An inventory model for non-instantaneous deteriorating items with time dependent quadratic demand, two storage facilities and shortages under trade credit policy

Abstract

In this paper, an EOQ model for non-instantaneous deteriorating items with two-phase demand rates, two storage facilities (own warehouse and rented warehouse) and shortages under trade credit policy has been developed. The demand rate before deterioration sets in is assumed to be time dependent quadratic and that is considered as a constant after deterioration sets in. Shortages are allowed and completely backlogged. The purpose of this research is to determine length of time at which the inventory level reaches zero in OW and cycle length simultaneously such that total variable cost has a minimum value. The corresponding economic order quantity will also be determined. The necessary and sufficient conditions for the existence and uniqueness of solutions are provided. Numerical examples are provided to illustrate the theoretical results of model. Sensitivity analyses are carried out to see the effects of changes in some system parameters on optimal solutions. Based on the results, several ways are suggested for the retailer to effectively reduce the total variable cost of the inventory system.