We address a retailer's challenge of matching supply with demand, under demand uncertainty. We first address the situation where the retailer cannot place orders for in-season replenishments. We conduct an empirical analysis of sales and price data from a retailer of women's apparel. We fit a demand model to the data and obtain estimates of revenues under various markdown pricing policies. We compare optimal prices and revenues under these policies to those of the study company. We conclude, e.g., that revenues can be improved significantly by taking smaller markdowns earlier in the season.
Next we consider simultaneous determination of pricing and inventory strategies. We first analyze a single location periodic review model. Demands in consecutive periods are independent, but depend on the item's price in accordance with general stochastic demand functions. The price in any period can be specified dynamically. Replenishment orders may be placed at the beginning of some or all periods. We address finite and infinite horizon models, maximizing total expected discounted profits or their time average value, assuming that prices can be adjusted arbitrarily or that they can only be decreased. We characterize the structure of the optimal strategies, and develop an efficient value iteration method to compute these strategies. We report on a numerical study characterizing various qualitative properties of the optimal strategies and corresponding optimal profit values.
We then address distribution systems with geographically dispersed retailers. The stochastic demand functions may vary by retailer and period. The demands faced by different retailers in any period may be correlated, but are independent across time. In each period, all retailers adopt a common price. Inventory replenishments are coordinated via a common facility. We derive an analytical approximation method for system-wide profits, which is also used to develop effective combined pricing, ordering, and allocation strategies. We show that the system's performance under these strategies is well reflected by the above approximations. We gauge the benefits of coordinated replenishments and assess the impacts of different types of geographic dispersion and various system parameters. We also study the impact of leadtime reductions and delayed geographic differentiation.