Joint pricing and inventory control for a stochastic inventory system with Brownian motion demand

摘要

In this article, we consider an infinite horizon, continuous-review, stochastic inventory system in which the cumulative customers'demand is price dependent and is modeled as a Brownian motion. Excess demand is backlogged. The revenue is earned by selling products and the costs are incurred by holding/shortage and ordering; the latter consists of a fixed cost and a proportional cost. Our objective is to simultaneously determine a pricing strategy and an inventory control strategy to maximize the expected long-run average profit. Specifically, the pricing strategy provides the price p_t for any time t ≥ 0 and the inventory control strategy characterizes when and how much we need to order. We show that an (s*, S*, p*) policy is optimal and obtain the equations of optimal policy parameters, where p* = {p_t*: t≥ 0). Furthermore, we find that at each time f, the optimal price p* depends on the current inventory level z, and It is increasing in [s*, z*] and decreasing in [z*, ∞), where z* is a negative level.