Delayed Payment Policy in the Inventory Model of Deteriorating Goods with Quadratic Demand in Order to Backlogging Shortage

In this paper, a comprehensive model for inventory control of deteriorating goods via considering backlogging shortage is proposed. The demand function is in quadratic form, the second-order function of time. A fixed deteriorating rate of goods and complete backlogging shortage condition as well as their related costs and planning requirements such as delayed payment policy are considered. The aim of the proposed mathematical model is to determine the appropriate order cycle time in order to maximize the total profit of the inventory management system. An exact solution algorithm is developed to solve the proposed complex model. The computational obtained results indicate the efficiency of the proposed model and solution algorithm for considering good deterioration under backlogging shortage condition with quadratic demand function.