Joint inventory-and-pricing strategy for a stochastic continuous-review system

We analyze an infinite-horizon continuous-review stochastic inventory system in which the selling price and inventory replenishment are determined simultaneously. The demand process is Poisson with a price-dependent arrival rate. The ordering cost includes a fixed setup cost and a variable cost proportional to the order quantity. We obtain closed-form solutions for the optimal inventory control strategy and optimal pricing strategy, which provide managerial insights as well as quantitative and qualitative relationships between decision rules and system parameters. We show that the optimal price is a unimodal function of the inventory level. We also develop efficient algorithms to compute the optimal strategies and present numerical examples.