Optimal Inventory Model with Stock-dependent Selling Rate under Maximal Total Present Value of Profits

K.-L. Hou and L.-C. Lin (Taiwan)

Keywords

Stockdependent selling rate; Inflation; Deteriorating; Backlogging; Inventory

Abstract

This paper presents an inventory model under inflation and time discounting for deteriorating items with stock-dependent selling rate. The selling rate is assumed to be a function of current inventory level and the rate of deterioration is assumed to be constant. We follow the discounted cash flow (DCF) approach to investigate inventory replenishment problem for deteriorating items with stock-dependent selling rate considering the time value of money over a finite planning horizon. The purpose of this paper is to determine the optimal number of replenishment and the corresponding cycle time to maximize the total present value of profits over a finite time horizon. In addition, an efficient procedure is developed to generate the optimal inventory policies. Finally, a numerical example is provided to illustrate the optimization procedure and sensitivity analysis is also performed.

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