We consider the problem of managing inventories and dynamically adjusting retailer prices in distribution systems with geographically dispersed retailers. More specifically, we analyze the following single item, periodic review model. The distribution of demand in each period, at a given retailer, depends on the item's price according to a stochastic demand function. These stochastic demand functions may vary by retailer and by period. The replenishment process consists of two phases: In some or all periods, a distribution center may place an order with an outside supplier. This order arrives at the distribution center after an "order leadtime" and is then, in the second phase, allocated to the retailers. Allocations arrive after a second "allocation leadtime."
We develop an approximate model that is tractable and in which an optimal policy of simple structure exists. The approximate model thus provides analytically computable approximations for systemwide profits and other performance measures. Moreover, the approximate model allows us to prove how various components of the optimal strategy (i.e., prices and order-up-to levels) respond to shifts in the model parameters, e.g., to shifts in the retailers' demand functions. In addition, we develop combined pricing, ordering, and allocation strategies and show that the system's performance under these strategies is well gauged by the above approximations. We use this model to assess the impact of different types of geographic dispersion on systems with dynamically varying prices and how different system parameters (e.g., leadtimes, coefficients of variation of individual retailers' demand, price elasticities) contribute to this impact. Similarly, we use the model to gauge the benefits of coordinated replenishments under dynamic pricing, and how these benefits increase as the allocation decisions of the systemwide orders to individual retailers are postponed to a later point in the overall replenishment leadtime.
We report on a comprehensive numerical study based on data obtained from a nationwide department store chain.