Purchasing inventory models for exponential demand with deteriorating items and discounted cost-in third order equation

Abstract

The purpose of this article is to present a solution procedure for the inventory problem of deteriorating items and exponential demand and taking account of time value of money. Also, most of the works on inventory models do not take the optimal solution in higher order equation. In this paper, inventory models for deteriorative items with time dependent exponential demand under inflation and the optimum solution is derived in higher order equations. Two models are developed and the optimum time and total cost are derived: 1) when the demand is exponential with deteriorative items; 2) demand is exponential with deteriorative items and discounted cost. Mathematical models are developed for each model and the optimum time and optimal lot size which minimises the total cost is derived. The objective of this paper is to find the optimal cycle time and optimal quantity which minimise the total cost. Numerical examples are given to illustrate the theoretical results and made the sensitivity analysis of parameters on the optimal solutions. The validation of result for this model was coded in Microsoft Visual Basic 6.0.