Coordinating pricing and inventory control in a fluctuating environment

This paper addresses the simultaneous determination of pricing and inventory replenishment strategies under a fluctuating environment. Specifically, we analyze the single item, periodic review model. The demand consists of two parts: the deterministic component, which is influenced by the price, and the stochastic component (perturbation). The distribution of the stochastic component is determined by the current state of an exogenous Markov chain. The price that is charged in any given period can be specified dynamically. A replenishment order may be placed at the beginning of some or all of the periods, and stockouts are fully backlogged. Ordering costs that are lower semicontinuous, and inventory/backlog (or surplus) costs that are continuous with polynomial growth. Finite-horizon and infinite-horizon problems are addressed. Existence of optimal policies is established. Furthermore, optimality of (s,S,p)-type policies is proved when the ordering cost consists of fixed and proportional cost components and the surplus cost (these costs are all state-dependent) is convex.