International Journal of Mathematics in Operational Research (109 papers in press)

Regular Issues

• Analysis of MAP/P H/1 queueing system with discarding customers having imperfect service, single vacation, feedback and impatient customers  
  by Ayyappan G, Archana Gurulakshmi 
  Abstract: In this paper, we analyse a single server queueing model where the service time follows a phase type distribution and the arrival process follows a Markovian arrival process with corresponding representations (D0, D1) of order m and (, T) of order n. When a customer enters for the service, a generalised Erlang clock with r stages is started concurrently. Due to the impatient, the customers may balk the system if server is in vacation period. By using matrix analytic method we find the steady state analysis in this model. Also we derive the expected waiting time, system performance measures, cost function and busy period. By using some performance measures we provide the numerical results and graphical representations.
  Keywords: Markovian arrival process; phase type service; imperfect service; Erlang clock; single vacation; Bernoulli feedback; balking.
  DOI: 10.1504/IJMOR.2023.10058201
   
  
• Analysis of MAP/PH/1 Retrial queueing system with Two-stage vacations with imperfect service, N-policy service, Delayed feedback, Unreliable server and Discouragement customer  
  by Ayyappan G, N. ARULMOZHI 
  Abstract: In the present study, we investigate a continuous-time single server constant retrial queueing with a limitless system of capacity, two-stage vacations that include single working vacation and multiple vacations with imperfect service, N-policy service, delayed feedback, unreliable server, and discouragement customer. Once the operating environment is empty during a normal busy period, it initially takes a working vacation, during which the server can still provide service but at a slower rate. If the system is empty after this working vacation, the server will take a vacation and stop serving entirely. Otherwise, the server resumes its normal service rate. If there are fewer than N customers in orbit after the vacation period ends, the server resumes normal operation. If not, the server starts another vacation. When approaching the system using the matrix-analytic method, steady-state vector, busy period, and cost analysis are generated for this model. Analytical performance indices are assessed numerically.
  Keywords: multiple vacation; working vacation; unreliable server; imperfect service; delayed feedback.
  DOI: 10.1504/IJMOR.2023.10058270
   
  
• Pricing and Return Strategies in a Dual-Channel Closed Loop Supply Chain considering Complementary Products and Sales Effort  
  by Subir Guin, Amit Sarkar, Brojeswar Pal 
  Abstract: Waste materials are polluting the environment as they are being stored. Additionally, with a shortage of raw materials and energy sources, remanufacturing would be beneficial. In this paper, we discuss a dual-channel closed-loop supply chain of a pair of complementary products involving two manufacturers and one retailer.The manufacturer of main products distributes the products through both online and traditional retail channels, while the manufacturer of complementary products does so only through the online channel. For remanufacturing, two manufacturers collect their end-of-used products through only the online channels. Then the pricing and remanufacturing decision problem is modelled based on four-game (centralised, vertical Nash, manufacturer Stackelberg, retailer Stackelberg) models, which differ in power structures. After that, the optimal results of the manufacturers and the retailer are analysed. Finally, a numerical result is proposed to analyse the analytical results and sensitivity to the respective parameters. Based on our research, we determined that channel and retailer profit along with return rate is highest for the centralised model, whether channel and retailer profit and sales effort are maximum for the manufacturer Stackelberg model under decentralised environment.
  Keywords: dual-channel; closed loop supply chain; complementary products; sales effort; vertical Nash; Stackelberg.
  DOI: 10.1504/IJMOR.2023.10058493
   
  
• Solving an Exploitation based Marxian fuzzy EOQ Model  
  by Biswajit Roy, Kousik Bhattacharya, Sujit Kumar De 
  Abstract: This article deals with the clinical study of Marxian economic order quantity (M-EOQ) model under fuzzy environment. Initially the model has been viewed as multi-objective cost minimisation and profit maximisation problem under optimum rate of exploitation. Then we transform the multi-objective optimisation problem into single objective optimisation problem under suitable constraints. For optimising this objective function, we need to solve analytically a biquadratic equation where order quantity assumes as one of the decision variables. According to the nature of the roots of this biquadratic equation, we split the model into various sub models where the exploitation varies differently with the change of demand function. Incorporating the negative root of the biquadratic equation, we have formulated three different backlogging EOQ models. Considering a case study, we perform the numerical experimentation with the help of a solution algorithm. Moreover, to capture the non-random uncertainty of the model parameters, we construct an equivalent fuzzy shortage model. Our findings reveal that, shortage model is more beneficial than other sub-models for the decision maker all the time. Finally, numerical illustrations, sensitivity analysis, graphical illustrations and comparative study are done for justify the model followed by managerial insight, conclusion and scope of future work.
  Keywords: EOQ model; Marx’s theory; exploitation; fuzzy set; algorithm; optimisation.
  DOI: 10.1504/IJMOR.2023.10058781
   
  
• Optimal Greening Efforts, Pricing and Inventory Strategies for Non Instantaneous Deteriorating Perishable Products under Price, Freshness and Green Efforts Dependent Demand with Price Discount  
  by DHARMESH KATARIYA, Kunal Shukla 
  Abstract: Nowadays, consumers who are concerned about their health prefer and expect nutritional and fresh sustainable products. Due to their freshness, healthfulness, and environmental friendliness, people are now using sustainable fresh perishable products. The price of products plays an important role in consumers purchasing behaviours. This article considers an inventory model for non-instantaneously deteriorating perishable fresh products with selling price, age of product (freshness), and greening efforts dependent demand. The quality of products reduces due to physical deterioration and degradation of the product's freshness, and hence, retailers offer a discount in the selling price to the buyer during a deteriorating period to boost demand. The objectives of the study are to determine the optimal selling price, an optimal period for replenishment cycle time, and an optimal value of greening efforts cost simultaneously while taking into account retailers total profit maximisation. A mathematical model is developed and validated using numerical results to reflect actual situations. To examine the reliability of the model, sensitivity analysis with regard to parameters is undertaken. Some keys managerial insights are presented, and the article concludes with a discussion of the future scope of related research.
  Keywords: inventory; freshness index; greening efforts; non-instantaneous deterioration; price discount; perishable products.
  DOI: 10.1504/IJMOR.2023.10058782
   
  
• Supplier - Retailer - Customer Trade credit policy for Perishables  
  by Jayashri P, Umamaheswari S 
  Abstract: Perishable items have a relatively short shelf life and degrade naturally. In particular, managing perishable inventory can be challenging, since shortages and wastage are closely associated. Preservation techniques are incorporated to maintain the shelf life of perishable items. The objective of this paper is to optimise the total inventory costs by minimising the deterioration rate and free up working capital for entrepreneurs. Genetic algorithm with one-point crossover, swap mutation and random selection is used to determine the optimal credit period and cycle time by varying different upstream credit periods. An economic order quantity is derived to determine an optimal ordering quantity for a trade credit inventory model. The total profit corresponding to various credit periods and time intervals is illustrated numerically. The effect of changes in key parameters of the optimal solution is investigated using sensitivity analysis. The model is applicable for perishable items like fruits, vegetables, meat, dairy products, and so on which need preservation to increase shelf life.
  Keywords: deteriorating; inventory; perishable; preservation technique; trade credit.
  DOI: 10.1504/IJMOR.2023.10058929
   
  
• Fractional Black - Scholes Equation described by the Conformable Fractional Derivative with Three Different Methods  
  by Vijayan C, Manimaran R, Racshitha N 
  Abstract: This study deals with the conformable fractional derivative (CFD) operator and three different methods for solving the fractional Black-Scholes equation (FBSE) and the generalised fractional Black-Scholes equation (GFBSE). They are the variation iteration method (VIM), reduced differential transform method (RDTM) and homotopy analysis method (HAM). The redefined proposed methods are the conformable variation iteration method (CVIM), conformable fractional reduced differential transform method (CRDTM), and conformable homotopy analysis method (CHAM). Finally, images and tables are used to display the results of FBSE and GFBSE. These methods can be used to accurately solve both the fractional Black-Scholes equation and the generalised fractional Black-Scholes equation.
  Keywords: Black-Scholes equation; BSE; conformable fractional derivative; CFD; variational iteration method; VIM; reduced differential transform method; RDTM; homotopy analysis methods; HAM.
  DOI: 10.1504/IJMOR.2023.10058977
   
  
• A two server tandem queueing model with Markovian arrival process, phase type service, working vacation, feedback, re-service, unreliable server, interrupted closedown and customers intolerance.  
  by Ayyappan G, Archana Gurulakshmi 
  Abstract: This paper intends to focus on two-server tandem queue with working vacation, feedback, re-service, unreliable server, interrupted closedown and impatient customers. Input flow of customers arrival is modelled using a Markovian arrival process (MAP) and the service time is considered to follow a phase type distribution. Customers impatience has been studied under phenomena of reneging and balking of this model. The essential and sufficient conditions for system stability is found. By using the matrix analytical method, the queueing model's steady-state probability distribution was derived. Additionally, we derived some performance indicators for the model. Finally, certain numerical examples were used to evaluate the impact of system parameters both numerically and graphically.
  Keywords: Markovian arrival process; MAP; phase type service; working vacation; re-service; interrupted closedown; reneging; balking; breakdown; repair.
  DOI: 10.1504/IJMOR.2023.10059085
   
  
• Copula Approach to Predict Reliability Factors of a Wide Range Communication System  
  by Abdul Kareem Lado, Abdulhadi Aminu, Ibrahim Yusuf 
  Abstract: Information can be passed between people, groups, gadgets, organisations, continents, and the rest of the globe through communication. Focusing on the aforementioned, this study takes into account a communication system made up of five subsystems: three servers, two switches, a router, and three clients, which are all grouped together in a series-parallel categorisation. Given that this system is operational, failure is inevitable. As a result, the failure of these subsystems appears to be constant and in accordance with the exponential function, general and copula repairs are offered to fix both partial and whole system failures. The mathematical transition figure of the system is used to construct partial differential equations, which are then solved with the use of a supplementary variable and the Laplace transformation method. The expressions for availability, reliability, mean time to failure (MTTF), sensitivity, and costs are realised using a mathematical tool. The study's findings are supported by specific examples.
  Keywords: availability; reliability; mean time to failure; MTTF; sensitivity; cost; communication; computer.
  DOI: 10.1504/IJMOR.2023.10059094
   
  
• The Topp-Leone-Marshall-Olkin-G Power Series Class of Distributions: Properties and Applications  
  by Peter T. Chinofunga, Broderick Oluyede, Fastel Chipepa 
  Abstract: This study introduces a new class of distributions known as the Topp Leone Marshall-Olkin-G Power Series (TLMO-GPS). TLMO-G fanily of distributions is compounded with the Power Series distribution to get TLMO-GPS. Some statistical properties including quantile function, linear representation, order statistics, R
  Keywords: Topp Leone; Marshall Olkin; Generalised Distributions; Power Series; Moments; Maximum Likelihood Estimation; Goodness-of-fit Statistics.
  DOI: 10.1504/IJMOR.2023.10059095
   
  
• The synthesis of the AHP as a well-posed mathematical problem and matrix norms appropriate for sensitivity analysis via condition number  
  by Gustavo Benitez Alvarez, Rafael G. De Almeida, Cecilia T. Hernández, Patrícia Alves Pereira De Sousa 
  Abstract: The analytic hierarchy process (AHP) is a decision making method, which has as its greatest criticism the rank reversal effect. This paper formulates the fourth step of the AHP (synthesis) as a well-posed mathematical problem. A theorem guarantees the existence of the square condensed original formulation for the AHP. This means that any decision problem modelled by AHP with a different number of alternatives and criteria can be condensed into a model with an equal number of alternatives and criteria without loss of condensed information. This condensed formulation can be better conditioned than the original rectangular formulation of the AHP. The square condensed equivalent formulation is also a well-posed mathematical problem. The concepts are applied to two practical cases from the literature, and sensitivity analysis is performed. Four classical matrix norms are reformulated to obtain theoretical bounds for the error estimate closer to actual error.
  Keywords: multiple criteria analysis; rank reversal; linear systems of equations; sensitivity analysis.
  DOI: 10.1504/IJMOR.2023.10059096
   
  
• Fuzzy Weak Autocatalytic Set for Decision Making and Its Application to the Project Manager Selection  
  by Siti Salwana Mamat, Siti Rahmah Awang, Tahir Ahmad 
  Abstract: In decision making procedures, the comparison of alternatives is often necessary to determine the most suitable option among a set of choices. One commonly used approach is pairwise comparison, where each alternative is compared to every other alternative based on certain criteria. FWACS method offers a way to represent the pairwise comparisons of alternatives as a directed graph with fuzzy edges. The FWACS is a technique used to address problems involving multiple criteria. In this study, a new ranking approach using FWACS is implemented on a previously published MCDM problem. The purpose of this implementation is to showcase the effectiveness of the FWACS method in addressing decision problems that involve multiple criteria.
  Keywords: fuzzy weak autocatalytic set; FWACS; decision-making; project manager selection; ranking; graph theory.
  DOI: 10.1504/IJMOR.2023.10059280
   
  
• Introduction of an arc rank order statistic for analysis of optimal solutions in traveling salesman problems  
  by Jerry Shaw, Donovan Fuqua, Hansuk Sohn, Manuel Ivan Rodriguez Borbon 
  Abstract: This research provides an empirically derived and previously unreported insight into the actual composition and common features of optimal solutions in travelling salesman problems (TSPs). One unreported characteristic of these solutions is the frequency with which a vertex is connected to another relatively near or distant vertex. Based on a mathematical question on optimal solution arc lengths, we introduce an arc rank statistic and use it to analyse optimal solutions for a range of standard TSPs. The resulting analysis shows, with few exceptions, that the frequency with which low-ranked arcs appear is a decreasing function. Further, the frequency distributions of arc ranks generally have fat tails. Log/log transforms of the frequency distributions were analysed to show linear relations; suggesting that the distribution of arc ranks in optimal TSP solutions generally follows a power law distribution. This knowledge suggests that statistical information about a solution may be sufficient to inform an observer about the quality of a solution.
  Keywords: optimisation; travelling salesman problem; TSP; graph theory; edge ranking.
  DOI: 10.1504/IJMOR.2023.10059334
   
  
• Pricing a Guaranteed Minimum Maturity Benefit in Uncertain Markets  
  by Justin Chirima, Frank Ranganai Matenda, Mabutho Sibanda 
  Abstract: This paper examines the problem of pricing a guaranteed minimum maturity benefit (GMMB) in uncertain markets. Several uncertainties are encountered in financial markets. The pricing process of a GMMB does not exhibit randomness alone, but also nonrandom uncertainties. We introduce uncertainty theory into pricing a GMMB. The assumption is that the stock price process, St, interpreted as an index for the fund assets, is driven by an uncertain differential equation (UDE). The solution to this UDE is regarded as a geometric canonical Liu process. We apply the UDE in pricing the GMMB problem and assume that the stock price evolution is driven by the canonical Liu process. Utilising the uncertain Liu option pricing approach, we formulate and examine a framework for pricing a GMMB in uncertain markets. Numerical computations are exemplified as well. The results of the study show that this approach is capable of pricing a GMMB.
  Keywords: uncertainty; uncertainty distribution; canonical Liu process; guaranteed minimum maturity benefit; GMMB; insurance policyholders; stock price.
  DOI: 10.1504/IJMOR.2023.10059337
   
  
• A QUEUEING SYSTEM WITH HETEROGENEOUS ARRIVALS, TWO KINDS OF VACATIONS AND IMPATIENT CUSTOMERS  
  by Yohapriyadharsini R. S, V. Suvitha, Rakesh Kumar 
  Abstract: We consider an M/M/1 queueing system with two kinds of vacations and impatient customers. The server begins the 1st kind of vacation each time the system becomes empty after serving all the customers. If the system is empty, when returning from this vacation it takes the 2nd kind of vacation. When the server comes back from either 1st kind or 2nd kind of vacation, if there is at least one customer in the system, the server immediately starts the service. If the server is busy or on 1st kind of vacation when a customer arrives at the system, it activates an impatience timer. If the customer’s service has not been finished before the customer’s timer perishes, the customer leaves the system and never returns. The balance equations of the model are all derived using a state-transition diagram. Probability generating functions (PGFs) technique has been used to derive the steady-state probabilities. Various measures of performance are presented and numerical illustrations are also provided.
  Keywords: busy state; vacations; steady state; performance measures.
  DOI: 10.1504/IJMOR.2023.10059372
   
  
• Optimal mean-variance portfolio selection with uncertain time horizon in a regime-switching market when asset returns are market path-dependent  
  by Reza Keykhaei 
  Abstract: In a financial market, the state of the underlying economy and investors’ mood affect market trends and consequently asset prices movements. Regime-switching models are used to describe changes in market states and trends. The main assumption in regime-switching models is that asset returns depend on the current state of the market. We generalises this assumption to the case where market states in the past, as well as the current state, affect asset returns. In fact, we assume that asset returns are market path-dependent. Under this assumption, we study a multi-period mean-variance portfolio selection problem in a Markovian regime-switching market when the time horizon is uncertain. Using the stochastic dynamic programming approach, we obtain the path-dependent optimal portfolio strategy and the mean-variance efficient frontier in a closed form. We show that the results obtained under conventional regime-switching model, can be obtained as special cases of the present model.
  Keywords: mean-variance portfolio selection; regime-switching; market path-dependent; uncertain time horizon; stochastic dynamic programming.
  DOI: 10.1504/IJMOR.2023.10059431
   
  
• Uncertain Multi-objective Student Project Assignment Problem by Fuzzy Programming Technique  
  by Sunil Bhoi, Jayesh Dhodiya 
  Abstract: This paper presents mathematical zero-one integer programming model of uncertain multi-objective student project assignment problem based on uncertain preferences of students and supervisor over projects or pairs of student and project. To develop this uncertain model, preferences are computed based on supervisor feedback and student result analysis, which are uncertain in nature. Two ranking criteria are utilised to deal with these uncertain preferences, which are expected value and optimistic value. Thereafter, uncertainty theory is applied to these uncertain model to transform uncertain models into deterministic form. Fuzzy programming technique with linear and exponential membership functions is utilised to solve deterministic multi-objective models and results are obtained using LINGO software. To check the strength and efficiency of proposed models, numerical data-based case is studied and results are discussed.
  Keywords: student project assignment; multi-objective optimisation; 0-1 integer programming; uncertain programming; fuzzy programming technique.
  DOI: 10.1504/IJMOR.2023.10059470
   
  
• Reduction of bounded variables in integer linear programming problems  
  by Abdelkrim Rezzag, Mohand Ouamer Bibi, Abdelhek Laouar 
  Abstract: In this paper, we suggest a new technique for reducing the number of variables in general integer linear programming problems with bounded variables. This technique involves fixing certain variables of the problem's optimal solution at one of their bounds, either lower or upper. A numerical illustrative example is presented, numerical experiments have been conducted to compare the execution time of the original problem with the execution time of the reduced problem and the pre-solving procedure.
  Keywords: integer linear programming; bounded variables; presolving procedure; numerical results and comparisons.
  DOI: 10.1504/IJMOR.2023.10059652
   
  
• New Weibull-Pareto Poisson Distribution: Properties, Actuarial measures, and Applications  
  by Fastel Chipepa, Mavis Pararai, Wilbert Nkomo 
  Abstract: A new power series distribution called the new Weibull-Pareto Poisson distribution is developed. The proposed model is very flexible in modelling heavy-tailed data. Some of the statistical properties are also derived and these include moments, moment generating function, and R
  Keywords: Weibull-Pareto distribution; power series distribution; maximum likelihood estimation; risk measures; poisson distribution.
  DOI: 10.1504/IJMOR.2023.10059698
   
  
• On the Numerical Solution and Mathematical Modelling of the Global Warming Data from the years 1970 to 1994 and from 1995 to 2019  
  by Zuhair Al-Hemyari, Jamal Alabasi 
  Abstract: In this paper, the numerical method, and modelling of a big data set related to global warming are developed using several techniques. The data is collected of daily temperatures from several cities over a 50-year period. To study the existence of the global warming precisely, the collected data is to be divided into two equal secondary periods. In addition, several methods of analysis and modelling will be applied in this paper. The analytical and modelling methods applied to the global warming in this paper are unique. In addition, the results on this paper are comprehensive, prominent and describe the essence of the problem and its perspective in the future. In specific, the results have shown that the changes occurring in the climate in the studied cities are significant and more severe than the changes occurring in the past (before 1970) and in other countries of Middle East region.
  Keywords: numerical solution; modelling; global warming; fitting; mixture distributions; EM algorithm.
  DOI: 10.1504/IJMOR.2023.10059729
   
  
• Joining Strategy for Double Orbit Retrial Queue with Imperfect Service and Vacation under N-policy  
  by Palak Mehta, Madhu Jain 
  Abstract: Optimal joining policy for Markovian retrial queueing system operating under N-policy and having ordinary and premium orbits, has been investigated. There is provision of additional service to the unsatisfactory ordinary orbit customers whereas unsatisfactory executive orbit customers may re-join the queue as a feedback customer. The proposed queueing system is investigated by implementing probability generating function (PGF) approach and evaluating various performance measures. Numerical experiments are performed to validate the analytical metrics obtained. The adaptive neuro fuzzy inference system (ANFIS) approach has also been implemented to authenticate the feasibility of intelligence computing for various metrics. The optimal joining probability is obtained by maximising the profit function value using particle swarm optimisation (PSO). The sensitivity of the queueing indices along with cost function has also examined by conducting the numerical simulation.
  Keywords: double orbit retrial queue; N-policy; imperfect service; feedback; joining strategy; particle swarm optimisation; PSO.
  DOI: 10.1504/IJMOR.2023.10059879
   
  
• Integrated Management and Optimization of Vaccination and Treatment Processes in a Batching System with Observation and Limited Space  
  by Ayyappan G, Sankeetha S 
  Abstract: This study examines a single-server system that incorporates multiple vacations. Customer arrivals adhere to a Markovian arrival process (MAP), and two types of service are applied, both following a phase-type distribution. Upon arrival, customers are grouped into batches of size L. Following service, customers enter an observation room, waiting for a predetermined duration. Subsequently, customers either leave the system if comfortable, or they join queue 2 for further service if not. Queue 2 follows a non-preemptive policy guided by the server. In the absence of customers, the server experiences multiple vacations following an exponential distribution. The server remains idle if customers are in the observation hall or if the number of customers in queue 1 is below L. This intricate system is represented as a quasi-birth-and-death (QBD) process, which we analyse using matrix-based methods. Also analysing the busy period, invariant probability, and performance metrics through graphical and numerical approaches.
  Keywords: Markovian arrival process; MAP; phase type service; multiple vacation; bulk service; non-preemptive priority.
  DOI: 10.1504/IJMOR.2023.10059922
   
  
• A New Heavy-Tailed Generalized Exponentiated Half Logistic-G Distribution with Actuarial Measures and Applications  
  by Thatayaoner Moakofi, Agolame Puoetsile, Broderick Oluyede 
  Abstract: This work introduce and investigate the new heavy-tailed generalised exponentiated half logistic-G (HT-GEN-EHL-G) family of distributions. The study involves the derivation and analysis of statistical properties associated with HT-GEN-EHL-G distribution. Employing the maximum likelihood estimation technique, we estimate model parameters and evaluate the consistency of these estimators through simulation studies. Additionally, we develop actuarial metrics (risk measures) tailored to this distribution. The practical utility of the HT-GEN-EHL-G family of distributions is demonstrated through the analysis of four real-life datasets from diverse fields. These applications emphasise the significance and versatility of the newly introduced HT-GEN-EHL-G family of distributions.
  Keywords: heavy-tailed distribution; exponentiated half-logistic-G distribution; estimation; applicability.
  DOI: 10.1504/IJMOR.2023.10059923
   
  
• Cost Optimization of MMAP/PH(1), PH(2)/1 Pre-emptive Priority Retrial Queueing model with Standby Server, Orbital Search, Server Breakdowns, Phase Type repairs and Impatient Customers  
  by AYYAPPAN Govindan, Thilagavathy Karthikeyan, Rakesh Kumar 
  Abstract: In this paper, we examine a single server queueing model in which priority customers arrive based on the marked Markovian arrival process (MMAP) and their corresponding service process is based on phase-type (PH) distribution. The primary server provides service to high priority or low priority customers, who may be affected by a breakdown, the standby server takes over service until the primary server has been repaired. Whenever either the primary or the standby server becomes idle, an orbital search of low priority customers is performed. We have established the stability condition for the model. Utilising the matrix-analytic method (MAM), the model is solved under steady state. Further, the busy period analysis of the model is carried out. Finally, the cost model is presented and the total cost of the system is analysed with the change in system parameters.
  Keywords: MMAP; PH-distribution; standby server; impatient customers; busy period analysis; retrials.
  DOI: 10.1504/IJMOR.2023.10060048
   
  
• Optimized Variable Step-Size Algorithm for the Solution of Dynamical Systems  
  by Joshua Sunday, Richard Olatokunbo Akinola, Joshua Amawa Kwanamu, Dominic Raymond 
  Abstract: This study focuses on the formulation of optimised variable step-size algorithm (OVSSA) for the solution of dynamical systems. In order to minimise the number of iterations and number of steps taken as well as improve the accuracy of the proposed algorithm, an embedded strategy was deployed in formulating the method using variable stepsize mode. One of the major advantages of the proposed OVSSA is that the algorithm automatically fine-tunes (or adjusts) the stepsize to suit the problem under consideration according to the variable stepsize strategy defined by the authors. Convergence properties of the OVSSA were also analysed theoretically in order to validate its stability and computational reliability. The OVSSA was employed in solving dynamical systems like the Van der Pol, Genesio-Tesi, Kepler and Lorenz systems. The results generated as a result of the application of the OVSSA on dynamical systems clearly showed that the method is convergent and computationally reliable.
  Keywords: algorithm; chaos; convergence; dynamical system; fixed stepsize; initial value problem; optimise; stability; stiffness; variable stepsize.
  DOI: 10.1504/IJMOR.2023.10060082
   
  
• A Queueing Model with Balking, Server Vacation and Working Breakdown  
  by Kamlesh Kumar, Dr. Madhu Jain 
  Abstract: This paper focuses on a single server queueing model that includes customer's balking, server vacation, and working breakdown. When there is no customer in the system or the system becomes empty, the server goes on a vacation and returns back when one or more customer available in the system. The server resumes service to the customers accumulated during its vacation period. There is always the possibility of a server breakdown while providing services to the customers, which may result in slower service rate. Slower service rate is considered as working breakdown state of the server or a defective mode of service. If the server is providing normal or defective service, customers may balk. For the system states, some practicable performance measures such as average number of customers in the system, average total cost function, and system throughput have been established for the various system states.
  Keywords: Markovian queue; balking; server vacation; working breakdown; probability generating function; PGF; cost function.
  DOI: 10.1504/IJMOR.2023.10060110
   
  
• A multi-machine bicriteria flow shop scheduling with sequence dependent setup time  
  by Meenakshi Sharma, Sameer Sharma, Nidhi Joshi 
  Abstract: Bicriteria flow shop scheduling problem with sequence dependent setup time (BPFSSP/SDST) is addressed in this paper. The objective of scheduling problem is to minimise weighted sum of makespan and system utilisation time, when both criteria are equal weighted. To solve the referred scheduling problem in small size machine-job environment, a mixed-integer programming model is developed and implemented. Since permutation flow shop scheduling problem with SDST is NP-complete in nature, therefore, the heuristic approach based on Nawaz, Enscore, Ham (NEH) neighbourhood structure and metaheuristic approach of hybrid iterated greedy algorithm with delay time, are proposed and implemented to optimise aforementioned scheduling bicriteria. The computation experiment is carried out to evaluate the performance of all developed heuristics and metaheuristics on varying size job-machine environment. The comparative analysis reported with response variable average relative percentage deviation (ARPD) verifies the effectiveness of proposed computation techniques over existing ones in solving the referred scheduling problem.
  Keywords: Scheduling; bicriteria; sequence dependent setup time; iterated greedy algorithms; local search.
  DOI: 10.1504/IJMOR.2023.10060188
   
  
• Recital facts of MX/G/1 Queues with Setup Time, Phases of Service, and Vacation  
  by S. Maragathasundari, K. Karthikeyan 
  Abstract: Researching group queueing systems that combine setup time and vacation work stages into a single server service is the aim of this MX/G/1 queueing study. In this queueing system, arrival time follows the Poisson distribution and service time follows a general distribution. The model is well equipped with setup time phases to do both a key maintenance task during the break and the necessary server pre-processing job. Additionally, the system is unavailable during the disruption because service disruptions are inevitable. The aforementioned mathematical queueing problem is solved using the supplemental variable technique, and the system’s performance metrics are obtained. From the calculated probability generation function of queue size at a random time for the different system states, we extract performance measures such as the server’s probability of idle time, the utilisation factor, the average queue length, and the average wait time. It is backed by methods for numerical portrayal, graphic representation, and real-world applications. This paradigm is entirely legal due to its practical use and algebraic demarcation mechanism. The graph provides precise readings of the implemented limitations.
  Keywords: non-Markovian queueing problem; batch arrival; supplementary variable technique; setup time stages; vacation; service interruption.
  DOI: 10.1504/IJMOR.2023.10060301
   
  
• Strong Perturbation Bounds for the Stationary Distribution of the Main Multiserver Retrial Queue Model  
  by Nabil Ait Yala, Badredine Issaadi, Karim Abbas 
  Abstract: Many queuing models are represented by Markov chains with infinite countable state space and we will often want to know their stationary distributions in order to deduce their characteristics, but the calculation of these distributions is generally difficult, if not impossible, and do not have closed form solutions because of the infinite number of equations to solve. This is why researchers try to obtain approximations that converge quickly to these distributions. Perturbation theory for Markov chains addresses the question of what impact can occur on a stationary distribution of a Markov chain if its transition matrix is slightly disturbed. In this paper, we use the strong stability approach based on the drift condition to establish analytic error bounds for the generalised truncation of a main multi-server retrial queue model. At the end of this article, we give numerical examples in order to show the quality of the error bounds obtained.
  Keywords: Markov chains; perturbation theory; truncation; strong stability; Lyapunov function; drift condition; retrial queueing systems.
  DOI: 10.1504/IJMOR.2023.10060302
   
  
• Solving the Vehicle Routing Problem with Search Algorithms: A Comparative Analysis  
  by Oladimeji Samuel Sowole  
  Abstract: The vehicle routing problem (VRP) is a well-known optimisation problem in operations research, with applications in logistics, transportation, and supply chain management. This paper offers a comparative analysis of search algorithms used to solve the VRP, focusing on their strengths and weaknesses. It introduces the VRP and its variants, highlighting the challenges and constraints involved. Various search algorithms, such as genetic algorithms, simulated annealing, and ant colony optimisation, are examined, discussing their principles, advantages, and limitations. Real-world case studies in package delivery, waste collection, and emergency response demonstrate the application of these algorithms. Factors influencing algorithm performance, including problem size, complexity, and parameters, are discussed. Recommendations for selecting appropriate search algorithms for different VRP instances are provided. The paper aims to provide readers with a comprehensive understanding of using search algorithms to solve the VRP, aiding decision-making in similar optimisation problems.
  Keywords: vehicle routing problem; VRP; search algorithms; metaheuristics; ant colony optimisation; ACO; particle swarm optimisation; PSO; genetic algorithms.
  DOI: 10.1504/IJMOR.2023.10060409
   
  
• Optimal joint dynamic pricing and inventory replenishment policy for perishable products with freshness-sensitive demand  
  by Mahmoud Dehghan Nayeri, Roghaye Haddad 
  Abstract: This paper aims to propose a mathematical model for joint pricing and inventory replenishment decisions of a retailer who faces a freshness-sensitive demand. The retailer has the option to submit fast replenishment orders with lower profit margins to other peer retailers within the short lifecycle of the perishable products in addition to the regular replenishment orders that take place at the start of the lifecycle. Also, the retailer can sell the end-of-season perished product at lower prices. The proposed model is capable of handling different types of demand and freshness functions. To show the applicability of the proposed model, it is used to optimise pricing, discounting, inventory, and replenishment decisions of two product categories of a major retailer in Iran using real-world data. Results indicate that the retailer should pursue a specific joint pricing and replenishment strategy in each product category. A sensitivity analysis is also performed for initial inventory and initial price for each of the categories. Results revealed that each of the factors contributes differently to the total profit in each category. The total profit showed a different level of sensitivity to changes in the two aforementioned tweaked parameters.
  Keywords: dynamic pricing; inventory management; perishable products; inventory replenishment.
  DOI: 10.1504/IJMOR.2023.10060510
   
  
• Analysis of Non-Markovian batch arrival retrial queue with priority services, Vacation and Vacation Interruption Under Random Environment, Negative Arrival, Immediate Feedback, Differentiate Breakdown, Repair  
  by Ayyappan G, NITHYA S 
  Abstract: In this study, we construct a single server retrial queueing system with two classes of customers, vacation and vacation interruption under random environment, negative arrival, immediate feedback, differentiate breakdown and repair. Customers can be divided into two distinct categories, such as priority and ordinary. This concept emphasises non-preemptive priority discipline. Customers arrive according to Poisson processes for priority and ordinary. The server constantly offers a single service for both priority and ordinary customers, and the service is distributed arbitrarily. In this study, we compute the Laplace transforms of the time-dependent probabilities of system states using the probability generating function and supplementary variable technique. Numerical results are obtained which are also examined to facilitate the sensitivity analysis of system descriptions.
  Keywords: Batch Arrivals; Priority Queues; Vacation and Vacation Interruption Under Random Environment; Negative Arrival; Immediate Feedback; Differentiate Breakdown; Repair.
  DOI: 10.1504/IJMOR.2023.10060515
   
  
• A Transient M[x]/M(k,k)/1 Queue with Reneging and Setup Time for Service  
  by Aliakbar Montazer Haghighi, Dimitar Mishev 
  Abstract: In this paper, we analyse a transient queuing model, in which tasks arrival in bulks of varying sizes with compound Poisson process, there is a single server serving batches of tasks with limited sizes with a minimum and a maximum, according with exponential distribution, with setup times for service with also exponential distribution, and impatient tasks that may renege while the server is busy with also exponential distribution. The transient probability generating function for the number in the system, special cases to verify it and some performance measures have been found.
  Keywords: transient queue; Markov process; Poisson; reneging; exponential service; setup time; probability generating function; moments.
  DOI: 10.1504/IJMOR.2023.10060539
   
  
• IOT-Botnet Attack Detection and Mitigation using Ensembled-Deep-Learning-Model  
  by Swapna Thota, D. Menaka 
  Abstract: In this study, we propose an ensembled deep learning model for robust IoT-botnet attack detection. The model comprises six phases: data preprocessing, data augmentation using SMOTE, feature extraction (central tendency, dispersion, and information gain), feature selection using the clan updated grasshopper optimisation algorithm (CUGOA), and attack detection. The detection model integrates DCNN, attention-based bi-LSTM, and optimised RNN, with fine-tuning using CUGOA. When an attack is detected, our new botnet traffic filter (BTF) mitigates it, enhancing network reliability. Our model outperforms existing approaches in terms of accuracy, sensitivity, specificity, and precision.
  Keywords: botnet; internet of things; deep learning cyber security; intrusion detection.
  DOI: 10.1504/IJMOR.2023.10060717
   
  
• An Inventory model with hybrid time-stock dependent demand for Seasonal products with trade credit policy  
  by Prokash Mondal, Sudhansu Khanra, Pritha Das 
  Abstract: This study examines an EOQ model with a hybrid time- and stock-dependent demand function for a seasonal product context of shortages. In several marketing strategies that have a strong connection to stock time and stock both play a crucial role in customer decision-making vendors always entice customers to buy more by displaying many products. This investigation aims to present the best inventory management technique for perishable products with hybrid demand that is time- and stock-dependent under partial backlog with a trade credit policy. The provided EOQ model is validated using a numerical illustration. Finally, sensitivity analysis has been employed to examine the effects of changes in the values of system factors using MATLAB software (Version 2014a).
  Keywords: inventory; time-stock dependent demand; partial backlogging; deterioration; trade credit policy.
  DOI: 10.1504/IJMOR.2023.10060978
   
  
• A study of transient solution of fractional M/M/2 queue with homogeneous and heterogeneous servers  
  by Nanduri Sujatha, GVSR Deekshitulu 
  Abstract: In queuing models with multiple servers, all the servers may not be completely active and may not work with same efficiency. Keeping this in view, a multiserver fractional queue with heterogeneous servers has been analysed in the present paper. Transient state probablities and also performance measures of the model such as average number of customers in the system, average number of customers in the queue, etc. have been computed. Variations in these performance measures have been observed both numerically and graphically with respect to partial activity of the server. Further, efficiency of transient M/M/2 fractional queueing model consisting of heterogeneous servers is compared with efficiency of transient M/M/2 fractional queuing model with homogeneous servers.
  Keywords: transient solution; fractional queue; Mittag-Leffler function; heterogeneous servers.
  DOI: 10.1504/IJMOR.2023.10061079
   
  
• Job Shop Scheduling in Wafer Fab with Random Job Arrivals using Hybrid Tabu Search  
  by Rosshairy Abdul Rahman, Kean Heong Lee, Syariza Abdul-Rahman, Azhar Mahdi Ibadi 
  Abstract: Job shop scheduling (JSS) plays an important role in the manufacturing sector to minimise makespan and avoid bottleneck situations. Wafer fabrication (Wafer Fab) is a costly and complex manufacturing system that demands several billion dollars investment with many repeated processes. Scheduling of Wafer Fab is vital to produce wafers and to achieve on-time delivery to customers. As such, this study proposes a hybrid tabu search model to solve JSS problem by minimising makespan while concurrently maximising the average machine utilisation. Initially, the concept of bin packing was deployed to obtain the initial solution using random greedy algorithm. Tabu search algorithm (TSA) was then employed to enhance solutions around the neighbourhood area. The findings successfully improved the schedule of jobs in Wafer Fab manufacturing, where the enhancement of 6.2% in makespan minimisation was achieved. Thus, it shows the ability to utilise the machines equally and avoid bottlenecks in Wafer Fab manufacturing.
  Keywords: job shop scheduling; JSS; random greedy bin packing; Wafer Fab; tabu search algorithm; TSA; makespan; manufacturing; tabu tenure size; metaheuristics.
  DOI: 10.1504/IJMOR.2023.10061422
   
  
• Optimizing inventory in business environments: Combining matrix analytic methods with a working vacation, cancellation policy, and working breakdown  
  by Ayyappan G, N. Arulmozhi 
  Abstract: The inventory system of the single-server Markovian arrival process with working vacations, working breakdowns under a Bernoulli schedule, and cancellation policy are discussed. The server begins to go on a working vacation when there is no customer in the system even if the inventory level is positive. If any customers arrive while he is end of his working vacation time, a normal busy period begins. If not, he will simply remain idle in regular mode. When a system breaks down, it either offers slowservice to the current customers with probability p or immediately undergoes a repair phase with probability q. We derive the invariant vector, busy period, waiting time distribution, total cost, and computation of performance measures using the matrix analytic technique.
  Keywords: Markovian Arrival Process; Phase-type service; (s,Q) policy; Working vacation; Working breakdown; Cancellation policy.
  DOI: 10.1504/IJMOR.2023.10061482
   
  
• Analysis of MAP/PH/1 Retrial Inventory Queueing System with Phase type Vacation and Unreliable Server  
  by Ayyappan G, MEENA S 
  Abstract: In this study, a retrial queueing inventory system with a fixed retrial rate, single vacation, breakdown, and repair is investigated. We have made the assumption that customers arrive through a Markovian arrival process and that the server will offer phase-type services to them. The (s, S) policy is used to replenish the inventory, and it is anticipated that the replenishing time will follow an exponential distribution. The server goes on vacation if there are no consumers in the orbit, or zero inventory, or both. When a server breaks down, it quickly starts the repair process, and the customer enters the infinite size of the orbit. In the steady state, it is possible to determine the number of customers in the orbit, the inventory level, and the status of the servers. The cost analysis is derived, and several significant performance measurements are established. Furthermore, a few numerical demonstrations are given to clarify our mathematical model.
  Keywords: Queueing-inventory; Markovian Arrival Process; Phase-type distribution;(s; S)-type policy; Retrial; Single Vacation; Breakdown and Repair; Matrix Analytic Method.
  DOI: 10.1504/IJMOR.2023.10061611
   
  
• On Efficient Solutions to Bi-objective Max-Linear Programming Problems  
  by Abdulhadi Aminu, Sunday Olowo, Salusi Usaini 
  Abstract: A number of methods for determining solutions to max-linear programming problem with one objective function have been developed. In this work, we introduce the concept of bi-objective max-linear programming problem subject to two sided constraints (BOMLP) for both minimisation and maximisation cases, then we proposed two methods for determining efficient solutions to the problem and developed improved algorithms based an alternating and bisecting method of solving two sided max-linear system. Performance of the methods were compared based on effectiveness, user friendly and task time, in fact the second method is found to be faster than the first method, some numerical examples were considered to test the problems and using MATLAB software .
  Keywords: bi-objective max-linear programming; two-sided system; optimal solution; efficient solution; pseudo-polynomial algorithms.
  DOI: 10.1504/IJMOR.2023.10061663
   
  
• An Enhancing IOT Security with a Trinary Deep Learning Paradigm and Squirrel Reptilian Optimisation  
  by K. Navaz, Muthuvairavan Pillai.N, G. Shanmugasundaram, T.Rajesh Kumar, C. Jehan 
  Abstract: This research work proposes a novel approach for IoT intrusion detection using a trinary deep learning paradigm. The proposed model aims to address the challenges of large data requirements and false positives commonly encountered in IoT network security. The model consists of four phases: pre-processing, multi-modal feature extraction, optimal feature selection, and intrusion detection. Initially, the collected raw data is pre-processed using data cleaning techniques and Z-score normalisation, which helps to standardise the data for further analysis. Following pre-processing, multi-modal feature extraction techniques are applied, including measures of central tendency, database features, statistical dispersion, and information entropy-based features. To select the most relevant features from the extracted set, the squirrel reptilian optimisation algorithm is employed. SRO combines the squirrel search algorithm and reptile search algorithm to optimise feature selection, ensuring that only the most informative features are utilised for intrusion detection.
  Keywords: IoT; intrusion detection; multi-modal feature extraction; squirrel reptilian optimisation algorithm; SRO; trinary-deep-learning-paradigm; CNN; RBFN; RBM.
  DOI: 10.1504/IJMOR.2023.10061665
   
  
• A Markovian two server queue with state dependent hybrid service discipline  
  by Kalyanaraman R, B. Anurathi 
  Abstract: A Markovian two server model is constructed by assuming a new concept. The concept is that upto the service of N customers, the two servers acts as homogeneous servers after which the servers acts like heterogeneous servers. In practice, in particular, if the servers are human beings, they cannot serve in the same spirit till the end of the busy period.~These practical situations leads to study of queues with heterogeneous servers.~This model is analyzed in steady state by deriving the difference equations and applying the recrussive concept for solution.~For this model the waiting time distribution and some system performance measures are obtained, particular cases are derived.~The practical applicability of the model is tested by presenting some numerical illustrations. A cost model is developed by defining the total expected cost function and also sensitivity analysis is carried out to investigate the effect of system parameters on the expected cost function.
  Keywords: two server queue; homogeneous server; heterogeneous server; performance measures.
  DOI: 10.1504/IJMOR.2023.10061666
   
  
• A Healthcare Divisions Inventory Model for Deteriorating Items with a Variable Deterioration Rate Under Permissible Delay in Payments  
  by Mukesh Kumar, Manoj Kumar Sharma, Ajay Sharma, Shalu Chaudhary 
  Abstract: The deterioration of medicines is an extensive trend in the healthcare sector. There are a lot of medicines and pharmaceutical products, such as generic injectables, caplets, ophthalmic liquids, ointments, tablets, etc., that have short expirations; therefore, there is a requirement to develop methods to use them within their expiration time. Most of the public health system encounters this problem frequently occurs. To solve this problem, the authors developed an inventory model based on four features of the healthcare sector: time-dependent demand rate, holding cost, deterioration rate, partially backlogged shortages in demand, and credit period offered by pharmaceuticals. We also considered the time duration, which is free from interest on credit, and the rate of interest. However, the hospitals have the reserve money to make the payments at the beginning, but they decide to take advantage of the credit period. We validated this model by using a numerical example and explaining the sensitivity analysis.
  Keywords: inventory; demand; pharmaceutical products; deterioration and permissible delay payments.
  DOI: 10.1504/IJMOR.2023.10062077
   
  
• A Genetic algorithm combined with mathematical programming to solve Generalised Quadratic Multiple Knapsack Problem  
  by Yassine Adouani 
  Abstract: In this paper, the generalised quadratic multiple knapsack problem (GQMKP) is tackled with an efficient hybrid approach, called GA&IP, which combines a binary genetic algorithm (GA) with integer programming (IP) to solve the GQMKP problem. In the GA&IP approach, a linearisation technique is used to transform the GQMKP into a linear problem called LGQMKP. After that, the LGQMKP is transformed into several dependent classical knapsack problems using a GA. Finally, an IP algorithm is applied to optimally solve each knapsack problem. The effectiveness of the GA&IP approach is demonstrated through experimentation on 96 diverse benchmark instances that are commonly used in the field. Experimental results show the effectiveness of the proposed GA&IP in solving the GQMKP problem and the hybridisation with integer programming can enhance the genetic algorithm.
  Keywords: generalised quadratic knapsack problem; genetic algorithm; integer programming.
  DOI: 10.1504/IJMOR.2023.10062398
   
  
• Analysis of Markovian Queuing Model with Two Phase of Services, Single and Multiple Working Vacations and Customer Balking  
  by K. Baby Saroja, V. Suvitha 
  Abstract: We analyse a single server balking queueing model with featuring two phases of service in series. During the first phase, customers receive individual service, and in the second phase, they have the option to choose between two distinct services based on their specific needs and receive batch service. To optimise resource utilisation, the server enters a working vacation when there is no customer in the system. We apply the Probability Generating Method to comprehensively analsze the system, considering both single and multiple working vacations. This research underscores the application's adaptability in addressing intricate data processing challenges within the queuing framework. Furthermore, we provide numerical results to demonstrate how the model performs under various conditions.
  Keywords: Two Phases in Series; Working Vacation; Balking; Batch Service.
  DOI: 10.1504/IJMOR.2023.10062491
   
  
• Enhancing Reliability and Performance of Sequential Chiller System using Copula  
  by Ameer Hassan Abdullahi, Abdulhadi Aminu, Ibrahim Yusuf 
  Abstract: Chiller systems play a pivotal role across various industries, providing essential cooling solutions. Ensuring their efficiency and reliability necessitates precise performance evaluation. The Gumbel-Hougaard family copula, an efficient approach for modelling multivariate dependencies, is used in this paper to carry out an in-depth examination of chiller machine systems. Through this method, we can capture intricate correlations between chiller system characteristics and performance metrics such as reliability, availability, mean time to failure (MTTF), cost and MTTF sensitivity. We further conducted sensitivity analysis using our copula-based model to identify key factors influencing chiller system performance. The efficacy of the copula-based approach in capturing intricate relationships between several chiller system features and critical performance measures is exemplified by numerical findings that are displayed in tables and graphs. We can make conclusions about the results since they have been validated using quantitative data and can be seen in tables and graphs. This deeper understanding will assist us in optimising system operations for improved cost-effectiveness and energy efficiency. Additionally, our copula-based approach enhances performance evaluation compared to traditional methods by allowing us to assess the system's resilience under varying operational conditions.
  Keywords: availability; efficiency; chiller systems; series-parallel system; transition diagram.
  DOI: 10.1504/IJMOR.2023.10062578
   
  
• Balancing Sustainability and Profitability in Inventory Management: Insights into Carbon Emissions, Consumer Demands, Payment Strategies, and Green Investments  
  by Manoj Kumar Sharma, Neha Rani, Anshika Rajpal 
  Abstract: Optimising inventory management practices is paramount in a world increasingly concerned with environmental stewardship. The present study focuses on four main aspects: 1) reducing carbon emissions; 2) responsiveness to price and freshness-dependent consumer demands; 3) evaluation of payment schemes; 4) assessment of investments in preservation and green technologies. By addressing these fundamental components of inventory management, the article offers valuable insights and practical recommendations for businesses striving to align their operations with sustainability goals. Achieving sustainability in inventory management contributes to environmental conservation and enhances competitiveness and long-term profitability. Payment methods wield significant influence in inventory management, impacting cash flow, supplier relations, and sustainability efforts. They serve as tools for sustainability, highlighting the trade-off between cash flow and environmental stewardship. Finally, a few computational instances and sensitivity analyses demonstrate the suggested model's features. The results and sensitivity analysis show that controllable carbon emissions favourably impact overall inventory model profit.
  Keywords: inventory management; carbon emissions; price and freshness dependent demand; comparison of payment scheme; preservation technology investment; green technology investment.
  DOI: 10.1504/IJMOR.2023.10062609
   
  
• Enhanced non-dominated sorting genetic algorithms for fuzzy multi-objective multi-route shortest path problem  
  by Aniket Todkar, Jayesh Dhodiya 
  Abstract: This study examines a fuzzy multi-objective multi-route short path problem (FMOMRSPP) by transforming it into a crisp multi-objective multi-route shortest path problem (MOMRSPP) using possibility distribution. Using -level sets, fuzzy judgement is categorised for the decision maker (DM) to optimise fuzzy objective function scenarios. This paper proposes aspiration level (AL)-based non-dominated sorting genetic algorithm (NSGA)-II and AL-based NSGA-III to obtain a Pareto-optimal solution that meets DM AL for the FMOMRSPP. A numerical example has been provided to demonstrate the usage of the presented methodologies. A comparison is presented between the proposed and several other approaches. The sensitivity of objective functions is also investigated with ALs and shape parameters. The coverage is determined to evaluate the effectiveness of the proposed methods.
  Keywords: multi-objective multi-route shortest path problem; MOMRSPP; NSGA-II; NSGA-III; aspiration level.
  DOI: 10.1504/IJMOR.2023.10062616
   
  
• Manufacturing supply chain with considering carbon cap policy and revenue from deteriorated items  
  by Santosh Shekhawat, Kalpna Sharma 
  Abstract: In presenting paper, a deteriorating nature inventories manufacturing supply chain studied. It is assumed that deteriorated and rejected inventories, instead of throwing out can be utilised to generate revenues which helps to increase profit, reduce carbon emissions, and solve the problem of disposal of deteriorated inventories. Price is an important factor that plays a decisive role for deteriorating nature inventories supply chain. The objective of the work is to establish a optimise profit model with some certain conditions. To authenticate the mathematical model a numerical example is considered. This work focused on utilise deteriorated inventories and reduce carbon emission. The use of deteriorated inventories at initial level of decay increases revenues, promote the balance utilisation of resources and decrease emission. This work is beneficial for manufacturers dealing with deteriorating inventories by providing mathematical design for deteriorated inventories utilisation, emission reduction emission and increase revenue.
  Keywords: deteriorating inventory; carbon emission; selling price-dependent demand; carbon cap.
  DOI: 10.1504/IJMOR.2024.10062716
   
  
• An adaptive hybrid direction algorithm for convex box-QP problems with enhanced pre-solving  
  by Abdelhek Laouar, Mohand Ouamer Bibi 
  Abstract: In this paper, we propose a new algorithm for solving quadratic programming problem with box constraints. The principle of the algorithm is to apply a preprocessing procedure to reduce the original problem. Then the resulting reduced problem will be solved by applying the adaptive method with a hybrid direction. A post-processing step (post-solving) is necessary to deduce the optimal solution of the original problem. In order to test the algorithm of the proposed method and to make sure of its effectiveness, a comparative study of the proposed method is made with active-set quadprog algorithm, the interior-point-convex quadprog algorithm of the MATLAB optimisation toolbox and the modified proportioning with reduced gradient projections algorithm (MPRGP). The obtained results show that the proposed algorithm presents good performances, it always performs better than the active set method and appears to be very competitive with the interior point method and the MPRGP algorithm, mainly for the problems having 'bi' sufficiently large with many active variables at the optimal solution and for problems where A is generalised diagonally dominant. In these cases, the optimal solution is obtained only by the pre-solving procedure.
  Keywords: Quadratic programming; Box constraints; Pre-solving; Adaptive method; Hybrid direction.
  DOI: 10.1504/IJMOR.2023.10062725
   
  
• Graphical Neural Network-Based MCDM for Evaluating Sustainable City Logistics Measures  
  by K. Vasantha Lakshmi, Udaya Kumara K. N 
  Abstract: This paper presents a novel approach to evaluate sustainable city logistics measures using a multi-criteria decision-making (MCDM) framework based on qualitative data. The proposed approach combines different weighing methods such as fuzzy DEMATEL, fuzzy AHP, to determine the weights of the criteria. The criteria are based on economic, environmental, social, and technical aspects, such as operational costs, energy consumption, revenues, air pollution, noise, land use, congestion, accidents, mobility, accessibility, freeing of public space, logistical efficiency, trip effectiveness, loading factor of vehicles, service quality, and customer coverage. The study also proposes a graphical neural network (GNN) with weighted MCDM for artificial intelligence-based decision-making, which helps in achieving a better selection of city logistics measures for urban freight logistics. The approach is implemented in MATLAB and compared with other deep learning models such as CNN, ANN, and DNN, showing higher performance. Furthermore, the paper presents an extrapolation-enhanced approach for modelling travel decision-making based on MCDM with GNN and error calculation, which provides higher performance. The results demonstrate the effectiveness of the proposed approach in selecting sustainable city logistics measures, which can contribute to improving urban freight logistics.
  Keywords: sustainable city logistics; social factors; multiple stakeholders; fuzzy logic methodology; normalised matrix; Pairwise similarity matrix; multi-criteria decision-making; MCDM.
  DOI: 10.1504/IJMOR.2023.10062726
   
  
• A sustainable demand disruption recovery model considering non-zero lead time and advance payment policy during any emergency like COVID-19 pandemic  
  by Dolagobinda Das, Gauranga Samanta 
  Abstract: This study considers three time frames (i.e., before lock-down, during lock-down, and after lock-down) and takes three distinct time-dependent demands that are effective for three time frames. Before lock-down, we use a linear time-dependent demand function; during lock-down, we use a demand function that suddenly drops close to zero due to lock-down restrictions; after a period of time, demand slowly increases to meet customers basic needs, and after the government relaxes lock-down restrictions, demand abruptly increases due to customers panic buying and overstocking nature. Subsequently, non-instantaneous deterioration rate is considered. Due to a significant rise in demand after lock-down, this research permits a shortage that is partially backlogged along with a non-zero lead time and also considers the advance payment policy to reduce the order cancellation rate. Also, green technology is implemented to reduce carbon emissions. Finally, sensitivity experiments are conducted on a few examples to validate the model.
  Keywords: demand disruption; deterioration; advance payment; COVID-19 lock-down; green inventory model; carbon emission.
  DOI: 10.1504/IJMOR.2024.10062828
   
  
• Reliability Measures of Repairable k-out-of-n System using Weighted Exponential-Lindley Distribution  
  by Sunita Sharma, Vinod Kumar, S.B. Singh 
  Abstract: This study focuses on the analysis of a k-out-of-n: F repairable system employing a novel lifetime distribution termed the weighted exponential-Lindley distribution (WXLD). The system under investigation assumes constant failure rates, while repair times follow the newly proposed WXLD. The repair process involves two personnel: a trainee for minor repairs and an expert for major repairs. Leveraging the supplementary variable technique and Laplace transformation, we derive key reliability measures for the system, including reliability, availability, expected profit, and sensitivity. To exemplify and validate the generalised results, the research employs a communication system as a practical application.
  Keywords: k-out-of-n: F system; weighted exponential-Lindley distribution; WXLD; supplementary variable technique; SVT; reliability; availability; expected profit; sensitivity; Laplace transformation; LT.
  DOI: 10.1504/IJMOR.2023.10062924
   
  
• A new approach for counting patterns in language theory, matchings, and set partitions.  
  by Fatima Hessas, Mouloud Goubi, Noria Benkhemmou 
  Abstract: The notion of pattern is widely studied in the literature. We focus our attention on patterns appearing in language theory, matchings, and set partitions. We start with some main tools of algebraic generating functions of sequences of numbers. We explain how the Bell, Fibonacci and generalised Fibonacci numbers can be used in the theory of patterns. In particular, we are interested in words containing patterns that are related to arbitrary length so as to provide enumeration formulae, and extract satisfying recurrence relations. Moreover, we revisit the work of Bloom and Elizalde concerning pattern avoidance in matchings and partitions in order to fulfil it with some enumeration formulae.
  Keywords: Language theory; patterns; generating functions; matchings; set partitions.
  DOI: 10.1504/IJMOR.2024.10062970
   
  
• Construction of distance measure for fermatean fuzzy sets and its application in educational assessment and medical diagnosis  
  by Dibakar Dutta, Palash Dutta, Brindaban Gohain 
  Abstract: Fermatean fuzzy sets (FFSs), an updated, expanded version of intuitionistic fuzzy sets (IFSs), are effective tools for expressing uncertainty and ambiguity in complicated issues. The distance measure is a crucial tool for illustrating the differences between two FFSs while dealing with Fermatean fuzzy information. It is currently unclear how to precisely calculate the distinction between two FFSs. We provide a novel distance measurement method for FFSs in this study. Then, we show that the chosen distance measurement method satisfies the distance functions axiomatic requirements. The presented distance measure is then evidenced with numerical examples to show that it is more accurate and reasonable than the Mizumoto(I) distance measure, Robert(I) distance measure, Robert(II) distance measure, Mizumoto(II) distance measure, Hellinger distance, Euclidean distance (ED) measure and triangle divergence distance measure, which is capable of overcoming the counter-intuitive circumstance. In addition, we successfully use the proposed distance measure approach to handle pattern recognition difficulties, educational assessment issues, and medical diagnosis issues in a fuzzy Fermatean environment. The experimental findings show how effectively the suggested distance measure method can handle real-world applications in a fuzzy Fermatean environment.
  Keywords: Fermatean fuzzy set; FFS; distance measure; educational assessment; medical diagnosis.
  DOI: 10.1504/IJMOR.2023.10062972
   
  
• Lexicographic multi-objective geometric programming problems with pentagonal fuzzy parameters using robust method  
  by Sudipta Mishra, Rashmi Ranjan Ota 
  Abstract: Fuzzy logic is the most useful method for simulating complex real-world problems. In the process of creating models and coming up with solutions, it integrates ambivalent information. This paper outlines the process for resolving lexicographic multi-objective geometric programming problems with fuzzy parameters. Geometric programming has been utilized as a solution technique for a specific solution to difficult non-linear problems for over 60 years. After the introduction of the pentagonal fuzzy parameters as the coefficients, the study utilizes the robust method to defuzzify the programming problems. Finally, the solution is reached using the geometric programming technique. Two numerical examples have been given to illustrate our proposed methodology.
  Keywords: geometric programming; multi-objective; lexicographic method; pentagonal fuzzy parameters; robust method.
  DOI: 10.1504/IJMOR.2023.10062978
   
  
• Self-Adjusting Formulae for the Solution of Fuzzy Differential Equations with Triangular Fuzzy Numbers  
  by Joshua Sunday, Joel Nimyel Ndam, Anthony Chukwuemeka Onyekonwu 
  Abstract: It is a known fact that in modelling real world phenomena, differential equations are indispensable. Uncertainty, unfortunately intervene with such real world problems. The uncertainty may arise from measurement error, determining initial/boundary conditions or even deficient data. Modelling these problems in the form of fuzzy differential equations (FDEs) helps in addressing such setbacks. This research focuses on deriving self-adjusting formulae (SAF) through the variable stepsize strategy for the solution of FDEs with triangular fuzzy numbers. The SAF, which is in the form of implicit block backward differentiation formulae (BBDF) was derived in such a way that it automatically adjusts the stepsize to fit the FDE under consideration. The BBDFs have been known for their unbounded region of absolute stability, thus making them suitable for solving FDEs. The results obtained showed that the SAF is computationally efficient, robust and reliable.
  Keywords: backward differentiation formulae; convergence; fuzzy differential equation; FDE; H-difference; Hukuhara derivative; interval differential equations; mathematical models.
  DOI: 10.1504/IJMOR.2023.10063110
   
  
• On Phase Inventory Model for (Non)Co-Operative Games  
  by Sujit Kumar De, Mrinmoyee Das 
  Abstract: This article develops an economic order quantity (EOQ) inventory model with infinite exhaustive cycle time. In this study the supply chain itself is viewed as the flow of current in the well-known L-C-R circuit of the physics discipline. We have shown that, those items which are not sold for an infinite time duration can easily be managed with the help of (non)cooperative games of the management followed by strategy of Nash-equilibrium solution. A schematic diagram of (non)cooperative game and a novel algorithm has also been presented to justify the new approach. However, our findings reveals that the arithmetic-geometric mean for the cases of non-cooperative games approach might be more beneficial of the decision maker than any other existing methods rather than cooperative games. Finally, numerical experimentation, sensitivity analysis and graphical illustrations are done to validate the model.
  Keywords: EOQ model; phase inventory; (non)cooperative game; Nash equilibrium; optimisation.
  DOI: 10.1504/IJMOR.2024.10063161
   
  
• Non-linear fuzzy programming - a case study  
  by Arpita Kabiraj, Swapan Raha, Prasun Kumar Nayak 
  Abstract: In this article, we would like to attempt finding a convergent near optimal solution of a fuzzy non-linear programming problem (FNLPP) in which the objective as well as the constraints defining the relationship between variables are so imprecisely stated that it is practically impossible to represent by any existing crisp model. The primary aim of this research is to provide more flexibility to the decision-maker. Accordingly, to solve such a FNLPP, we use approximate reasoning which involves three stages: fuzzification, aggregation and defuzzification. The process is repeated till a convergent near optimal solution is attained. An algorithm is designed for the implementation of the proposal. Artificial examples have been considered to illustrate our approach and existing results are used for comparison. Finally, a case study is undertaken to demonstrate the effectiveness of our proposal.
  Keywords: Fuzzy non-linear programming problem (FNLPP); fuzzification; aggregation; defuzzification.
  DOI: 10.1504/IJMOR.2024.10063164
   
  
• Dynamic service management and priority handling in dual server queuing systems with breakdowns  
  by Ayyappan G, Sankeetha S 
  Abstract: This paper examines a dual-server system comprising server 1 and server 2, each with its dedicated queue (queue 1 and queue 2). Queue 1, with lower priority, can handle an unlimited number of tasks, while queue 2, with higher priority, has a maximum capacity of N tasks. Task arrivals follow a Markovian process, and their service times adhere to a phase-type distribution. In the event of server's breakdown, server 1 seamlessly takes over, minimising service disruptions. To address customer dissatisfaction, server 1 provides prompt feedback during these transitions. The study employs the quasi-birth-death (QBD) process, utilising matrix analytic methods with finite-dimensional block matrices to analyse steady-state behaviour. Performance metrics like busy periods, costs, and other relevant measures are assessed, yielding insights into system efficiency. Numerical computations and graphical representations showcase the system's performance across various scenarios, providing a comprehensive understanding of its operation.
  Keywords: Markovian arrival process; phase type service; vacation; priority queues; breakdown; repair.
  DOI: 10.1504/IJMOR.2024.10063513
   
  
• Investigation on inventory replenishment policy for a queueing system with catastrophic failure, negative arrival and discouraged customers  
  by Ayyappan G, N. Arulmozhi 
  Abstract: The single queues of inventory systems (IS) with warehouse catastrophes and negative arrivals (NA) occur in the service area were examined in this work. Arriving positive customers (P C) can queue up infinitely to make purchases. Customers in the system are still waiting for stock replenishment after catastrophes even when all of the system's commodities are destroyed. The positive customer that is now getting service from the server is disrupted and removed as a result of the negative arrival. The server is instantly impacted by the breakdown as a result of the negative customer's arrival. After examining queueing inventory system's stability conditions, busy period, and the transition probability vector was calculated using the matrix-analytic method. The results of numerical assessments have been presented together with formulas for performance measures.
  Keywords: Markovian arrival process; MAP; phase-type service; negative arrival; catastrophic failure; (s; S) and (s; Q) policies; repair.
  DOI: 10.1504/IJMOR.2024.10063626
   
  
• An Inventory System for Imperfect Products with the Effect of Carbon Emissions and with Free Transportation on a Prepaid Basis  
  by Sandeep Kumar, Robin Singh, Manoj Kumar, Mukesh Kumar, Prachi Fartyal 
  Abstract: The EPQ model is a mathematical model used for inventory management in shop floor systems. However, it assumes manufacturers pay upfront costs and may have low-grade items. The classical inventory model assumes no imperfect items are manufactured, but the production process may shift from controlled to uncontrolled states due to various causes. To make the current study more realistic, we represent a model with imperfect production that accounts for random carbon emissions under continuous prepayment. We also assumed that the production process was imperfect, so we got some defective items, and out of these, some were reworked. Further, it is assumed that the producer provides free shipping to the retailers on a prepaid basis. The concept of carbon emissions is related to transportation and production decisions. Due to environment-saving rules, a tax on carbon emissions is required to be paid by the manufacturer. The model is validated using a numerical example and sensitivity analysis.
  Keywords: inventory; carbon emission; imperfect products; transportation cost; prepayment.
  DOI: 10.1504/IJMOR.2024.10063627
   
  
• Solving Mixed Integer Linear Programming Problems with bounded variables by the Adaptive Method  
  by Houria Boussouira, Mohand Ouamer Bibi 
  Abstract: Unlike linear programming problems, mixed integer programming problems are very difficult to solve. In this paper, we elaborate a new cut for Mixed Integer Linear Programming (MIP) with upper and lower bounded variables. The obtained problems are solved by the adaptive method developed by Gabasov (1980) for solving linear programming problems. This algorithm allows solving directly the considered problem, without modifying it and avoids the drawbacks of the increase in the number of the variables and the constraints. In order to compare our method with the intlinprog method of the Matlab optimisation toolbox, numerical experiments on randomly generated test problems are presented, that involve the CPU time.
  Keywords: Mixed Integer Linear Programming; Generating Valid Inequalities; Adaptive Method.
  DOI: 10.1504/IJMOR.2024.10063628
   
  
• Towards Sustainable Two Warehouse Inventory Management: Flexible Payments and Demand-Driven Optimisation with Preservation Technology and Carbon Emission Considerations  
  by Neha Rani, Manoj Kumar Sharma 
  Abstract: This study explores the transformative impact of conservation and eco-friendly technologies on two warehouse inventory, aiming to prevent product degradation and substantially reduce carbon emissions in greenhouse operations. The research underscores the urgent need for government-led carbon emission laws to address environmental and economic repercussions. With a focus on the proposed model, two key contributions emerge: 1) strategic investments in eco-friendly technologies and conservation methods for minimising carbon emissions and product degradation; 2) the application of preservation technology to curtail product deterioration. The comprehensive model integrates factors such as demand dynamics, pricing, stock, expiry dates, payment delays, and inflation, seeking optimal order quantities, cycle durations, and selling prices for profit maximisation. Validated and exemplified quantitatively, the model's efficacy is demonstrated, complemented by a thorough sensitivity analysis. This research not only advances inventory management practices but also advocates for environmentally sustainable strategies with direct financial implications.
  Keywords: two warehouses inventory; price-stock and lifetime dependent demand; inflation; preservation technology; carbon emission.
  DOI: 10.1504/IJMOR.2024.10063711
   
  
• A Two-Tier Sustainable Supply Chain Model with the Influence of Carbon Release under a Fuzzy Environment  
  by Varuna Bhardwaj, Sunil Kumar, Vipin Kumar Tyagi 
  Abstract: Environmental sustainability is a worldwide issue in the present-day business management environment, and scholars have been concentrating broadly on this subject. It is difficult to run an organisation efficiently while ensuring the environment, and lots of companies have understood that they have to prioritise production with minimum waste and carbon emissions. Government measures to promote sustainability have also led corporations to emphasise minimising their carbon footprints across the supply chain by utilising green supply chain strategies. Green inventories contribute significantly to system design by minimising unfavourable environmental effects while enhancing positive economic and social consequences. In the course of production, keeping inventory, depreciation, shipping, and scrap management, the investigation evaluates concerns related to carbon emissions in both developer and vendor channels. In order to reduce total average expenses, a crisp model has been developed. Using the signed distance approach, the total average expenditure is defuzzified and proven to be convex with a unique approach. Both crisp and fuzzy scenarios undergo numerical analysis. Sensitivity analysis and visual representations are used to demonstrate how innovative the suggested technique is.
  Keywords: sustainable; degradation; carbon emission; developer; vendor.
  DOI: 10.1504/IJMOR.2024.10063847
   
  
• Analysis of Batch Arrival Bulk Service Priority Queue with Multiple vacation, Close down, Set up, Differentiate Breakdown and Repair  
  by Ayyappan G, NITHYA S 
  Abstract: The steady state analysis of a single server non-preemptive priority queueing system under Multiple vacation, Close down, Set up, Differentiate breakdown, Repair. Priority and ordinary customers arrive according to Poisson processes, and their service time based on the general distribution. The server constantly offers a single service for priority and bulk service for ordinary customers. Ordinary customers will only be served if the batch size is more than a or less than or equal to b. We compute the Laplace transforms of the time-dependent probabilities of system states using the probability generating function and supplementary variable technique. Numerical results are obtained which are also examined to facilitate the sensitivity analysis of system descriptions.
  Keywords: Bulk service; Priority queues; Batch arrivals; Differentiate Breakdown; Multiple Vacation; Closedown; Setup.
  DOI: 10.1504/IJMOR.2024.10063854
   
  
• A Sustainable Production Model for Industry 4.0 with Fuzzy Optimization Approach  
  by Manisha Pant, Neelanjana Rajput, Seema Sharma, Anand Chauhan 
  Abstract: A clean and sustainable environment has become a primary goal for any organisation. Industrial Revolution 4.0 and sustainable development are two new technological and organisational patterns that are impacted by improving efficiency and ensuring long-term sustainability. The aim of this work is to make a sustainable supply chain smarter for which an autonomation inspection policy has been considered to reduce human mistakes. The demand rate for the retailer depends on marketing parameters that have been considered here. This study also explores a production system that switches from an in-control to an out-of-control state at random. There are uncertainties in some parameters of the system, the triangular intuitionistic fuzzy number has been used and the signed distance defuzzification method is applied to get the final total inventory cost in fuzzy environment. The proposed model is validated by using numerical illustration and sensitivity analysis of the relevant parameters has been provided.
  Keywords: optimisation; supply chain management; Industry 4.0; autonomation inspection policy; imperfect production; intuitionistic fuzzy number; defuzzification.
  DOI: 10.1504/IJMOR.2024.10064014
   
  
• The New Odd Burr III -G power series class of distributions: properties and applications to censored and uncensored data  
  by Wilbert Nkomo, Broderick Oluyede, Fastel Chipepa 
  Abstract: The odd Burr III-G power series (OBIII-GPS) class of distributions (CoDs) and its subclass, the odd Burr III-Weibull power series (OBIII-WPS), are the new distributions presented in this article. The statistical properties of the newly developed CoDs were derived. These encompass, the hazard rate function, quantile function, moments, order statistics, and Renyi entropy. Five different estimation methods are presented for estimating the unknown model parameters. The evaluation criteria used to assess the performance of these estimation techniques in a Monte Carlo simulation framework were the root mean square error and average bias. Two data examples, including a censored dataset were used to demonstrate the viability of the suggested paradigm.
  Keywords: censoring; generalised distribution; moments; odd Burr III-G; parameter estimation; power series distribution; Weibull distribution.
  DOI: 10.1504/IJMOR.2024.10064016
   
  
• Exploring Sustainable Inventory Control Models from 2011 to 2023: A Comprehensive Review  
  by Manoj Kumar Sharma, Neha Rani, Kanika ., Khushi Saini 
  Abstract: In recent years, the growing focus on sustainability has prompted the incorporation of external logistics costs into the EOQ model. The increasing importance of sustainable inventory management is becoming more evident in the current business environment. Companies widely acknowledge that adopting sustainable practices is imperative to achieve multiple objectives, including cost reduction, waste minimisation, and long-term viability assurance. Reducing the carbon emissions caused by inventory processes is paramount in this field. Because lowering one's carbon footprint is just as crucial as lowering one's traditional inventory expenses, this research dives into how these two concepts might be integrated into sustainable inventory management. This review provides a current and comprehensive overview of sustainable inventory models while concurrently encompassing the critical themes in publications spanning from January 2011 to February 2023 within the realm of carbon emissions.
  Keywords: sustainability; sustainable inventory management; SIM; carbon emission; optimisation.
  DOI: 10.1504/IJMOR.2024.10064134
   
  
• Optimising Communication and Performance in IoT with RabbitMQ: A Bulk Arrival Single Server Retrial Queueing Model with Multi-Phase Service  
  by Vivesini D, Ebenesar Anna Bagyam J, Poongodi T 
  Abstract: RabbitMQ is an advanced messaging technology in which the communication layer interfaces with a message broker and a message queue. This system has opted for a specific message queue, enabling asynchronous communication by implementing message-oriented middleware. This approach encourages applications to be loosely connected, potentially enhancing system performance and optimizing resource utilisation. In this study, RabbitMQ serves as an intermediary for sending and receiving user messages. Queueing models can be employed to determine the necessary resources for providing high-quality service. For RabbitMQ (IoT) based on the computing system, we propose a bulk arrival single server retrial queueing model with a mandatory multi-phase second service phase for theoretical modelling. We solve steady-state equations and derive various performance metrics. Subsequently, we develop a cost model. To compute the total expected cost of the service rate, we utilise the Particle Swarm Optimization algorithm. Finally, we perform a numerical analysis on our model to gain insights into its behaviour.
  Keywords: Cloud computing; Bulk arrival; Retrial queue; Two phase Service; Rabbit MQ; Particle swarm optimization.
  DOI: 10.1504/IJMOR.2024.10064149
   
  
• Dynamic Terminology for Supplier-Retailer Collaboration Metrics in Inventory Model  
  by Atma Nand, Waqar Younus 
  Abstract: The proposed models consider factors like product deterioration, shortage, backordering, and various costs associated with inventory management. The research compares the outcomes of the decentralised system, where the retailer determines replenishment cycles, with the centralised system, where the supplier dictates the cycles. Different algorithms are employed to find the optimal schedule for both retailer and supplier. The study also formulates optimality conditions for minimising the total cost functions for both retailer and supplier. The retailer uses the Hessian matrix as a tool to make sure that the function describing the total costs is positive definite. The research concludes with an analysis of the suggested optimal total costs for the retailer under different replenishment cycle scenarios.
  Keywords: Dynamic Inventory; Fuzzy Inventory; Supplier-Retailer Collaboration; Defuzzification; Optimality Conditions; Inventory Management.
  DOI: 10.1504/IJMOR.2024.10064476
   
  
• An Attempt on Neutrosophic Multi Attribute Decision Making based on Generalised Signed Distance Method  
  by Manas Karak, Tuhin Bera, Mahendra Rong, N.K. Mahapatra 
  Abstract: Decision making in todays uncertain scenario is a most challenging task to the experts. To assist the decision makers, this study deals with a ranking of neutrosophic number based on generalised signed distance method. Some important definitions like level-1 neutrosophic points and level (, , )-neutrosophic intervals are drawn initially. Then a number of properties and theorems on ranking of neutrosophic numbers are developed here. Finally, to establish our theoretical idea on ranking, we consider a real life multi-attribute decision-making problem and find the desired result. After that we make some comparative study of our model with some existing decision-making models.
  Keywords: Neutrosophic number and its ranking; neutrosophic points; neutrosophic intervals; signed distance method.
  DOI: 10.1504/IJMOR.2023.10064900
   
  
• The Strategic Value of Seller's Option in Buyback Guarantee Financing  
  by Yang Huang, Wenxuan Wang, Qiangqiang Wang 
  Abstract: This paper extends traditional bank credit (BC) and buyback guarantee (BG) financing models by considering uncertain salvage value, and proposes a novel buyback guarantee financing with seller's option (SBG). We derive the optimal decisions for the bank, retailer, and manufacturer under each financing scheme. Additionally, we compare the optimal decisions for the retailer and manufacturer when the BC contract, BG contract, and SBG contract are feasible. The results reveal that the optimal financing schemes for the manufacturer and retailer are not always aligned. Both parties stand to increase profits with the SBG contract compared to other contracts when the salvage value is high. Furthermore, there is a significant range where the supply chain could generate greater profits with the SBG contract compared to other contracts.
  Keywords: seller’s option; buyback guarantee financing; bank credit financing; supply chain management.
  DOI: 10.1504/IJMOR.2024.10064996
   
  
• Analysis of MAP/PH1,PH2/1 Retrial Inventory Queueing System with Phase type Vacation, Working Breakdown, Repair, Essential and Optional Inventories  
  by Meena S, Ayyappan G 
  Abstract: This research analyses an inventory retrial queueing system with a constant retrial rate, working breakdown, repair, single vacation and inventory items that are essential and optional. We assume that an arrival follows the Markovian arrival process and that the server will provide them with phase-type services. The (s1, S1) and (s2, S2) policies are used to replenish the essential and optional inventory items, respectively, and there will be an exponential distribution in the replenishment time. The server takes a single vacation if there are no orbital customers, no essential inventory, or both. The server provides an optional item, if there exists a positive inventory level, otherwise the customer gets only the essential item and then leaves the system. When a server breaks down, the server provides the slow mode service for the current customer and then starts the repair process. The number of consumers in orbit, inventory level, and server status may all be determined in the steady state. Numerous key performance indicators are defined, and a cost analysis is obtained. In order to make our mathematical concept clearer, a few numerical examples are provided.
  Keywords: queueing-inventory; (s; S) policy; retrial; essential and optional item; single vacation; working breakdown; repair; Markovian arrival process; MAP; phase-type distribution.
  DOI: 10.1504/IJMOR.2024.10065048
   
  
• The Ristic-Balakrishnan-Exponentiated Half Logistic-G Family of Distributions with Applications  
  by Broderick Oluyede, Kethamile Rannona 
  Abstract: In this paper, we introduce a new family of distributions called the Ristic-Balakrishnan-Exponentiated Half Logistic-G (RB-EHL-G) family of distributions. Statistical properties of the new family including hazard function, quantile function, moments, distribution of the order statistics and Renyi entropy are derived. Some special cases of the new family are presented. The maximum likelihood estimation technique is used to estimate the model parameters. A Monte Carlo simulation study is conducted in order to examine the bias and mean square error of the maximum likelihood estimators. Finally, the new family is applied to real life datasets to illustrate the usefulness of the proposed distribution.
  Keywords: Ristic and Balakrishan-G Distribution; Exponentiated Half Logistic-G Distribution; Maximum Likelihood Estimation.
  DOI: 10.1504/IJMOR.2023.10065419
   
  
• Optimising Inventory Replenishment System  
  by Le Dao, Huynh Nhat Huy 
  Abstract: Abstract: Inventory management and replenishment are considered as important process in supply chain, especially in the retail industry. The replenishment process requires businesses to consider a large amount of information to support the decisions related to the appropriate quantity and timing of replenishment. The goal is to minimize costs associated with inventory including purchasing, holding and shortage costs at retail stores and maintain a high customer service level. The problem of the paper is formulated with mixed integer linear programming and to be solved by genetic algorithm to achieve optimal distribution cost for Firm. The results of the paper will support businesses in providing product replenishment strategies while considering related constraints on demand, budget, thereby providing businesses with the lowest operating costs and increasing competitiveness in the future.
  Keywords: Inventory replenishment model genetic algorithm mixed integer linear programming.
  DOI: 10.1504/IJMOR.2024.10065465
   
  
• Sustainable Supplier Selection and Order Allocation Using Hybrid Fuzzy Weighting Methods, Scenario-Based Programming, and Flexible Robust Optimisation  
  by Mahtab Saneei, Mehdi Seifbarghy, Mohsen Hamidi 
  Abstract: In this research, a sustainable supplier selection and order allocation problem under uncertainty is modelled and solved. To weigh supplier selection criteria, four fuzzy methods have been applied. To determine suppliers' scores, two approaches of fuzzy Taguchi loss function (F-TLF) and fuzzy technique for order preference by similarity to ideal solution (F-TOPSIS) are used. Suppliers' scores are then incorporated into an objective function of a multi-objective optimisation model to allocate orders to suppliers. Three models of scenario-based programming, flexible robust programming, and a new scenario-based and flexible robust hybrid programming are presented. The optimisation objectives are minimising purchasing cost, maximising supplier desirability, and maximising value of purchasing from best suppliers. To solve the models, a hybrid method of Lai and Hwang and Torabi-Hassini is proposed. The three models have been solved using real data from the electronics industry.
  Keywords: supplier selection and order allocation; SSOA; fuzzy Taguchi loss function; F-TLF; flexible robust optimisation.
  DOI: 10.1504/IJMOR.2024.10065534
   
  
• EOQ-Type Inventory Models Incorporating Discount Policies and Carbon Emission with Warehouse Capacity and Capital Constraints  
  by Tiara Alamanda, Dharma Lesmono, Jonathan Hoseana 
  Abstract: In 2019, Kristiyani and Daryanto proposed an EOQ-type inventory model which takes into account the company's total carbon emission, and assumes that the item's purchase obeys the all-unit-discount policy. In this paper, we construct a modication of the model, by replacing the all-unit-discount policy with the incremental-discount policy. Furthermore, we complement both models with warehouse capacity and capital constraints. Using both models, we compute numerically the optimal order quantity satisfying both constraints, in the scenario of a building materials company in Bandung, Indonesia. At the obtained optimal state, we analyse the sensitivity of both the company's total cost and total carbon emission with respect to some of the models' parameters. The results show that both quantities depend particularly significantly on the fuel consumption of the vehicle used to transport the purchased items from the supplier to the company's warehouse.
  Keywords: EOQ; carbon emission; all-unit discount; incremental discount; warehouse ca- pacity; capital.
  DOI: 10.1504/IJMOR.2024.10065578
   
  
• Kernel Estimation Analysis of the Finite Source M/G/1 Queue with Retrial and Vacation  
  by Lyes Ikhlef, Karim Labadi 
  Abstract: In this work, we study the finite source queueing system with retrial and vacation when the service distribution of customers is unknown. We compute the qualitative analysis of this queueing system by the use of the Markov regenerative process and the kernel method. The two main quantities, one step transition probability matrix P of the embedded Markov chain (EMC) defined at regenerative instants and the mean time matrix A, that the queue spends in any state between two successive regeneration instants, for the system considered are obtained. The matrix P (resp. A) depends on the probability density function (pdf) (resp. cumulative distribution function (cdf)) of the service time. These two functions (pdf and cdf) are unknown and are estimated by using the two asymmetric kernels gamma and Birnbaum-Saunders. Finally, we establish an algorithm which gives us the estimators of: the one step transition probability matrix P, the mean time matrix A, the probability distribution of the number of customers in the orbit and the state of the server and the characteristics of our queueing system considered.
  Keywords: Retrial Model; Markov Regenerative Process; Gamma Kernel; Estimation; Vacation Policy.
  DOI: 10.1504/IJMOR.2024.10065624
   
  
• Goal Programming Approach to Vehicle Routing Problems for Optimal Route Determination in Bus Rapid Transit (BRT)  
  by Hagni Wijayanti, Fajar Delli Wihartiko, Fitria Virgantari, Arif Wicaksono 
  Abstract: The bus rapid transit (BRT) service faces challenges in determining routes to fulfill customer service requirements and consider operational costs, bus capacity, distance, and travel time. This research aims to determine optimal BRT routes that can fulfill all desired objectives. In this study, a goal programming model is formulated for vehicle routing problems (VRP), integrating multiple objectives by minimising deviations from the set targets. The objectives include minimising travel time and distance. The enumeration followed by optimisation (EFBO) method is applied to determine the optimal solution to solve the BRT route problem. This method consists of two stages: enumeration for feasible route determination and multi-objective optimisation. The proposed method is analysed through numerical results on the Bogor City BRT system. The BRT route problem in Bogor was successfully addressed using this method, resulting in optimal solutions.
  Keywords: bus rapid transit; BRT; vehicle routing problem; VRP; multi-objective; goal programming; optimisation.
  DOI: 10.1504/IJMOR.2024.10065811
   
  
• A Note on an EOQ Inventory Model with Varying Time-Dependent Demand and Shortages under the Conditions of Delay in Payment  
  by Trailokyanath Singh, Itishree Rout, A.K. Nayak 
  Abstract: In most of the classical inventory models, only demand is considered as the main factor for formulating the model. However, demand and deterioration are two main competitive factors that are necessary to represent any inventory model for deteriorating items. In this paper, an EOQ model has been framed to study the items over a finite time horizon with the following characteristics: 1) delay in payment is permitted; 2) demand is time-dependent quadratic function of time; 3) grace period for settling the account is known; 4) shortages in the system are fully backlogged. The formulation of the model is derived under case 1 the grace period is less than shortage period and case 2 the grace period is greater than shortage period of the inventory system. Finally, a couple of numerical examples and sensitivity analysis of the optimal solution with respect to different parameters of the model are presented.
  Keywords: constant deterioration rate; deteriorating items; economic order quantity; permissible delay in payments; shortages; time-dependent quadratic demand.
  DOI: 10.1504/IJMOR.2024.10065820
   
  
• An Optimal Inventory System under Markdown Dependent Demand Environment  
  by Sonia Dua, Sandeep Kumar Mogha, Himani Dem 
  Abstract: Green supply chain management (GSCM) prioritises sustainability-focused approaches that strategically manage risk and environmental concerns while optimising operational efficiencies, reducing costs, and maximising profits as traditional supply chain management does. However, coordinating various individual participants of any supply chain working towards a common objective presents perennial challenges for executives in managing a supply chain, particularly considering various strategic aspects of environmental issues. Thus, this study employs a hybrid approach to selecting a GSCM strategy and aims to identify the most suitable one. For this purpose, a multi-criteria decision-making technique was applied to data collected from supply chain executives in the defence industry to fill the methodological gap. The findings of this research reveal that the legislative perspective holds the highest criterion weight, while risk-based strategies are identified as the most effective GSCM approach. Notably, this study contributes to advancing strategic management research by presenting a hybrid approach demonstrating a grey-based hybrid application of the PIPRECIA-G and OCRA methods to GSCM strategy selection.
  Keywords: inventory model; markdown dependent demand; discount policy; carbon emission.
  DOI: 10.1504/IJMOR.2024.10065897
   
  
• A Behavioural Analysis of a Fly Ash Bricks Manufacturing System  
  by Ritu Rathi  
  Abstract: This paper analysed the behaviour of reliability on fly ash bricks manufacturing system which having three subsystems such as pan mixing, belt conveyor, and bricks forming and they are organised in series manner. Both pan mixing and belt conveyor system contains single unit of machinery and the bricks forming subsystem contains two unit of machineries they are rotary press and hydraulic press. In bricks forming subsystem, both machineries are organised in parallel. Here, when the distribution of subsystem's repair time is taken as arbitrary, the distribution subsystem's failure time of the fly ash bricks manufacturing system is considered as exponential. The fly ash bricks manufacturing unit is investigated by utilising the supplementary variable technique. Here, the particular case is taken for discovering the availability, profit and mean time to system failure (MTSF) of the manufacturing system. Finally, the numerical analysis is performed to validate the impact of failure and repair rates on the availability and profit of the fly ash bricks manufacturing system.
  Keywords: availability; profit; supplementary variable technique; mean time to system failure; MTSF; fly ash bricks manufacturing system.
  DOI: 10.1504/IJMOR.2023.10066056
   
  
• Benchmarking Decision-Making Units' Efficiency for the Case of Integer-Valued Data and Fixed Factors: a Super Efficiency Slacks-Based Measure Approach  
  by Mushtaq Taleb, Mamdooh AttAllah, Ruzelan Khalid, Rosshairy Abdul Rahman 
  Abstract: The purpose of this paper is to develop a mixed integer SE-SBM approach with fixed inputs and outputs. The proposed approach is developed by modelling the integer requirements and fixed inputs and outputs into the objective function and the input and output constraints of Tone's (2002) SE-SBM approach in envelopment analysis (DEA). The scalar measure of the proposed approach depends on the discretionary mixed integer input excesses and discretionary mixed integer output shortfalls, as well as discretionary mixed integer input savings and discretionary mixed integer output surpluses. The approach can also identify sources of super-efficient status of efficient banks by identifying their discretionary mixed integer inputs that can be increased and/or discretionary mixed integer outputs that can be decreased. The proposed approach guarantees the feasibility condition under the variable returns-to-scale and constant returns-to-scale technologies. A banking sector application of the proposed approach with four inputs and four outputs is run.
  Keywords: Integer-valued data envelopment analysis; fixed factors; Slack-based measure; Super efficiency; Banking sector.
  DOI: 10.1504/IJMOR.2024.10066066
   
  
• A Weighted Neutrosophic Fuzzy Goal Programming Approach to Optimise Multi-Objective Assignment Problem  
  by Debasmita Sarkar, Pankaj Kumar Srivastava 
  Abstract: Assignment problems (APs) hold significant in industrial organisation, resource allocation, developing service systems, etc. Assigning appropriate jobs to the right employees is crucial when aiming to achieve objectives like cost-saving, ensuring production quality, and estimating production time. Decision makers (DMs) face immense pressure to optimise all of the objectives simultaneously determined to thrive in todays rapidly evolving market. Therefore, here considers, multi-objective assignment problems (MOAPs) to optimise all the objectives comprehensively. Additionally, only a tiny portion of the literature concentrates on both the quality of the commodities and the consistency of the objective functions while solving MOAPs and the consistency of the objective functions. Thus, in the proposed study, each tasks quality undergoes evolution using a neutrosophic linguistic scale. Weights are determined employing the neutrosophic analytic hierarchy process (NAHP) to avoid comparisons and ensure the consistency in the objective functions. The weighted single valued neutrosophic fuzzy goal programming (WSVNFGP) method is proposed toresolve the deterministic MOAP and find Pareto-optimal solutions by combining weights. The study is strengthened by a fair contrast of the proposed algorithm with other widely-used approaches, leading to approval of the reasonability of the proposed algorithm over other schemes.
  Keywords: multi-objective assignment problem; single-valued neutrosophic triangular fuzzy numbers; weighted neutrosophic fuzzy goal programming; pareto-optimal solution.
  DOI: 10.1504/IJMOR.2024.10066170
   
  
• Solving an EOQ model for Stock, Selling Price and Customer's Income Dependent Demand under Dense Lock Fuzzy Environment  
  by Suman Maity, Sujit Kumar De, Madhumangal Pal, Sankar Prasad Mondal 
  Abstract: In this paper, we have developed an economic order quantity (EOQ) model for degrading items in which two decision-makers collaborate to make decision, one of them acting as the industrialist (developer) and the other as the accountable manager. Although, customers' income might create a vital impact on the demand rate of the products. But none of the researchers took it into account for their model. In this study, the demand rate is considered as a function of selling price, stock, and customers' income and later it has been fuzzified. The problem is solved by using dense lock fuzzy environment. The notion of a dense fuzzy set, which depends on number of turnovers made at industrial process. Additionally, we have covered the basic idea of dense lock fuzzy sets along with the relevant membership functions and defuzzification techniques via solution algorithm. Numerical outputs reveals that the joint decision-makers provide the objective function finer optimum. To support the new approach, a thoughtful analysis, a graphical representation, and a conclusion are provided.
  Keywords: EOQ model; deteriorating items; dense lock fuzzy set; defuzzification; optimisation.
  DOI: 10.1504/IJMOR.2024.10066259
   
  
• Short-term origin-destination demand forecasting in rail transit systems: parallel model architecture and gravity approach  
  by Tissawat Asavanant, Hiroshi Morita 
  Abstract: Short-term origin-destination (OD) forecasting in passenger rail transit is notoriously difficult due to the high magnitude of scale, dimension, noise, and skewness of the OD matrices. Additionally, unforeseen OD data remains an issue for the data-driven models. In this paper, we address the issue of unforeseen OD data in real-time forecasting case, by using the adjusted parallel model architecture (APMA), a forecasting improvement strategy, and the reconstruction of the problem into an origin-based vector sum projection gravity (OVG) model. The forecasting problem can be split into concatenation and chained forecasting scenarios. Variations of the APMA model are tested on real-time datasets from Bangkok Subway. The proposed APMA-OVG model performs satisfactorily when compared to recent benchmarks for the unforeseen data on the concatenation case. The performance deteriorates in the chained forecast case due to accumulated error of the step-wise forecasting process when forecasting steps are broken down.
  Keywords: parallel model architecture; PMA; origin-destination matrices; gravity model; hybrid model; public transportation network; short-term forecasting.
  DOI: 10.1504/IJMOR.2024.10066486
   
  
• Supplementary variable technique approach on retrial queue with feedback and backup server during Bernoulli's lengthy vacation and random repairs.  
  by R. Poornima , K. Kirupa  
  Abstract: This paper explores a steady-state retrial queueing system with a single server, coupled with a backup server. Client arrivals occur in batches following a compound Poisson process. If the server is idle, one of the clients from the batch receives service immediately, and the remaining clients enter the orbit. Otherwise, the entire incoming batch joins the orbit. Unsatisfied clients after receiving service may become feedback clients. After the completion of each service, the server may enter a vacation period of random length. The server has the option to extend its vacation with certain probability. Breakdowns of the main server can occur at any point during the busy state. Repairs of the server commence without delay. During vacation and repair time of the main server, clients receive service from a backup server. Performance metrics, such as the mean of the system size, mean of the orbit size, server availability and server failure frequency are computed. Cost analysis has been carried out with the cost parameters. The stochastic decomposition law is verified for the proposed model. Numerical results are also presented to validate the impact of parameters on the system.
  Keywords: batch arrival; Bernoulli extended vacation; backup server; random breakdown and feedback.
  DOI: 10.1504/IJMOR.2024.10066498
   
  
• Replenishment of Bhadla Solar Park using Interval Valued Neutrosophic Threshold Graph  
  by R. Keerthana, Venkatesh S, R.U. Gobithaasan 
  Abstract: In this article, an interval valued neutrosophic threshold graph (IVNTG) G, a novel perspective on interval valued neutrosophic graph has been newly introduced. The concept of interval valued intuitionistic fuzzy threshold graph (IVIFTG) G, a special case of IVNTG is also defined together with alternating four-cycle, threshold dimension and threshold partition number for IVNG and IVIFG. Further, the bounds (G) '(G)' and (G) '(G)' are found and the equality becomes true only when G and G are triangle free graph. To demonstrate a practical significance, the article uses IVNTG to solve the replenishment problem on Bhadla Solar Park, an application which contributes towards SDGs, 7, 8 and 13 and the proposed algorithm helps to determine the allocation, consumption and distribution of solar energy in Bhadla Solar Park.
  Keywords: Interval Valued Intuitionistic Fuzzy Threshold Graph; Interval Valued Neutrosophic Threshold Graph; SDG; Bhadla Solar Park.
  DOI: 10.1504/IJMOR.2024.10066814
   
  
• Bifurcation Analysis and Effective Approaches to Control for Measles using SEIR Mathematical Model  
  by H.A. Bhavithra, S. Sindu Devi 
  Abstract: The aim of this work is to create the SEIR model for measles in Indonesia. The model has four compartments built into its construction. The SEIR model analysis yields local stability at the basic reproductive number and the fuzzy disease-free equilibrium is calculated. Sensitivity analysis has been done as part of control strategies, and after that, a fuzzy reproduction number control approach has been put into practice. The bifurcation theorem deals with dynamical systems that have one or more external parameters and how the parameters might change and affect the way the solution set is structured. In essence, this type of behaviour is dictated by the stability of solutions and how they may alter when the parameters change. The Euler method is used to carry out the numerical stimulation.
  Keywords: fuzzy equilibrium points; fuzzy basic reproduction number; backward bifurcation analysis; Euler method.
  DOI: 10.1504/IJMOR.2024.10066815
   
  
• Designing of Single Acceptance Sampling Plan based on Time Truncated Life Test under New Weibull-Pareto Distribution  
  by S. Swathi Sundari, G. Kannan, S. Balamurali, K. Lakshmanan, G. Selvaraj 
  Abstract: This article focuses on designing a single acceptance sampling plan (SASP) that guarantees the percentile lifetime (lifespan) of a product follows a new Weibull-Pareto distribution (NWPD) on the basis of a time-truncated life test (TTL) with a known shape parameter. Considering both producers risk () and consumers risk (), a two-point technique to the operating characteristic (OC) curve is applied in this study to find the most appropriate suitable plan parameters like sample size (n) and acceptance number (c). Our aim is to simultaneously satisfy the expectations of both producers and consumers. To select the most appropriate plan parameters, we generate tables representing various percentile values of the NWPD.
  Keywords: new Weibull-Pareto distribution; NWPD; percentile life; single acceptance sampling plan; SASP; time truncated life test; TTL test.
  DOI: 10.1504/IJMOR.2024.10066816
   
  
• Performance Comparison of Random Forest and BILSTM for Intrusion Detection in Cyber Security Environment  
  by A. Prashanthi, R. Ravinder Reddy 
  Abstract: The widespread adoption of the internet has led to an increase in network attacks, making traditional signature-based detection methods less effective against zero-day attacks. This research examines the efficacy of anomaly-based detection techniques in identifying these threats, using two artificial intelligence models: CNN-BiLSTM and random forest classifier. Data for training and testing these models was sourced from the CICIDS2017 dataset. Results showed a high success rate, with CNN-BiLSTM achieving 95% and random forest classifier achieving 98%. These findings suggest that anomaly-based detection offers a robust strategy for detecting zero-day network attacks. The research also underscores the necessity of assessing detection systems through various performance metrics, including accuracy, precision, recall, and F1 score. Such metrics provide a comprehensive understanding of an algorithm's effectiveness in diverse scenarios, which is crucial for developing more advanced and secure network security systems capable of addressing emerging threats.
  Keywords: anomaly-based detection; zero-day attacks; machine learning; BiLSTM; random forest classifier; CICIDS2017.
  DOI: 10.1504/IJMOR.2024.10066924
   
  
• Numerical Investigation of Phase type Inventory Queueing System with (s,S) policy, Degrading Service, Single Vacation, Closedown, Breakdown, Repair and Impatient Customers  
  by Ayyappan G, Meena S 
  Abstract: This analyses an inventory queueing system with degrading service, single vacation, breakdown, repair, closedown, and impatient customers. We assume that an arrival follows the Markovian arrival process, and that the server will provide them with phase-type services. The (s, S) policy to replenish the items and the replenishing duration follow an exponential distribution. The arriving customer should get the service whenever the inventory item level is positive. Otherwise, they must wait in front of the service station. The rate of service will decrease until the degradation is resolved. The number of customers in the system, the inventory level, and server status may all be determined in a steady state. Numerous key performance indicators are defined, busy period analysis is obtained, and cost analysis is obtained. To make our mathematical concept clearer, a few numerical examples are provided.
  Keywords: queueing-inventory; (s,S) policy; degrading service; single vacation; breakdown; repair; closedown; Markovian arrival process; MAP.
  DOI: 10.1504/IJMOR.2024.10066932
   
  
• Analysis of a Finite Retrial Queuing System with Orbital Search using Generalised Inverses  
  by Kalyanaraman R, S.B. Pattabiraman 
  Abstract: A simple, efficient, numerically stable algorithm to the analysis of a M/M/1/3/3 retrial queue with orbital search is given in terms of group generalized inverses. The interarrival time and service time are two different exponential distributions. There are three sources, each source generate primary customers. The primary arrivals first check whether the server is idle. If the server is idle, he enters the service station. Otherwise, he enters the orbit and retries, the inter retrial times follows negative exponential distribution. After being serviced, the customer returns to the source. Also, after completing service no one competing for service, with probability p, the server carries search for customers in the orbit and instantly picks up a customer, if available, directly from the orbit.Such a queue is called retrial queue with orbital search. Using the algorithm developed in Kalyanaraman and Pattabiraman (2010), the stationary distribution andmean first passage time distributions are obtained. Some operating chracteristics are calculated. Some particular models are also given.
  Keywords: Retrial queue - Orbital search - Generalised inverses - Stationary distribution - Mean first passage time - Operating characteristics.
  DOI: 10.1504/IJMOR.2024.10066959
   
  
• M/G/1 Queue with Regular and Optional phases of Services and Vacations  
  by Kalyanaraman R, Vidya K 
  Abstract: This paper deals with a non-Markovian single server queue with phase type service and phase type vacation. The service time and vacation time of each phase is generally distributed. The probability generating function of number of customers in the system at an arbitrary time point and at departure point is obtained in steady state. Some important performance measures are derived. Some numerical illustrations are also provided.
  Keywords: Non-Markovian queue; Phase type service; Phase-type vacation; Probability generating function; Performance measures; Numerical example.
  DOI: 10.1504/IJMOR.2024.10066961
   
  
• Strategic Pricing: Examining the Impact of Showrooming Behaviour on Manufacturer-Retailer Dynamics in a Supply Chain  
  by Ping Su, Xiangling Hu, Jaideep Motwani 
  Abstract: We study a two-stage supply chain where a manufacturer sells through two competing retailers: a brick-and-mortar retailer and an online retailer. Using a Stackelberg game model, we examine the manufacturers wholesale price and the BM retailers sales effort decisions in the presence of customers showrooming behaviour. We analyse how the availability of price-matching guarantees affects two product categories: non-showrooming and showrooming. Our findings show that price-matching strategy enhances the BM retailers sales effort, the manufacturers profit, and overall supply chain profitability for non-showrooming products, but is ineffective for showrooming products. For non-showrooming products, price-matching guarantee complements sales effort, with the manufacturer lowering its wholesale price to encourage more sales effort. For showrooming products, price-matching guarantees substitutes for sales effort, with the manufacturers aggressive pricing discouraging sales efforts. Therefore, we recommend universally offering price-matching guarantees for non-showrooming products and restricting them to customer requests for showrooming products.
  Keywords: Showrooming; Sales Effort; Stackelberg Game; Strategic Pricing.
  DOI: 10.1504/IJMOR.2024.10067161
   
  
• A Fuzzy MS-TORO Approach for Aircraft Rerouting Problem  
  by Miriam Bongo 
  Abstract: Stakeholders of the commercial aviation industry seek to uphold their individual interests but are faced to generate a unified decision which does not only satisfy their own interests but also of others. In this paper, fuzzy multiple stakeholder-based target-oriented robust-optimisation (MS-TORO) approach is utilised to address a choice problem in the aircraft rerouting process. The proposed model is based on an optimisation model which primary goal is to balance the interests of stakeholders at a certain extent of deviation from the target metric. The key results of the model showed an aggregated solution to the apparent conflict of interests among stakeholders. Furthermore, the model also highlighted the risk profile of stakeholders via the deviation metric. Such a novel framework serves beneficial to balance the interests of stakeholders in the decision process not only in the air transportation domain but also to other similar areas.
  Keywords: aircraft rerouting; airline industry; airport management; air traffic management; fuzzy set theory; multiple stakeholder-based target-oriented robust-optimisation approach.
  DOI: 10.1504/IJMOR.2024.10067164
   
  
• A Discussion of Newton's Law of Cooling using Difference Equations in Fuzzy Frames as an Alternative to the Traditional Continuous Dynamical System  
  by Abdul Alamin, Mostafijur Rahaman, Soheil Salahshour, Sankar Prasad Mondal, Shariful Alam, Kamal Hossain Gazi, Md Jahangir Mian 
  Abstract: This study, a notable one in the field of heat transfer, adapts a discrete and continuous heat transfer model in a fuzzy environment using fuzzy assumptions. This model was developed using the idea of discrete actual observation data and explored using a fuzzy framework in an effort to thoroughly analyse the experiments on natural occurrences. Using the Hukuhara difference notion, fuzzy arithmetic and difference calculus approach, fuzzy solutions to the governing model are demonstrated. In order to visualise the graphical solution and for usefulness to the suggested approaches, experimental data (both in crisp and fuzzy) of heat transfer of a hot glass of 40 ml water is taken in Newton's law of cooling. In discrete fuzzy frame Newtons law of cooling gives stable solution for some a [0, 1] and significant outcomes are observed from graphical solutions.
  Keywords: Hukuhara difference; fuzzy difference equation; Newton’s law of cooling.
  DOI: 10.1504/IJMOR.2024.10067203
   
  
• An Inventory Model with Power Demand and Preservation Technology Investment under Advanced and Delayed Payment Policies  
  by Loganayaki S, Kirupa K 
  Abstract: This study focuses on an inventory model for non-instantaneous, time-varying deteriorating items with preservation technology investment. The customer demand follows a power pattern function over time. During stockout periods, customer demands are partially backlogged. Additionally, the retailer pre-pays a certain amount of the purchasing cost as an advance payment to the supplier, with the balance paid at a later credit period. Three possible cases are identified based on the available credit period. The retailer incurs a carbon tax for each unit of carbon gas emitted during the processes of ordering, holding, and disposing of deteriorated items. The objective of the study is to minimize the total cost by determining the optimal cycle time, preservation technology investment, and positive inventory time. An algorithm is presented for the numerical optimization of the proposed model. Sensitivity analysis is conducted to evaluate the impact of parameters on model outcomes, providing valuable managerial insights.
  Keywords: inventory; non-instantaneous deterioration; power demand pattern; partial backlogging; advance payment; delay in payment; preservation technology investment; carbon tax.
  DOI: 10.1504/IJMOR.2024.10067204
   
  
• Numerical Solutions of Initial Value Problem by using Modified Euler's Method and Taylor's Method  
  by Rashmi Kumari, V.K. Pandey 
  Abstract: The numerical solution of differential equations (DEs) holds paramount importance in mathematical modeling for applications in science and engineering. It is frequently challenging to find accurate solutions to differential equations that define real-life issues due to their complexity. Since analytical solutions are unavailable for most differential equations, the main way to gain meaningful insights into the solution is through numerical computations. This article describes the numerical solutions of Fractional Differential Equations (FDEs) with Initial Value Problem (IVP) using the Modified Euler's Method (MEM) and Taylor's Method (TM). In addition to calculating the precise analytical solution, we also found the solutions to a few numerical problems. Next, for validation, a list of the accuracy discrepancies between analytical and approximation answers is provided. We found that the accuracy of a solution increases with minimal step sizes. Numerical models and figures are shown and analyzed to illustrate the efficacy of the proposed methodology.
  Keywords: Initial value problem; Taylor's method; Modified Euler's method; Numerical solution.
  DOI: 10.1504/IJMOR.2024.10067271
   
  
• Analysis of Optional Jockeying in Queueing Systems with Theoretical Insights and Practical Applications  
  by Vijaya Laxmi Pikkala, Anjalidevi Gilaka 
  Abstract: In this paper, we consider two Markovian queues in parallel with optional jockeying model, wherein the customers can join the queues with some probabilities and after joining the queue, can switch from one queue to another queue for faster services or may stay back in the same queue. The jockeying is a natural customer strategy and assumes a key role in areas such as grocery stores, amusement parks, computer networks, and retail outlets, where multiple checkout lines or service counters are available. We assume that the arrivals are Poisson, each of the exponential servers has his own queue. The model's steady state solution is discovered using the matrix geometric approach. Further, multiple system performance measures are obtained and a cost optimization problem is taken into consideration. Graphs and tables are used to display the numerical outcomes.
  Keywords: Jockeying; Optional Jockeying; Matrix Geometric Method; Queues.
  DOI: 10.1504/IJMOR.2024.10067283
   
  
• Gerber-Shiu Analysis of the MAP/PH Omega Risk Model with Level-Dependent Premium Rate  
  by Sreeshamim P. P., M.J. Jacob 
  Abstract: This paper investigates the Gerber-Shiu function (G-SF) of the MAP/PH omega insurance risk process with level-dependent premium arrival. The omega model differentiates between ruin and bankruptcy, providing a more realistic assessment of an insurance companys financial stability. By incorporating Markovian arrival processes (MAPs) for claim arrivals and phase-type (PH) distributions for claim sizes, the MAP/PH omega risk model offers a robust framework for analysing risk. The level-dependent premium rate adjusts based on the insurers reserve levels, making the model more flexible and applicable to real-world scenarios. We derive integro-differential equations for the G-SF, providing insights into the expected discounted penalty at bankruptcy. Numerical solutions demonstrate the models practical applications, revealing that higher initial surpluses correlate with lower expected penalties and bankruptcy probabilities.
  Keywords: MAP claim arrivals; phase-type (PH) claims; bankruptcy probability; level-dependent premium rate; dividend barrier; Gerber-Shiu function (G-SF).
  DOI: 10.1504/IJMOR.2024.10067523
   
  
• Optimal Order Policy based on Three-Item Inventory Models with Weibull Distribution Deterioration and Price-Dependent Demand  
  by Claudia Priscilla, Dharma Lesmono, Jonathan Hoseana 
  Abstract: We construct three one-item inventory models with Weibull distribution deterioration, corresponding to three different dependences of the item's demand rate on its selling price: linear, quadratic, and exponential. We combine the three models to obtain five different three-item inventory models, corresponding to the existing five different order policies: the individual order policy, the three semi-joint order policies, and the joint order policy. We carry out a computational analysis of these models, which reveals that the joint order policy - that of ordering the three items simultaneously - gives the highest total profit, and that under this policy, the total profit depends most sensitively on the constant coefficient of the quadratic demand-rate function, i.e., the second item's demand rate in the case of zero selling price.
  Keywords: inventory model; Weibull distribution; deterioration; price-dependent demand; order policy.
  DOI: 10.1504/IJMOR.2024.10067565
   
  
• Uncertainty Propagation in M/G/1/K Queue Modelled by Parametric p-box using Taylor Series Expansion Approach  
  by Zina Hamoudi, Sofiane Ouazine, Karim ABBAS, Kamel Haouam 
  Abstract: The main purpose of the current paper is to use the multivariate Taylor series expansion for analysing of the M/G/1/K queue, we give a new formula of the closed-form expressions for the higher-order sensitivity of discrete-time Markov chain stationary distribution with respect to multiple parameter using a fundamental matrix. We also include the probability boxes, we assume that all parameters have a uniform distribution. In addition, we use the Markov's inequality to estimate the risk incurred by working with uncertain performances of the M/G/1/K queue. Several numerical examples are also presented and the obtained results are compared to the corresponding Monte Carlo simulation.
  Keywords: M/G/1/K queue; Probability-boxes; epistemic uncertainty; multivariate Taylor-series expansions; Risk analysis; Monte Carlo simulation.
  DOI: 10.1504/IJMOR.2024.10067569
   
  
• A Study on Retrial Queueing Model with Additional Breakdown Services and Complete Vacation  
  by Madhumidha Ramachandran, S. Balaji 
  Abstract: In this research, we explore a retrial queuing model with additional breakdown service and complete vacation. If a customer accesses the system and discovers that the server is busy, they enter an orbit, a space with an unlimited capacity. From the orbit, they keep attempting to access the service. The main server crashes as a result of a disaster. In the event of a breakdown, the main server is sent for repair; in the meantime, it will operate more (working breakdown). The server will attempt a complete vacation if the orbit is empty as soon as the working breakdown is completed. By utilizing the supplementary variable technique (SVT), the performance metrics are acquired. Also, the mean busy period and mean busy cycle are discussed. Several specific cases of this model are provided. Further, some numerical results are demonstrated to explore the act of different variables on distinct system performance metrics.
  Keywords: retrial queues; working breakdown services; repair; complete vacation.
  DOI: 10.1504/IJMOR.2024.10067578
   
  
• The Refractory Emission during Inspection Waiting under Pentagonal Fuzzy Number in a Sustainable Inventory Model  
  by Saranyaa P, C. Sugapriya, Nagarajan Deivanayagam Pillai, Kavikumar Jacob 
  Abstract: Every item in traditional inventory control problems is of the highest quality and that the inspection procedure operates flawlessly. In this paper, it is extended for imperfect items, where mistakes of types I and II happen while the inspection is being done and also expands the economic production quantity model. When a batch of perfect items is finally replaced after a special inspection procedure, customers who receive and return imperfect items wait for it in the suggested inventory problem. In the inspection, the defective goods are under the rework plant through electrical vehicle to become the defective goods as finished goods. In addition, the lower-quality items are discounted and sold out quickly, a numerical example was given, and the impact of the primary parameters on the overall profit was examined through a sensitivity analysis.
  Keywords: Waiting Expenses; Defuzzification; Refractory; emission; kiln refractory.
  DOI: 10.1504/IJMOR.2024.10067845
   
  
• A Mathematical Approach to Solve Multi-Objective Pentagonal Fuzzy Linear Plus Linear Fractional Programming Problems  
  by Sujit Maharana, Suvasis Nayak 
  Abstract: Optimization algorithms efficiently deal with many real life problems. In numerous practical circumstances, the concept of fuzziness can be utilized for the problems with uncertainty. This paper deals with a computationally simple and efficient solution approach to solve a mathematical model of fuzzy multi-objective linear plus linear fractional programming problem which is designed in an environment of pentagonal fuzzy numbers. In this model, fuzzy cuts are used in the objective functions to transform the fuzzy valued functions into crisp interval-valued forms and the concept of ranking function is used in the constraints to convert the fuzzy valued inequalities into deterministic expressions. First order Taylor's series approximation is used as the linearization process. Furthermore, the weighting sum method with analytic hierarchy process is applied to tackle the multi-objective optimization. To justify and validate the feasibility, two existing numerical examples are solved and also the computational results are comparatively studied.
  Keywords: Linear plus linear fractional programming; Multi-objective optimization; Pentagonal fuzzy numbers; Interval valued functions.
  DOI: 10.1504/IJMOR.2024.10067850
   
  
• Integrating Durability and Fault Tolerance in Heterogeneous Distributed Systems: an Extensive Copula-Based Study of Server-Client Architectures' Reliability and Performance  
  by Ibrahim Yusuf, Ismail Tukur 
  Abstract: This study delves into the investigation of reliability and performance metrics, specifically focusing on availability, reliability, mean time to failure (MTTF), sensitivity, and cost analysis. The system under study is a tree-topology computer networking system, comprising five subsystems labelled A, B, C, D, and E, which are configured in a series-parallel. The system is prone to two types of failures: complete failure and degraded failure. The study employs the Laplace transform and supplementary variables techniques. These methods are utilised to derive explicit expressions for key metrics: availability, reliability, MTTF, sensitivity, and the cost function. The results are illustrated in tables and graphs. Reliability personnel can enhance their strategies to improve system dependability, maintenance managers can better plan maintenance schedules, and engineers can gain a deeper understanding of system performance dynamics. Through this comprehensive investigation, the study contributes valuable knowledge to the fields of reliability engineering and network system performance analysis.
  Keywords: Availability; Mean time to system failure; Reliability; Topology; Cost Analysis. Structural query language server.
  DOI: 10.1504/IJMOR.2024.10067854
   
  
• Bernoulli Vacation Bulk Queue with Essential, Optional Service, Unreliable Server and State Dependent Arrival Rates  
  by Kalyanaraman R, Sivasuprajha R.V 
  Abstract: This paper presents the steady state analysis of a single server, bulk arrival, fixed batch service, Bernoulli vacation queue. The arrival follows compound Poisson process with state dependent arrival rates. The service time follows general distribution and services are given in batches of fixed size. The server provides two types of services called, essential and optional service to each batch. At each service completion point, the server takes vacation of Bernoulli type. The vacation period is generally distributed. In addition, during server's busy state, the server may breakdown immediately, the server is send for repair. The number of breakdowns follows Poisson process where as the repair period follows general distribution. For this queueing system the steady state probabilities are derived in terms of probability generating function. The expected number of customers and mean waiting times at various server states are derived. Numerical illustrations are given.
  Keywords: Non-Markovian queue ; Bulk arrival queue ; Fixed batch size ; Bernoulli vacation ; Essential and Optional service ; Unreliable server ; State dependent rates.
  DOI: 10.1504/IJMOR.2024.10067988