Single-vendor single-buyer multi-product economic production quantity problem with stochastic constraints: a modified generalized elimination method

This study designs a single-buyer single-vendor multi-product Economic Production Quantity (EPQ) model to optimize the total cost in an inventory system. To do so, a Non-Linear Programming (NLP) model is developed considering a set of stochastic constraints on space or warehouse capacity, backordering cost, procurement, ordering, and obtainable budget. A modified Generalized Elimination Method (GEM) is then offered to treat the complexity of the model wherein the variables are eliminated by adding two equations. The developed method generates much more high-quality solutions compared with the classic GEM, while the number of iterations slightly increases. Three problem instances in different scales are then taken into account to assess the efficiency of the modified GEM in terms of optimality criteria. The results demonstrate that the modified GEM has an excellent performance with respect to optimal solutions, infeasibility, number of iterations, complementarity, and errors of optimality. Finally, the behavior of the objective function is analyzed against order quantity fluctuations to draw out practical implications.