Development of an EPQ Model for Deteriorating Product with Stock and Demand Dependent Production rate under Variable Carrying Cost and Partial Backlogging

Abstract

In the present article, an economic production quantity (EPQ) model is developed for deteriorating product with time dependent demand and the time dependent inventory carrying cost. Here,it is assumed that the production rate at any instant depends on both the stock and the demand of the product. To make the model more realistic, the shortages are allowed and partially backlogged. The backordering rate is taken as a decreasing function of waiting time for the next refill.The main objective of the present study is to find the optimal total cost per unit time of the production system. To validate the optimal resuts, numerical example is provided. To analyze the effect of variations in the optimal resuts with respect to change in one parameter at a time, sensitivity analysis is carried out and the results are presented graphically.