Deterministic inventory model for deteriorating items with finite rate of replenishment dependent on inventory level

Abstract

In industry, the replenishment rate of a manufacturing system at any time is constant and determined depending upon the demand of the production in the market and the present stock of the produced in the godown at that time. Until now, this practical aspect has not received the attraction of inventory researchers. In this paper, two models have been formulated and solved for deteriorating items with linearly time dependent demand where replenishment rate changes linearly with the change in demand and on-hand inventory amount. Different types of functional relations of replenishment rate with demand and on-hand inventory can be incorporated in this analysis. Using the present methodology, the above practical aspect can be incorporated to the problems of multi-item, multi-storage, discount, etc. In this paper, two deterministic inventory models for deteriorating items have been developed and solved with and without allowing shortages which are backlogged. The replenishment rate is finite and dependent on the instantaneous inventory level and also on demand. In both models, the rate of demand and deterioration at any moment of time is a linear increasing function of time. Two numerical examples are given to illustrate the results and the significant features of the results are discussed. Also, the effects of changes in the demand and deterioration parameters on the optimal average cost are graphically presented.