Multi-item EOQ model with nonlinear unit holding cost and partial backordering: moth-flame optimization algorithm

Abstract

In this paper, a multi-item multi-constrained Economic Order Quantity model with nonlinear unit holding cost and partial backordering is proposed. To develop an applicable model, different technical, physical, and strategic constraints are considered such as available budget, warehouse capacity, total permissible holding cost, and total permissible backordering cost constraints. The goal is to determine the lengths of inventory cycles, where the inventory level is positive and negative such that the total inventory costs are minimized. In addition, backordering rate during shortage period for each product is considered as a decision variable which can significantly reduce the total inventory costs. Due to complexity and nonlinearity of the proposed model, interior-point method and Moth-Flame optimization algorithm are utilized to solve the model in different sizes. At the end, the performance of the solution methods is compared statistically considering three measures to determine the superior solution method.