A Multi-objective Possibilistic Programming Model for Material Order Allocation under Uncertainty

Material order allocation is a critical challenge in supply chain management under uncertainty. Traditional deterministic models fail to address fluctuations in several factors such as cost, quality, and lead time, leading to inefficient procurement decisions. This study proposes a Multi-Objective Possibilistic Programming (MOPP) model to enhance decision-making. The model employed possibility distributions and the α-cut approach to evaluate supplier performance under optimistic, likelihood, and pessimistic scenarios, ensuring risk-aware allocation. A case study in the electronics industry dealing with five suppliers for the key products demonstrated that the optimistic scenario was as follows: the total cost was minimized to $88,785, with the highest quality of 97.75% and the shortest lead time of 39.63 days. As uncertainty increased, costs increased to $98,650 for the likelihood scenario and $108,515 for the pessimistic scenario, while the quality declined to 93.58% and 91.23% for those two scenarios, respectively, with lead times extended to 47.13 days and 52.73 days, accordingly. Material allocation planning was completed by assigning material items to all suppliers differently, which depended on the scenarios. Moreover, the unused capacity of each supplier was also investigated. Suppliers with minimum cost, maximum quality, and minimum lead time were consecutively utilized, which aligned with the preemptive priority of the three objectives of the proposed MOPP. These findings highlight the effectiveness of the proposed method in handling uncertainty by balancing cost efficiency, supplier diversification, and risk mitigation across varying scenarios.