Robust possibilistic programming for multi-item EOQ model with defective supply batches: Whale Optimization and Water Cycle Algorithms

This paper proposes a new mathematical model for multi-product economic order quantity model with imperfect supply batches. The supply batch is inspected upon arrival using “all or None” policy and if found defective, the whole batch will be rejected. In this paper, the goal is to determine optimal order quantity and backordering size for each product. To develop a realistic mathematical model of the problem, three robust possibilistic programming (RPP) approaches are developed to deal with uncertainty in main parameters of the model. Due to the complexity of the proposed RPP models, two novel meta-heuristic algorithms named water cycle and whale optimization algorithms are proposed to solve the RPP models. Various test problems are solved to evaluate the performance of the two novel meta-heuristic algorithms using different measures. Also, single-factor ANOVA and Tukey’s HSD test are utilized to compare the effectiveness of the two meta-heuristic algorithms. Applicability and efficiency of the RPP models are compared to the Basic Possibilistic Chance Constrained Programming (BPCCP) model within different realizations. The simulation results revealed that the RPP models perform significantly better than the BPCCP model. At the end, sensitivity analyses are carried out to determine the effect of any change in the main parameters of the mathematical model on the objective function value to determine the most critical parameters.