Optimal Ordering Policies for Inventory Problems with Price Change

Abstract

The problem of determining the optimal order quantities for an inventoried item when the vendor offers a price reduction for a limited time but of a random duration is both interesting and important. Solutions to the one time discount models have been carried out in two directions. First when the discount is fixed and known in advance and the other one is when discount is offered but end date is random. In the deterministic discount duration, equal order sizes are optimal. However, when discount duration is random, the optimal ordering sizes should be varying because probabilities of residual discount duration in each period are different. Complication of the solution increased since every time order has to be placed the residual distribution of remaining duration of discounted price keeps changing. A myopic policies are suggested based on mixer of the profit function due to the first order and combination of remaining orders that is based on the residual distribution of the discount. Resulting order sizes and reorder sizes are varying over the discount period. Numerical examples justifies that adaptive myopic solutions are much superior to equal order solutions and are significant improvement over earlier methods. newlineProfit function is also derived by taking various order levels under discount price into consideration. Optimal order levels being not easy to implement by the inventory managers, alternative methods are suggested here. The best possible functional relationship between order levels and hazard rate function and also mean residual life function are obtained. Based on these relations easy to implement order levels can be obtained. newline