An Order Quantity Model for Delayed Deteriorating Items with Time-varying Demand Rate and Holding Cost, Complete Backlogging Rate and Two-level Pricing Strategies under Trade Credit Policy

Abstract

In some classical inventory models for non-instantaneous deteriorating items, it is tacitly assumed that the selling price before and after deterioration sets in is the same.  However, in real practice, when deterioration sets in, the retailer may decide to reduce the selling price to encourage more sales, reduce the cost of holding stock, attract new customers and reduce losses due to deterioration.  This research developed an economic order quantity model for non-instantaneous deteriorating items with two-phase demand rates, linear holding cost, complete backlogging rate and two-level pricing strategies under trade credit policy.  It is assumed that the holding cost is linear time-dependent, the unit selling price before deterioration sets in is greater than that after deterioration sets and the demand rate before deterioration sets in is considered as continuous time-dependent quadratic, after which it is considered as constant up to when the inventory is completely exhausted.  Shortages are allowed and completely backlogged.  The proposed model determines the optimal time with positive inventory, cycle length and order quantity such that the total profit of the inventory system has a maximum value.  The necessary and sufficient conditions for the existence and uniqueness of optimal solutions have been established.  Numerical experiments have been conducted to illustrate the theoretical result of the model.  Sensitivity analysis of some model parameters on the decision variables has been carried out, and suggestions towards maximising the total profit were also given.