On an inventory model for deteriorating items with stock dependent and time-varying demand rates

Abstract

In this paper, we present an inventory model for deteriorating items with stock dependent and time-varying demand rates for a finite time planning horizon. We also suggest a procedure for finding the optimal replenishment schedule and show in a rigorous way that the policy suggested is indeed optimal. Further, we present a numerical example and conclude the paper with suggestions for possible future research. Scope and purpose Finding a mathematical inventory model that describes accurately the dynamics of the stock and yet is simple enough to allow mathematical manipulation is difficult. In an earlier work one of the authors of this paper and his co-workers succeeded in proposing an inventory model with deteriorating items and increasing (decreasing) demand rates. An algorithm for finding the optimal replenishment schedule for finding planning horizon was proposed. The nice structure of the algorithm initiated a search and a general model that would encompass all previous models and yet be mathematically tractable to be solved by a similar algorithm. The present paper is a step towards achieving this goal. This is done by looking at inventory models in which demand is a function of the stock on hand and where items are allowed to deteriorate. The mathematics details are presented in whole since it is thought they could form a basis for a general treatment of similar problems.