Optimal pricing and inventory control policy in periodic-review systems with fixed ordering cost and lost sales

This paper studies a periodic-review pricing and inventory control problem for a retailer, which faces stochastic price-sensitive demand, under quite general modeling assumptions. Any unsatisfied demand is lost, and any leftover inventory at the end of the finite selling horizon has a salvage value. The cost component for the retailer includes holding, shortage, and both variable and fixed ordering costs. The retailer's objective is to maximize its discounted expected profit over the selling horizon by dynamically deciding on the optimal pricing and replenishment policy for each period. We show that, under a mild assumption on the additive demand function, at the beginning of each period an (s,S) policy is optimal for replenishment, and the value of the optimal price depends on the inventory level after the replenishment decision has been done. Our numerical study also suggests that for a sufficiently long selling horizon, the optimal policy is almost stationary. Furthermore, the fixed ordering cost (K) plays a significant role in our modeling framework. Specifically, any increase in K results in lower s and higher S. On the other hand, the profit impact of dynamically changing the retail price, contrasted with a single fixed price throughout the selling horizon, also increases with K. We demonstrate that using the optimal policy values from a model with backordering of unmet demands as approximations in our model might result in significant profit penalty.