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

Abstract

In this paper, we consider an infinite horizon, continuous-review, stochastic inventory system in which 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 $t\ge 0$ and the inventory control strategy characterizes when and how much we need to order. We show that an $(s^{\ast },S^{\ast },p^{\ast })$ policy is optimal and obtain the equations of optimal policy parameters, where $p^{\ast }=\{p_t^{\ast }:t\ge 0\}$. Furthermore, we find that at each time $t$, the optimal price $p_t^{\ast }$ depends on the current inventory level $z$, and it is increasing in $[s^{\ast },z^{\ast }]$ and is decreasing in $[z^{\ast },\infty )$, where $z^{\ast }$ is a negative level.

29 pages, 2 figures

References in corpus (1)

• Drift rate control of a Brownian processing system

Cited by in corpus (1)

• Optimal Drift Rate Control and Impulse Control for a Stochastic Inventory/Production System