Joint Pricing and Inventory Control with Setup Costs and Demand Uncertainty

摘要

This paper considers the joint pricing and inventory control problem with setup costs and demand uncertainty. Specifically, this paper develops an infinite horizon model that integrates pricing and inventory replenishment in a distribution environment. We allow for dynamically varying prices in response to changes in inventory levels and by taking advantage of price-sensitive demand. Assuming demands to follow Poisson processes parameterized with prices, we identify a class of pricing and inventory policies which is optimal among all policies. For instance, when there are just two price levels, high and low, to be considered, the optimal joint pricing and ordering policy is characterized by the form of (s, d, D, S), where parameter s refers to reorder level, S to order-up-to level, d and D to pricing reference levels, and s ≤ d ≤ D ≤ S. This policy works as follows: Once inventory level reaches or below s, an order is placed to bring it up to 5; when inventory level is above D or below d, the product is sold at the low price, while when it is above d and below D, the product is sold at the high price. We also develop a simple yet exact algorithm to compute the optimal joint pricing and ordering policy.