A comparative analysis of approaches for determining optimal price and order quantity when a sale increases demand

Both average cost (or profit) and present value of cost (or profit) methods have been used in developing inventory policies. Although the present value method represents the costs and revenues better, both methods generate identical solutions for the classical economic order quantity (EOQ) case. This paper discusses the differences between the two methods and illustrates situations where these two methods generate drastically different policies. Specifically, when a supplier reduces the price of a product temporarily, a retailer might place a special order and offer a discount on these units to its customers to increase demand. This paper uses an average profit method to develop profit functions for different combinations of supplier's sale period and retailer's replenishment time and presents methods for determining the optimal price and order quantity. Experiments are then conducted to compare the results of average profit and present value of profit approaches for solving the problem. The results indicate that these models may generate drastically different policies for the problem and neither model will consistently generate a larger order quantity. This paper suggests that the present value approach be used to determine optimal policies when there is a temporary change in price and demand.