetime value (CLV). model aims to maximise the stakeholders-perceived value (SPV), which is calculated based on the customer's mentality towards the price before making a purchase decision. If the customer's mentality is greater than the amount paid, the perceived value for the chain store is used as the basis for SPV calculation; otherwise, the perceived value for customers is used. application of our model shown in a chain store. Using Taguchi pricing and discount model, managers can calculate product portfolio discounts and adjust their marketing strategies according to the specific strategies of the store and product portfolio for customer segments.
  Keywords: customer-perceived value; CPV; discount pricing; customer lifetime value; CLV; Taguchi loss function; discount pricing strategies.
  DOI: 10.1504/IJOR.2023.10060847
   
  
• Improved managerial decisions for fuzzy stochastic bi-objective linear programming models: A Trade-off ratio-based autonomized approach  
  by Arindam Garai, Santanu Saha, Kajal De 
  Abstract: Industry-derived fuzzy stochastic bi-objective linear programming (FSBOLP) models typically focus on a single major objective function. However, mathematical analysis based classical minmax method fails to distinguish between two competing objectives. This sometimes causes Pareto optimal solutions failing to meet with managerial goals. Additionally, to assume that both objectives in a FSBOLP shall attain the same highest standard is unrealistic. To overcome these limitations, the proposed amended minmax model uses the absolute difference operator. This pushes intermediate nondominated points closer to predefined reference levels, generating more desirable Pareto optimal solutions. Then this study frames one trade-off ratio-based autonomised optimisation algorithm, updating reference levels throughout iterations and reducing the need for frequent manager interactions. A numerical case study validates the effectiveness of proposed approach. This way, this study provides an improved framework for FSBOLP models, addressing the shortcomings of the traditional method and providing better decision-making support for industry managers.
  Keywords: fuzzy stochastic bi-objective linear programming; FSBOLP; preferred Pareto optimal solution; interactive optimisation; autonomised reference membership level; trade-off ratio; minmax method.
  DOI: 10.1504/IJOR.2023.10060979
   
  
• Impact of Slippage Cost and Risk Cost on Software Development under Imperfect Debugging Environment  
  by Neha Gondwal, Abhishek Tandon, Anu G. Aggarwal 
  Abstract: Computers have become an integral part of everyone’s life in this modern information society, and they are especially important in several fields that save lives. Consequently, it is necessary to develop reliable and cost-efficient software systems. This study discusses a cost model that integrates slippage and risk costs and looks at how these cost factors affect the timing of software releases. The reliability growth model, which is developed by taking into account the testing coverage function in an imperfect debugging environment, is used to study the cost model. The model is validated using a real-life failure dataset and with the estimated values, we formulate an optimisation model to develop the cost model concerning reliability function. With the aid of sensitivity analysis, the study also examines the potential effects of cost variation on the overall budget and delivery schedule.
  Keywords: software reliability growth model; SRGM; testing coverage; imperfect debugging; optimisation.
  DOI: 10.1504/IJOR.2023.10061339
   
  
• Dividend decision-making Algorithm Among Multi-Firms of Available and Required Capacity within Constrained Horizontal Coalitions  
  by P.P. Mishra, Chipem Zimik 
  Abstract: In this paper, our extended algorithm is used to achieve an optimum horizontal coalition among multi-firms of available and required capacity space. And also it calculates the Shapley values for profit distribution of all participating firms in the coalition. In this coalition, only suppliers are players and form subgames to manage the capacity space to achieve optimum profit. We establish the relationship between the core and the Shapley values of these subgames along with their geometrical interpretation. The numerical illustration is also shown for a better understanding of our model.
  Keywords: cooperative game; subgame; capacity space; horizontal cooperation; optimal coalitions.
  DOI: 10.1504/IJOR.2023.10061343
   
  
• Performance Analysis and Optimisation of Secondary Queue: A Study of Railway Passenger Reservation System  
  by S.M. QASIM, Jamal Ahmad Farooqui 
  Abstract: Every day, millions of people travel by rail in India. Even still, tens of thousands of waitlisted tickets are cancelled because there is no room on the chosen train on a given day. Such cancellations leave waitlisted ticket holders disgruntled and uncomfortable, costing the Indian Railways' passenger sector revenue. A secondary queue of waitlisted ticket holders occurs when the number of berths in demand is fewer than the number available in the requested accommodation class on a particular train on a specific day. The few customers from this line are served using confirmed tickets that have been relinquished by the person having confirmed tickets from the main line (primary queue). To validate the real queuing model, the study employs field data from the Centre of Railways Information System to establish the secondary queue's statistical distribution of arrivals and services. Furthermore, it analyses the secondary queue's performance characteristics using G/G/c/K queuing science and optimises the secondary queue design. This facilitates sensitivity analysis (changing values).
  Keywords: queuing in service operations; primary queue; secondary queue; queuing science; optimal design; Indian railways.
  DOI: 10.1504/IJOR.2023.10061608
   
  
• Inventory model for non-instantaneous deteriorating items with hybrid price and stock-dependent demand in the view of delay in payments, inflation, and customer returns  
  by Jayasankari Chandramohan, R. Uthayakumar 
  Abstract: This study creates an inventory model for a product that deteriorates gradually over time, with a hybrid price and stock-dependent demand that is affected by inflation and customer returns. We know from experience that demand is not necessarily constant, linear, or nonlinear; it is uncertain. The selling price, stock, and time value of money all influence demand. Shortages are allowed and partially backlogged. Customer returns are thought to rise in direct proportion to the portion vended and the product cost. The principle goal is to find the ideal cost structure, the time when there is no supply shortage, the appropriate restocking cycle, and the order amount all at the same time. The actual value of total profit is maximized over an indefinite time horizon.
  Keywords: Hybrid-price-stock dependent demand; Inflation; non-instantaneous deterioration; Delay-in-payments; Customer returns.
  DOI: 10.1504/IJOR.2023.10061609
   
  
• The Harris-Odd Burr Type X-G Family of Distributions with Applications  
  by Broderick Oluyede, Neo Dingalo, Fastel Chipepa 
  Abstract: This note introduces the new Harris-odd Burr type X-G (Harris-OBX-G) family of distributions and thoroughly investigates its statistical properties. These encompass essential features such as the quantile function, moments, moment generating function, the distribution of order statistics, and the Renyi entropy. To estimate the model parameters, we employ the maximum likelihood estimation technique, and we assess the reliability of these estimates through simulation studies. Furthermore, the versatility and practicality of the Harris-OBX-G family of distributions are demonstrated through its application to analyse two distinct real-world datasets from diverse fields.
  Keywords: Harris-G distribution; odd Burr type X-G distribution; simulations.
  DOI: 10.1504/IJOR.2023.10061696
   
  
• The Effect of Preservation Technology Investment on Inventory Model with Quadratic Demand Rate and Time dependent Holding Cost Under Two-Level Trade-Credit Policy  
  by Manoj Kumar Sharma, Mukesh Kumar, Satya Jeet Singh, Divya Mandal 
  Abstract: In this paper, we developed a deterministic inventory model that includes some genuine parameters, such as items that deteriorate over time, so we implemented a Weibull distribution rate that gives it a broader application scope. After that, preservation technology to reduce the rate of decaying items, and two levels of credit policy were applied to increase the demand rate. Also, we considered a quadratic demand rate, which is a function of time and time dependent holding cost. These parameters are reliable in economic terms. The model has also been verified via a numerical example (for all cases). The solution procedure and the sensitivity analysis have been discussed for each situation.
  Keywords: quadratic demand; preservation technology; two-levels trade credit policies; time-dependent holding cost.
  DOI: 10.1504/IJOR.2023.10061805
   
  
• A Markov Model for Prediction of Academic Manpower System in Nigerian Colleges of Education  
  by Shamsuddeen Ahmad Sabo, Nitesh Kumar Adichwal, Ibrahim Zakariyya Musa, Yakubu Isyaku Kibiya, Badamasi Abba, Syed Aqib Jalil, Akhil Damodaran 
  Abstract: This research employed a Markov model to assess the progression of the academic staff workforce in Nigerian colleges of education, using Sa'adatu Rimi College of Education, Kano as a case study. The objective was to underscore the importance of effective workforce planning in mitigating staff shortages or surpluses. By analysing transition probabilities derived from college planning department data, the study constructed a transition probability matrix depicting staff flow over time. The Markov model's findings projected an estimated 568 academic staff members for the college in the 2024/2025 session, distributed across academic ranks. Notably, the forecasted staff structure skewed towards higher ranks. Furthermore, the study offered insights into new staff members' anticipated years of service at different academic ranks. The research underscores the pivotal role of workforce planning in educational institutions, highlighting the Markov model's value in guiding staffing and workforce management decisions.
  Keywords: Markov Model; Prediction; Workforce; Stationarity; Transition Probability.
  DOI: 10.1504/IJOR.2023.10062344
   
  
• A numerical approach for fuzzy quadratic programming problems with an application to dairy farming  
  by Sumati Mahajan, S.K. Gupta 
  Abstract: Quadratic programming (QP) involving fuzzy parameters can be regarded as an extended version of conventional QP A vast variety of practical applications makes fuzzy QP (FQP) a preferred choice Fully FQP (FFQP) is a further generalisation of FQP by including fuzzy decision variables so as to avoid enforcement of crisp decision variables The study proposes a numerical approach using suitable weights attached to lower and upper value of the objective function after applying -cut in order to retain the fuzzy aspect of FFQP The equivalence between the new formulation and original model has been established through various theorems. The numerical examples are also solved to clarify the proposed method. Besides generalisation, the study brings forth its significance in real life applications viz. dairy farming problem, which is first modelled and then solved using the proposed algorithm.
  Keywords: Quadratic programming problems; Fuzzy decision variables; Numerical approach; Real life problem.
  DOI: 10.1504/IJOR.2023.10062450
   
  
• An improved Bombus-Terrestris bee optimisation algorithm implementation for enhancement of PQ in smart grid environment with hybrid renewable energy sources  
  by S. Mani Kuchibhatla, D. Padmavathi, R. Srinivasa Rao 
  Abstract: The escalating demand for distributed generating systems has driven the adoption of grid-connected hybrid renewable energy sources like wind, solar, and fuel cells. However, their integration into modern smart grid systems induces significant voltage fluctuations, impacting power quality and grid stability. This study proposes a hybrid optimal compensation scheme to enhance power quality in hybrid renewable energy systems (HRES) within smart grids. Employing a modified termite alate optimisation (MTAO) algorithm improves system performance. Addressing total harmonic distortion (THD) through suitable filtration techniques and assessing harmonic reduction efficiency, the study tackles THD issues in industrial distribution networks penetrated by renewable energy using a static switched filter compensation (SSFC) scheme. This approach aims to regulate voltage, curtail power loss, and minimise THD, thereby bolstering the overall performance and stability of hybrid renewable energy systems in smart grids.
  Keywords: hybrid renewable energy system; HRES; power quality; total harmonic distortion; THD; static switched filter compensation; SSFC.
  DOI: 10.1504/IJOR.2023.10062499
   
  
• A new optimisation model of the visitor routing problem applied to smart tourism  
  by Safae Rbihou, Nour-Eddine Joudar, Khalid Haddouch 
  Abstract: The visitor routing problem (VRP) is currently a major issue facing the tourism sector. The increasing flow of visitors demands efficient scheduling of their movement to ensure optimal visitor experience. In this paper, we propose a new mathematical programming model for managing tours for multiple groups of visitors based on their individual preferences. The proposed model takes into account various criteria such as distance, duration, budget, and risk factors. The well-known heuristic simulated annealing algorithm is well-suited to solve the proposed model. We applied the proposed routing model to a real-world problem related to the development of Fez city in Morocco. The experiments demonstrate that the proposed model offers numerous advantages for the development of the tourism sector.
  Keywords: Visitor routing problem; Mathematical programming; Tourism in Fez-Morocco; Heuristic; Simulated annealing.
  DOI: 10.1504/IJOR.2023.10062571
   
  
• Analysis the Performance of SDN Cloud Controllers Using Non-Markovian Queueing Models  
  by Najeeb Al-Matar 
  Abstract: Cloud computing is valuable for businesses, offering benefits like measured service. Implementing software-defined networks (SDN) instead of physical switches reduces hardware costs. SDN provides better control, scalability, and flexibility. Efficient SDN management is crucial for cost savings in cloud computing. Concerns with SDN include issues with data plane performance, ternary content addressable memory (TCAM), and controllers. Effective controller handling maximises throughput. Cloud computing generates high traffic volumes, with data and control traffics operating in different planes. Optimising traffic can enhance performance, and utilising queueing mechanisms can improve controller performance. Non-Markovian queueing models are proposed to handle heterogeneous buffers with varying traffic intensities. Models like M/M/1, M/M/n, M/M/s/n are used to manage traffic and improve controller performance. Both centralised and distributed systems are considered, taking into account behavioural distributions. Queueing models enhance QoS metrics, reducing waiting time, average queue intensity, and probability of idle server.
  Keywords: cloud SDN; SDN controllers; SDN controllers queue; SDN queue; SDN queue performance.
  DOI: 10.1504/IJOR.2024.10062717
   
  
• Scenario reliability assessment for CVaR minimization in two-stage stochastic programs  
  by Ghazal Shah Abadi, Sarah M. Ryan 
  Abstract: Reliable scenarios are needed to obtain a high-quality solution to a stochastic program. Considering sets of scenarios and corresponding observed values of the uncertain parameters over a collection of historical instances, reliability is defined loosely as goodness of the scenario's fit to the observations. For two-stage, risk-neutral models, a statistical tool was developed previously to assess the reliability of any given scenario generation method. This tool can diagnose over- or under-dispersion and/or bias in the scenario sets. For risk-averse decision makers who aim to minimise conditional value-at-risk (CVaR), only the scenarios that define the upper tail of the optimal cost distribution at the optimal solution are important. We develop a tool to assess the reliability of these so-called effective scenarios for CVaR minimisation. Simulation studies of a financial investment problem demonstrate the ability of the tool to detect mismatches in mean, variance, or kurtosis between scenarios and the corresponding observations.
  Keywords: risk-averse stochastic programming; conditional value-at-risk; CVaR; scenario reliability assessment; goodness of fit.
  DOI: 10.1504/IJOR.2023.10062719
   
  
• An Optimal Policy on a Two-Warehouse Model for Deteriorating Inventory Items with Varying Time-Dependent Generalised Demand and the Conditions of Delay in Payments  
  by Itishree Rout, Trailokyanath Singh, A.K. Nayak 
  Abstract: The objective of this research is the extension of extend Liang and Zhous (2011) two-warehouse inventory model by incorporating of the following characteristics: 1) the two-warehouse system considers only one type of items; 2) the grace period is fixed; 3) the supplier offers a grace period to the customer for setting the account; 4) deteriorating items follow the two different constant deterioration rates in two warehouses; 5) demand is a time-dependent generalised demand pattern and is a cubic function of time; 6) shortages are not allowed to occur in this system. The grace period is offered with the three main circumstances such as the grace period is less than the cycle length, the grace period is less than or equal to the cycle length, and the grace period is greater than the cycle length of the system. An easy-to-use solution procedure with the technique of maxima and minima are provided to determine the optimum total cost of the two-warehouse system. At the end, a couple of numerical examples along with sensitivity analysis of system parameters are illustrated. The adoption of time-dependent cubic demand reflects a real market demand for seasonal and newly launched products having short life span.
  Keywords: Deteriorating items; grace period; inventory; time-dependent generalized demand; two-warehouse system.
  DOI: 10.1504/IJOR.2024.10062826
   
  
• Approximate Solutions of Ordinary Differential Equations Modelling Queue Length Dynamics  
  by Zeina Mueen  
  Abstract: Investigation regarding queue length dynamics have been explored using various kinds of models including ordinary differential equations (ODEs). ODEs possess the advantageous property of having a continuous-time representation of queue length dynamics, thus its adoption in this article in modelling various scenarios as system of first-order ODEs. Specifically, a multi-server queue is considered and a numerical approach for solving first-order ODEs using MATLAB is adopted to obtain approximate solutions of the resultant models. The results display the dynamics of the queue length in each scenario, thus showing the usefulness of ODEs in analysing the behaviour of queues using system of ODEs.
  Keywords: first-order; multi-server; ordinary differential equations; queue length.
  DOI: 10.1504/IJOR.2024.10063068
   
  
• Enhancing Project Selection: Elicitation of Parameter Values for Effective Multiple Criteria Project Sorting  
  by Efrain Solares, Eduardo Fernández, Abril Flores, Reimundo Moreno-Cepeda, Raymundo Diaz, Edy Lopez Cervantes 
  Abstract: Effective decision making is crucial to the success of an organisation's project selection problem as it involves addressing complex challenges. One such challenge, known as multiple criteria sorting, is to assign projects into ordered classes considering the preferences of a decision maker (DM). The authors recently proposed a comprehensive method to address highly complex problems based on the outranking approach. However, it is widely acknowledged that determining parameter values for methods based on the outranking approach can be difficult. This difficulty stems from the large number of parameters involved and the DM's limited familiarity with them. Here, we focus on two aspects: 1) how to obtain the parameter values for the method; 2) how to incorporate imperfect knowledge during the sorting process. We adopt the preference disaggregation paradigm and employ evolutionary algorithms. Our proposed approach demonstrates excellent performance in a wide range of computational experiments.
  Keywords: Project selection; multiple criteria classification; parameter elicitation; evolutionary algorithms; outranking methods.
  DOI: 10.1504/IJOR.2023.10063107
   
  
• Application of Mixed-Integer Linear Programming Problems to Optimize Timetables and Classroom Arrangements  
  by Dinh Son Nguyen, Dinh Nhiem Le, Cong Hanh Nguyen 
  Abstract: The University of Danang-University of Science and Technology in Vietnam currently manages over 3,000 courses annually for more than 15,000 students. The task of scheduling and allocating classrooms for these courses is particularly challenging, given the limited availability of 127 classrooms across various buildings and the substantial number of 300 lecturers. As a result, many lecturers' teaching schedules are suboptimal. Therefore, this paper proposes a comprehensive mathematical model aimed at optimising timetables and classroom allocations. Furthermore, it suggests the development of an algorithm to solve this optimisation problem, enabling the automatic generation of timetables and classroom allocations using Python.
  Keywords: operations research; linear programming; integer linear programming; optimisation problems; MIP.
  DOI: 10.1504/IJOR.2024.10063244
   
  
• Optimizing meal delivery through travelling salesman problem and cluster analysis  
  by Erkan Kose, Danışment Vural, Merve Yılmaz, Gizem İnci, Pınar Nur Oral 
  Abstract: Food companies confront the challenge of ensuring timely meal deliveries to prevent spoilage, requiring the implementation of efficient distribution strategies. This study was designed to minimise the total distance and time travelled by a catering company in food distribution. Two distinct approaches are employed to optimise the delivery process. In the first approach, customers are grouped through cluster analysis, and optimal distribution routes for each group are determined using the traditional travelling salesman problem. Conversely, the second approach consolidates customers into a single group, examining scenarios with multiple vehicles. The multiple travelling salesman problem is then applied to determine optimal routes for each vehicle. Results from a practical case study demonstrate a noteworthy reduction in delivery time and total distance covered, underscoring the effectiveness of both approaches. By presenting numerical evidence, this study contributes valuable insights to the enhancement of meal delivery efficiency in the food industry.
  Keywords: mathematical modelling; cluster analysis; travelling salesman problem; multiple travelling salesman problem; meal delivery problem.
  DOI: 10.1504/IJOR.2024.10063345
   
  
• Bi-objective multiple drones and trucks combined operation parcel delivery  
  by Bhawesh Sah, Shalabh Singh, Rohit Titiyal, Sonia Singh 
  Abstract: Drones have the capability to work in co-ordination with trucks to improve the last mile delivery process. The traveling salesman problem with drone (TSP-D) is one such recently introduced problem, where drones and a truck work together to make deliveries. We propose a bi-objective drone truck combined operations model with multiple drones and trucks working out of a depot to make deliveries to customers. The two objectives considered are makespan completion time and the delivery cost, both of the objectives are of minimization type. We propose a Non-dominated Sorting Genetic Algorithm II (NSGA-II) to solve the proposed variant and present a thorough sensitivity analysis to discuss the efficacy and efficiency of our work.
  Keywords: Drone logistics; parallel drone scheduling travelling salesman problem; travelling salesman problem; time-cost trade-off.
  DOI: 10.1504/IJOR.2024.10063707
   
  
• An Inventory Models for Product Life Cycle for Deteriorating Items with Growth of Demand - a Comparative Statement  
  by Sivashankari C.K. 
  Abstract: A product life cycle is the life span of a product which period begins with the initial product specification and ends with the withdrawal from the market of both the product and its support. In all inventory models, a general assumption is that the demand rate is constant. But in real life, the demand rate fluctuates over the period. Growth of demand refers to an increase in demand over an extended period. Two different inventory models are developed for deteriorating items with: 1) the constant demand rate is studied first; 2) the growth of demand is investigated next. A comparative statement between constant demand and growth of demand is carried out The objective of this paper is to find the optimal cycle time, which minimises the total cost and optimal amount of shortage. The relevant model is built and solved numerical examples are furnished and justified.
  Keywords: mathematical models; product life cycle; PLC; growth of demand; production and deteriorating items.
  DOI: 10.1504/IJOR.2024.10063808
   
  
• Entrepreneurship Sustainability Prediction System: A study based on Climatic Changes  
  by Srinivas Subbarao Pasumarti, Ansumalini Panda 
  Abstract: The present study relates to a system and method for predicting entrepreneurship sustainability which aids to develop their social and environmental responsibilities towards the society and increase their own sustainability with the available and predicted resources. The system comprises a business data module (BDM), an environmental data module (EDM), an analysing module (AM), a ranking module (RM), and a suggestion module (SM). Thus, the entrepreneur is suggested with the chances and risks in the future with the available resources in a specific geometrical region or with the changes in the environment based on the ranking allocated.
  Keywords: entrepreneurship sustainability; prediction system; climatic changes; risks; decision-making; business data module; BDM; environmental data module; EDM.
  DOI: 10.1504/IJOR.2022.10064006
   
  
• A Location Analysis and Modeling Approach for Optimizing Public Access to an Automated External Defibrillator Network  
  by Trevor Angel, Lihui Bai, William Paul McKinney 
  Abstract: Sudden cardiac arrest (SCA) remains a major public health concern among industrialised nations, especially the US reporting approximately 350,000 SCAs annually. There is a clear need for strategic placement of AEDs within public spaces to promote more rapid treatment of SCA. We propose a multi-disciplinary method by using an optimum location model in conjunction with population health and ArcGIS block level data. Analytics reveal that certain population segments are at higher risk for SCA, and we propose a total risk-adjusted coverage value (TRACV) as the objective of the optimum location model. Data collected from PulsePoint, a public AED registry, for Boone County, Kentucky is used as a case study. Extensive solution and policy analyses are reported. The analyses suggest that simply purchasing more AED units unsystematically is not the best answer to improving AED access, thereby amplifying the significance of employing location analysis and modelling approach for public health planning.
  Keywords: analytics; automated external defibrillator; health services; location.
  DOI: 10.1504/IJOR.2024.10064237
   
  
• A Framework for Nurse Scheduling Problems Based on Prevent Bad-Relationships  
  by Mehboob Kanhio, Zain-Ul-Abdin Khuhro, Farhat Naureen Memon, Muhammad Saleem Chandio 
  Abstract: The scheduling problem is one of the most studied and well-known problems in mathematics. The scheduling problem is used to allocate resources in the most efficient way. In any hospital, scheduling the nurse's timetable has a big impact on their performance. Nurse scheduling is a complex problem that requires careful consideration of various factors, including skill heterogeneity, unfavourable relationship factors, and expenses. This research proposes a framework for nurse scheduling that uses integer linear programming (ILP) to minimise unfavourable relationship factors and reduce expenses. The framework is validated using a few well-known benchmark scenarios, and the results show that the proposed model performs as expected and will be helpful for management.
  Keywords: scheduling; staff preferences; job satisfaction; skill heterogeneity; healthcare; nurse scheduling problem; NSP; hard constraint; soft constraint.
  DOI: 10.1504/IJOR.2024.10064338
   
  
• Government subsidies for downstream innovation with cost-sharing under different power structures  
  by Chengli Wei, Hongzhuan Chen, Yuanfei Kang 
  Abstract: Our game model analysis reveals that subsidy schemes significantly impact downstream innovation with cost-sharing under different power structures in a two-tier supply chain. Specifically, government subsidies benefit R&D innovation, while customer subsidies increase members' profits regardless of power structure. However, the effect of R&D subsidies on individual members' profits varies. Manufacturer profits rise with the proportion of R&D subsidies, but only when the supplier lacks dominance in the supply chain. The impact on supplier profitability depends on the supplier's R&D investment share and government contributions to manufacturer R&D spending. The choice of subsidy scheme depends on the government's primary objective. Consumer subsidies effectively promote subsidised product growth and increase supply chain participant profits, while R&D subsidies aim to minimise government expenditure and optimise capital utilisation. Both subsidies are crucial for maximising R&D innovation levels.
  Keywords: government subsidies; cost-sharing; innovation; channel power; game theory.
  DOI: 10.1504/IJOR.2024.10064424
   
  
• An Optimisation Method for Ranking College Football Teams  
  by Mohsen Hamidi, Mehdi Seifbarghy 
  Abstract: This study presents a new optimisation method for ranking college football teams in the Football Bowl Subdivision (FBS). The ranking method is referred to as rating discrepancy minimisation ranking method (RDMRM). The RDMRM takes the strength of schedule, margin of victory, number of wins and losses, and conference championship factors into account. In this research, a rating discrepancy metric is defined, and a new mathematical optimisation model is developed to minimise the mean and standard deviation of rating discrepancies for all games. Incorporating the standard deviation results in balanced minimisations of rating discrepancies. To assess the reliability of this new ranking method, the RDMRM rankings are compared with the College Football Playoff (CFP) rankings. The comparison analysis shows that the results of postseason games are more consistent with the RDMRM rankings. The analysis also indicates that the RDMRM rankings are more proportional to the competitiveness of postseason games.
  Keywords: sports ranking systems; mathematical optimisation; college football; Football Bowl Subdivision; FBS.
  DOI: 10.1504/IJOR.2024.10064633
   
  
• Deteriorating Inventory Management Model: Adapting to Variable Lead Time and Consumer-Driven Shortages  
  by Atma Nand 
  Abstract: Nowadays, businesses work together and create supply chain alliances under a particular framework, such as vendor-managed inventory. The collaboration increases visibility, which reduces costs. It aids in enhancing the environmental performance of the supply chain. Inventory model suggested here helps managers choose the optimum inventory options while considering logistics costs. It elevates the provider to a dominant position, and clients are solely supplied by that vendor. Two models are presented in this research. In the first model, the vendor and customer are expected to make a non-collaborative decision. In the second approach, the merchant and the customer decide. This work proposes an iterative process for determining the best answer, which is then tested using numerical examples demonstrating the presented models' outcomes. The current research proposes a unique evidential theory-based technique for solving an inventory model with stochastic deterioration rates and lead times that appears in a single-vendor multi-buyer inventory system.
  Keywords: supply chain management; vendor-managed inventory system; integrated inventory model; merchant-consumers model; deterioration.
  DOI: 10.1504/IJOR.2023.10064634
   
  
• Exploring Reliability Factors in a Sequential Solar System: A Copula-based Investigation of Dependability Substances  
  by Abdulhadi Aminu, Abdul Kareem Lado, Ibrahim Yusuf 
  Abstract: Solar power is presently the most popular energy source compared to other energy sources. Therefore, companies all over the globe have been working hard to develop solar-powered devices to equalise the demand. According to the claim above, this study focused on a sequential multi-state solar system that involved five subsystems: a photovoltaic, a diode, a resistor 1, a resistor 2, and a voltage, which are all built in a series pattern. The exponential and copula schemes are expected to go hand in hand with system failure and repair. Partial differential equations were formed from the system's transition plot, analytical results were acquired using supplementary variable and Laplace conversion techniques. Dependability substances such as availability, reliability, mean time to failure, sensitivity, and cost were generated using the Maple software package. For validating the outcomes, an illustration of the numerical exhibits was included. Numerous system managers, including those in charge of system modelling, system reliability, system designers, and engineers, are expected to find the study's findings beneficial.
  Keywords: system; dependability; solar; factor; powered.
  DOI: 10.1504/IJOR.2024.10064704
   
  
• Robust Neutrosophic Modelling and Optimisation Approach for Solving Multi-objective Multi-Product Production Planning Problem  
  by G. Tamilarasi 
  Abstract: Neutrosophic set theory is a generalized version of fuzzy and intuitionistic fuzzy set theory, where membership degrees of acceptance, rejection, and indeterminacy are both measured. In this article, we formulate a multi-product production planning problem with multiobjectives with parameters as neutrosophic environments. The uncertain parameters are depicted as trapezoidal neutrosophic numbers, and the crisp version is developed by a new accuracy function. In the solution procedure, we have investigated interactive neutrosophic optimization techniques with neutrosophic parameters. Furthermore, various sorts of membership functions, such as linear, exponential, and hyperbolic, are depicted so that the marginal evaluation of each objective is determined. The proposed method represents an opportunity for select decision-makers with desired membership functions. To show the relations among the multiobjective multi-product production planning problem, its equivalent crisp formulation obtained by applying three different membership functions is established. Finally, the stepwise solution procedures are discussed, and compared with different membership functions.
  Keywords: Trapezoidal Neutrosophic Numbers; Neutrosophic Optimization; Accuracy Function.
  DOI: 10.1504/IJOR.2024.10064719
   
  
• Inventory Decisions for Deteriorating and Ameliorating Items with Partial Backlogging and Time Varying Demand  
  by Praveen V. P, Manoharan M 
  Abstract: The observations from real life examples indicate that the consideration of ameliorating and deteriorating items is important in developing inventory models. This research paper deals with both these factors along with demand rate which is linearly time varying over a fixed planning time frame. The shortages are partially backlogged during the time frame. Here, amelioration rate is taken to follow two parameter Weibull distribution as these items increases with time and decreases due to death. In the first phase of time horizon deterioration occurs and its rate increases with time. The model is developed under these situations. Using numerical examples and sensitivity analysis, the model is illustrated and verified the effect of changes of model parameter on the optimal solutions.
  Keywords: inventory; time dependent deterioration; Weibull distribution amelioration; time dependent demand; partial backlogging.
  DOI: 10.1504/IJOR.2024.10064792
   
  
• Distinctive representations of icosagonal fuzzy numbers along with novel defuzzification techniques for solving fuzzy assignment problems  
  by Jaya Bhadauria, Suneel Kumar, Deepak Kumar, Anita Kumari 
  Abstract: In this paper, we represent icosagonal fuzzy numbers in a variety of ways, both symmetrically and asymmetrically, linearly and nonlinearly as well as single valued and interval-valued. Along with this, we have also developed some defuzzification procedures with different approaches based on centroid method, the mean of alpha-cut method and bounded area method. In order to demonstrate the significance of these strategies, defuzzification approaches can be applied to many optimisation problems in operational research. We have applied these strategies to solve the numerical example based on fuzzy assignment problem in the interview board panel with 20 parameters. This study deals with the situation where icosagonal fuzzy numbers are used to represent ambiguous information in the form of linguistic terms. The ranking function for icosagonal number is also proposed in this paper for the better comparison of two icosagonal fuzzy numbers and its primary goal is used in this research for the appropriate allocation to resolve the fuzzy assignment problem.
  Keywords: icosagonal fuzzy number; defuzzification techniques; ranking function; fuzzy assignment problem.
  DOI: 10.1504/IJOR.2024.10065167
   
  
• Multiple Drone and Truck Combined Operations  
  by Bhawesh Sah, Mohammad Moshref-Javadi, Sung Hoon Chung 
  Abstract: Drones, also known as unmanned aerial vehicles (UAVs), have the capability to improve the responsiveness in parcel distribution process, however, drone delivery suffer from shortcomings such as limited battery life, and weight carrying constraints. These shortcomings can be overcome if a drone works in conjunction with a truck to make parcel deliveries. In contrast to earlier models which focus on single drone and truck, in this paper we propose a novel model in which multiple drones and trucks can work together to fulfill the logistics operations, a drone can depart from a truck and return back to the same or a different truck after completing the operations and a truck can house multiple drones. We present a mixed integer linear programming formulation of the problem and present results from several heuristics such as Genetic Algorithm (GA), Simulated Annealing(SA), and Greedy search combined with the Insertion method.
  Keywords: Drone Logistics; Last-mile delivery; Unmanned aerial vehicle; Transportation planning; Optimization.
  DOI: 10.1504/IJOR.2024.10065379
   
  
• A Dual Channel Supply Chain considering Different Preferences of Delivery Cost Bearing in Presence of a Third Party Platform  
  by Soumita Kundu 
  Abstract: This paper explores the operation decisions of a dual-channel supply coordination consisting of a manufacturer, a retailer and a third-party platform (3PP). In reality, in the presence of the third-party platform manufacturers can opt for various options of bearing delivery cost: 1) the manufacturer will bear the delivery cost; 2) the 3PP will bear the delivery cost; 3) the customer will bear the delivery cost. Here, we address all these situations. Furthermore, the delivery time, to which the online customers are more sensitive, is taken into consideration by customers' channel choice and the manufacturer or the third party makes efforts to reduce delivery time. Finally, sensitivity analysis with graphical illustrations has been performed to investigate whether it is profitable for the manufacturer to pay product delivery cost in the online channel, if not, under what condition the third-party platform or the online customer will bear this cost.
  Keywords: dual-channel; third-party platform; delivery time; revenue sharing; pricing.
  DOI: 10.1504/IJOR.2024.10065581
   
  
• Sperm Flagellum Motility Algorithm: a Novel Metaheuristic Optimiser for Solving Optimisation Problems  
  by Imad El Karkri, Abdelghni Lakehal 
  Abstract: The challenges and intricacies associated with real-world numerical optimisation problems have significantly increased, necessitating the development of efficient optimisation methods. While numerous metaheuristic approaches have been proposed, only a select few have gained recognition within the research community. This paper introduces a novel metaheuristic algorithm known as the sperm flagellum motility algorithm (SFMA) to address optimisation problems. SFMA emulates the motility principle of a sperm flagellum immersed in a two-dimensional fluid. Representing a population of solutions, the sperm flagellum navigates the search space to discover an optimal solution for the given problem. To evaluate the effectiveness of SFMA, a suite of 23 benchmark functions and five engineering problems were solved and compared against the performance of other widely recognised optimisers. The optimisation results demonstrate that the SFMA is highly competitive when compared to both conventional methods and state-of-the-art meta-heuristic algorithms.
  Keywords: sperm flagellum motility algorithm; SFMA; optimisation algorithm; benchmark functions; meta-heuristic algorithm; engineering problems.
  DOI: 10.1504/IJOR.2024.10065705
   
  
• Optimising Fresh Produce Demand with Expiration Date and Carbon Mitigation Strategies under Learning Effect and Non-Linear Holding Cost: A Quadratic Modelling Approach of Time-Price-Freshness for Profit Maximization  
  by Vrushali Ajitkumar Surve, Monika Naik 
  Abstract: In todays health-conscious society, there is a growing demand for fresh produce. This demand depends on factors like freshness, visibility, expiration date, and pricing, influencing customer purchases. This article suggests modelling fresh produce demand as quadratic function, incorporating freshness, price, shelf space, and expiration date under learning effects and with nonlinear holding costs. Surprisingly, it proposes maintaining significant stock towards replenishment cycle ends, challenging the zero-ending inventory norm. Simultaneously, nations are tackling carbon emissions as a major driver of global warming. Economists endorse carbon cap and tax policies. To optimise strategies (cycle time, price, and green technology), a systematic approach is proposed for profit maximisation. Numerical example validates this model, offering insight to ideal pricing, ending inventory, replenishment cycle, and backroom clearing timing, and ordered quantity. Classical optimisation techniques compute these values. Moreover, by analysing eigenvalues of a Hessian matrix, the convexity of profit function is established. A numerical illustration and sensitivity analysis on inventory parameters verify the model, yielding vital managerial insights. In essence, this article explores fresh produce demand modelling and carbon mitigation strategies while providing practical optimisation solutions and empirical validation.
  Keywords: Deterioration; Learning effect; freshness index; carbon emission; carbon tax; carbon cap; stock-time-price-freshness dependent demand.
  DOI: 10.1504/IJOR.2024.10065911
   
  
• Solving a Flexible Job-Shop Scheduling Problem considering Changes in Resources Capacity  
  by Sandra Sousa, Lopes Rui Borges 
  Abstract: This paper addresses a flexible job-shop scheduling problem (FJSP) with a set of processing characteristics commonly found in several real-world manufacturing applications. The processing characteristics considered are release dates, precedence constraints within and between different jobs, resource capacity (including downtimes, changes in capacity, and infinite capacity), and sequence-dependent setup times. The goal is to find a schedule minimising the total number of tardy jobs. To tackle the newly proposed FJSP some heuristic approaches are put forward. New constructive and improvement heuristics are proposed and some of them are used within metaheuristic frameworks, namely greedy randomised adaptive search procedure (GRASP) and iterative local search (ILS). To evaluate these approaches, two sets of test instances from the general FJSP literature have been adapted to meet the specifications of the proposed FJSP.
  Keywords: scheduling; flexible job-shop; resources capacity; heuristics; flexible job-shop scheduling problem; FJSP; iterative local search; ILS.
  DOI: 10.1504/IJOR.2024.10065977
   
  
• An Improved Chemical Reaction Optimisation for the Dynamic CVRP with Two-Dimensional Loading Constraints  
  by Nadia Dahmani, Ines Sbai, Takwa Tlili, Saoussen Krichen 
  Abstract: Efficient packing and routing are key to minimising supply chain costs and delivery times. This is particularly critical with two-dimensional items like appliances or forklifts, where maximising cargo space and optimising routes are crucial. In this study, we investigate the dynamic vehicle routing problem with two-dimensional loading constraints. This problem involves assigning routes to vehicles while considering items dimensions and minimising transport costs. To tackle this problem, we propose an improved chemical reaction optimisation algorithm. The algorithms effectiveness lies in its balance between finding known good solutions and exploring new possibilities, leading to optimal solutions. Additionally, we perform a local search scheme to refine the solution further. To address the complexity of dynamic packing, a next-fit decreasing heuristic is designed. To assess the effectiveness our algorithm, we adapt the static benchmark instances using various degrees of dynamism. Based on performance metrics, results demonstrate the competitiveness of our algorithm.
  Keywords: Dynamic vehicule routing problem; Two-dimensional loading constraints; Chemical reaction optimization; Local search; Next Fit Decreasing Heuristic.
  DOI: 10.1504/IJOR.2024.10066264
   
  
• Price Dependent Demand and Inflation Deteriorating Inventory Model with Shortages  
  by Nilesh Kumar, Quazzafi Rabbani, Nurul Khan 
  Abstract: The aim of this research is to develop a model of declining stock levels and shortages in an environment of price-dependent consumer demand and inflation. The purpose of this model is to have a conversation on how to handle an inventory system for perishable goods when demand is price-dependent on supply. Here it is believed that shortages will occur and inflation will be used to make up for some of the shortfall. As a result, the economic order quantity is calculated to maximise profits per unit of time.
  Keywords: deteriorating; shortages; inventory model; price dependent demand; inflation.
  DOI: 10.1504/IJOR.2024.10066329
   
  
• A fuzzy medication inventory model with Weibull deterioration and shortages for any epidemic or medical emergency  
  by Swadhin Banerjee, Tripti Chakrabarti 
  Abstract: As medication costs are a large portion of operating expenses of any hospital, improving the medication inventory management is a great way to decrease overall healthcare cost. Again, in recent COVID-19 pandemic, healthcare sector faced many challenges, especially uncertain increase in the demand and shortages of supply of medical items. Thus, this study aims to derive an optimal medication inventory model to manage any future epidemic or medical emergency as well as to reduce overall healthcare costs. We would use Gaussian fuzzy number which is more realistic to counter uncertainties of epidemic or medical emergency. Also, we would present a numerical illustration with sensitivity analysis to exemplify our proposed model.
  Keywords: EOQ model; deterioration; time dependent demand; shortages; fuzzy environment.
  DOI: 10.1504/IJOR.2024.10066450
   
  
• Performance Analysis of M/M/1/N Queue with Balking and Reneging using Statistical Mechanics  
  by Krishan , Neetu Gupta, Amita Bhagat 
  Abstract: Customer's behaviour is the most important parameter in deciding the effictiveness of a queueing system. Sometimes out of impatience the customers get discouraged and behave differently on analysing the queue. In this article, statistical methods are used to analyse finite markovian M/M/1/N queueing system with balking and reneging. The performance measures and cost model are constructed and numerical examples are illustrated to analyse the sensitivity of the model.
  Keywords: Balking; Reneging; Performance Measures; Steady-State Probabilities; Cost Model.
  DOI: 10.1504/IJOR.2024.10066698
   
  
• Exploring Metaheuristic Strategies and Risk Mitigation Techniques for Diversified Portfolio Management  
  by Jhuma Ray, Soma Panja 
  Abstract: Recent portfolio selection models pose considerable challenges for optimization due to the introduction of nonlinearities, discontinuities, and high-dimensional efficient frontiers. Exact techniques need to address these complexities effectively. Consequently, researchers here have turned to metaheuristics as robust tools capable of finding near-optimal solutions, or even the global optimum, within reasonable computational time. Metaheuristics, including Genetic Algorithms (GA), Differential Evolution (DE), and Particle Swarm Optimization (PSO), along with Ant Colony Optimization (ACO), have demonstrated their efficacy in handling the intricacies of complex portfolio optimization problems as reported here. Following the examination of four meta-heuristic methods, consensus results are derived. Subsequently, a Friedman test is employed to determine the method's superiority. Differential Evolution along with Particle Swarm Optimization emerges as the superior choice among the four proposed metaheuristic methods, with the other two as points of comparison emphasizing single-objective metaheuristics (SOMHs) offering natural framework for addressing portfolio selection challenges involving intricate risk measures and diverse real-world constraints.
  Keywords: Genetic Algorithm; Differential Evolution; Particle Swarm Optimization; Ant Colony Optimization; Conditional Value at Risk; Value at Risk.
  DOI: 10.1504/IJOR.2024.10066702
   
  
• Continuous Review Inventory Model under Partial Permissible Delay in Payment Policy and Capacity Constraint  
  by M. A. Darwish  
  Abstract: In this paper, we propose a continuous review inventory model incorporating the following real-world aspects; randomness in lead time, partial permissible delay in payment, and capacity constraint on retailer's warehouse. Given the current disruptions in lead times due to epidemics and wars, the deterministic lead time assumption is probably not valid. We, thus, relax this assumption to match the real-world situations. We model the lead time randomness by a general probability distribution. Moreover, we use the partial permissible delay in payment policy where the retailer pays a down payment at the time of placing the order and the outstanding amount is settled by the time of placing the next order. Further, we relax the infinite capacity assumption by imposing a constraint on the lot size. The model determines the optimal lot size and reorder point that minimize the net expected total cost per time unit.
  Keywords: Inventory; stochastic lead time; partial permissible delay in payment policy; capacity constraint.
  DOI: 10.1504/IJOR.2024.10066917
   
  
• Analysis of AS/RS Performance for Different Storage Location Policies  
  by Aravindh Kumaran L, Pradeep Arul Pragash A 
  Abstract: Automated storage and retrieval systems (AS/RS) play a significant role in storing and retrieving inventory in warehouses and manufacturing plants. These systems rely on storage location policies to guide the effective storage and retrieval of inventory. These storage location policies are in alignment with the inventory handling systems including AS/RS. This paper aims to analyse the impact of different storage location policies on the runtime and performance of AS/RS. Data was collected from a chocolate manufacturing company's warehouse, and a simulation of an AS/RS model with a single storage rack was conducted to analyse the performance with different settings. The results showed that the first available storage policy performed well for a setting called no batch dispatches. The findings contribute to a better understanding of the factors influencing the performance of AS/RS and can assist in optimising inventory handling processes in warehouses and manufacturing plants.
  Keywords: automated storage and retrieval systems; AS/RS; storage location policies; warehouse; simulation; inventory.
  DOI: 10.1504/IJOR.2024.10066958
   
  
• A Sustainable Deteriorating Inventory Model under Controllable Carbon Emission with Green Investment Strategy and Quality Reliant Demand  
  by Sandeep Kumar, Sanjai Sharma, Anirudh Bhargava, Dharmendra Yadav 
  Abstract: In this era of technological progress and its applications, which offer enhanced survival facilities, on one side, the use of technology reduces the burden of work, and on the other, it has become the main cause of carbon emissions. The present work focuses on the reduction of carbon emissions and the development of an inventory model that maximises the retailer’s profit. In this work, a model incorporating a quality-reliant demand with shortages and an expiration rate of deterioration is developed. Energy-efficient green technology is adopted to make in a greener environment. The model was developed with the objective of determining the time period at which inventory vanishes and the value of the scale parameter, which determines a reasonable selling price that is a multiple of the unit purchase cost so as to maximise profit. To elucidate the model’s applicability, different numerical examples have been illustrated.
  Keywords: shortages; quality dependent demand; single item; green investment; quality dependent holding cost; expiration date reliant deterioration.
  DOI: 10.1504/IJOR.2024.10067082
   
  
• Economic Analysis of MAP/PH/1 Queueing Model with Degrading Service Rates, Multiple Vacations, and Reactive Maintenance based on Feedback  
  by Nitin Mahla, Alka Choudhary, Dinesh Chandra Sharma 
  Abstract: The proposed model introduces a queueing model with a Markovian arrival process and Phase type service distribution where the server undergoes degradation over time, leading to a reduction in service rates, and customer feedbacks are collected to evaluate customer satisfaction. Reactive maintenance is implemented on the server after the accumulation of a predetermined quantity of adverse feedback occurrences. Vacation policies are implemented to restore the server to its optimal service rate either when a degradation threshold is reached or when there are no customers in the system. Steady-state probabilities and performance metrics are derived using the Matrix geometric method. Economic functions are developed and the Particle Swarm Optimisation (PSO) technique is used to optimize the predicted profit. The effects of system parameters are summarised in the numerical example section.
  Keywords: Markovian arrival process; Phase type distribution; Feedback; Reactive maintenance; Service rate degradation; Multiple vacation.
  DOI: 10.1504/IJOR.2024.10067165
   
  
• A Multi-Objective Optimisation of Airport Gate Assignments integrating Economic, Environmental, and Social Sustainability  
  by Jeremy Gabriel Uy, Jarvy Larz San Juan, Mateo Urera, Edrik Aaron Chan, Ezra Emmanuel Cruz, Nathaniel Harvey Tang, Richard Li, Jayne Lois San Juan, Charlle Sy 
  Abstract: With the increasing trend in the number of passengers in air travel, especially after the pandemic. As such, researchers have been attempting to optimise airport systems to stop problems from arising. While optimisation studies in AGA systems have been looked into with the economic, environmental, and social perspective separately, studies yet to consider integrating the three considerations and optimising the problem simultaneously, which would allow multiple parties to benefit at the same time minimising the compromission made in each objective individually. A multi-objective mathematical optimisation model has been developed for AGA optimisation considering economic, environmental, and social objectives simultaneously. An illustrative case study was executed to understand the tendency of the model. The model has been validated to be effective in minimising total turnaround costs, minimising total walking distance, and minimising carbon emissions simultaneously.
  Keywords: airport management system; triple bottom line; green transportation; aircraft gate assignment; air transport.
  DOI: 10.1504/IJOR.2024.10067262
   
  
• Hybrid Algorithm: Estimation of Distribution Algorithm and Local Search Method for the 0-1 Quadratic Knapsack Problem  
  by Amina Arousse, Bassem Jarboui, Mohamed Cheikh 
  Abstract: In this paper we propose a hybrid algorithm based on an estimation of distribution algorithm (EDA) and the local search method (LS) to solve the problem of the quadratic knapsack. It is important to note that the estimation of distribution algorithm and the local search method are often less powerful on certain types of problems. It does not guarantee efficient results in a finite time. To solve this deficiency, we suggest this hybridization. The proposed algorithm was tested over a set of small-sized instances with 100 and 200 binary variables and the results were compared to those reported from the literature.
  Keywords: Estimation of Distribution Algorithm; Local Search Method; 0–1 quadratic knapsack problem.
  DOI: 10.1504/IJOR.2024.10067264
   
  
• Development of Two-Shop Inventory Model with Multi-Variate Demand and Screening Errors under Controllable Carbon Emission  
  by Sundar Lal, Ashok Kumar, Sandeep Kumar 
  Abstract: This study proposes an inventory model for the retailer by considering two shops under single management. This study considers that: 1) receive lot contains defective items; 2) manual screening process is carried out which is an erroneous process; 3) demand is multi-variate; 4) carbon emissions due to operational activities linked to inventory which is regulated by cap-and-tax policy; 5) capital investment in green technology to curb carbon emission. The present study aims to determine the values of order quantity and backorder level that optimise the retailers profit. Developed model is illustrated with the help of numerical analysis as well as sensitivity analysis. In the end, the effect of promotion activities, selling price, cap-and-tax regulation policy, and investment in green technology on the optimal decision have been analysed. Based on the analysis, managerial implications are also presented.
  Keywords: EOQ; imperfect lot; screening error; cap-and-tax regulation; carbon emissions; multi-variate demand; two-shop management.
  DOI: 10.1504/IJOR.2022.10067281
   
  
• Safety Stock Optimisation with Guaranteed Service Approach under Different Supply Chain Topologies  
  by Joaquim Jorge Vicente  
  Abstract: Supply chain structure is an important driver to estimate de safety stock level in each entity. Supply chain inventory planning is studied under uncertain demand. The present paper uses guaranteed service approach to optimise safety stocks. The problem is formulated as a mixed integer linear program (MILP) that consists of determining the optimal locations and quantities of safety stock in the network to meet a given service level. The model is applied to different supply chain structures to study the impact on safety stock optimisation. Also, it determines inventory levels in each entity and reordering plan for the operating network that minimises the overall operation cost. A case study with two supply chain structures is presented and solved.
  Keywords: supply chain management; safety stock; optimisation; mixed integer linear programming; MILP; guaranteed service approach; supply chain topology.
  DOI: 10.1504/IJOR.2024.10067644
   
  
• Sustainable Freight Transportation: a Bi-Objective Multi-Choice Goal Programming Framework  
  by Nitin Sahu, Garima Mittal 
  Abstract: Sustainability has gained significant prominence in transportation policies and planning. The surge in air pollution, primarily attributed to greenhouse gas emissions from industrial transport, has impacted both developed and developing nations, including India, prompting the pursuit of sustainable transportation solutions. This paper presents an integrated, multi-objective, multi-choice optimisation model to address the challenging problem of sustainable freight transport in the industrial sector. The model considers real-world constraints to lower transportation costs and greenhouse gas emissions. We employ a multichoice goal programming technique to develop optimal allocation strategies. We recognize that decision-makers use interval values to designate multiple aspiration levels for transportation cost and greenhouse gas emissions objectives. To demonstrate the practical application of the proposed optimisation model and the solution methodology, we present a numerical illustration in the context of the transportation of municipal solid waste to an energy generation plant.
  Keywords: Multi-choice goal programming; transportation problem; Sustainable transportation; Greenhouse gas emissions.
  DOI: 10.1504/IJOR.2024.10067865