Title: A fuzzy-probabilistic bi-objective mathematical model for integrated order allocation, production planning, and inventory management

Authors: S. Solikhin; S. Sutrisno; Abdul Aziz; Purnawan Adi Wicaksono

Addresses: Department of Mathematics, Diponegoro University, Jalan Prof. Soedarto, SH, Tembalang, 50275 Semarang, Indonesia ' Department of Mathematics, Diponegoro University, Jalan Prof. Soedarto, SH, Tembalang, 50275 Semarang, Indonesia ' Department of Mathematics, Diponegoro University, Jalan Prof. Soedarto, SH, Tembalang, 50275 Semarang, Indonesia ' Department of Industrial Engineering, Diponegoro University Jalan Prof. Soedarto, SH, Tembalang, 50275 Semarang, Indonesia

Abstract: An optimisation-based decision-making support is proposed in this study in the form of fuzzy-probabilistic programming, which can be used to solve integrated order allocation, production planning, and inventory management problems in fuzzy and probabilistic uncertain environments. The problem was modelled in an uncertain mathematical optimisation model with two objectives: maximising the expectation of production volume and minimising the expectation of total operational cost subject to demand and other constraints. The model belongs to fuzzy-probabilistic bi-objective integer linear programming, and the generalised reduced gradient method combined with the branch-and-bound algorithm was utilised to solve the derived model. Numerical simulations were performed to illustrate how the optimal decision was formulated. The results showed that the proposed decision-making support was successful in providing the optimal decision with the maximum expectation of the production volume and minimum expectation of the total operational cost. Therefore, the approach can be implemented by decision-makers in manufacturing companies.

Keywords: decision-making support; fuzzy parameter; order allocation; probabilistic parameter; production planning; uncertain programming.

DOI: 10.1504/IJADS.2024.141828

International Journal of Applied Decision Sciences, 2024 Vol.17 No.6, pp.772 - 798

Received: 19 Jan 2023
Accepted: 27 Jun 2023
Published online: 02 Oct 2024 *

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