A Note on the Relationship between Pricing and Capacity Decisions in Inventory Systems with Stochastic Demand

We address the simultaneous determination of pricing and capacity investment strategies in a multi-period setting under demand uncertainty. In our model a monopolistic firm makes three decisions: capacity investment (or disinvestment), production (inventory), and price, all of which can be specified dynamically as a function of the state of the system. We analyze the optimal joint strategy and investigate the relationships between the main strategic decision variables: price and capacity. We consider models that allow for either bi-directional price changes or models with markdowns only. We show that the optimal capacity adjustment is given by a target interval policy: there is a (state dependent) target interval for each period such that capacity is adjusted ``as little as possible" to bring the available level into this interval. Once the capacity level is determined, we show that if bi-directional price changes are allowed, a modified-base-stock list price is the optimal inventory-pricing decision. In both cases we derive the structure of the optimal policy, and in the latter case we prove that capacity and price are strategic substitutes.