Optimal prices and order quantities when temporary price discounts result in increase in demand

Suppliers often offer temporary price discounts to retailers. The discount motivates retailers to increase their order quantity and offer a discount to their customers to increase demand and profit. In this paper the change in price and the resulting change in demand and their effect on inventory policy and total profit is analyzed simultaneously to determine retailer’s optimal price and optimal ordering policies. The simultaneous analysis considers the joint effect of marketing and inventory policies on profits and prohibits the suboptimality that is inherent in the customarily serial treatment of these policies. This paper uses a general price-demand relationship and develops general models for determining optimal price and order quantity. Any specific price-demand relationship may be substituted in these models to determine the optimal price and optimal order quantity for specific cases.