Synchronizing Pricing and Replenishment to Serve Forward-Looking Customers with Lost Sales

[Problem Definition] We incorporate heterogeneous customer valuation and the strategic customer behavior in the classical economic order quantity (EOQ) setting. The seller incurs setup costs when replenishing inventory, and can set the prices differently over time and implement capacity rationing. [Academic/ Practical Relevance] While similar ideas of market segmentation and intertemporal price discrimination can be carried over from the travel industries to other industries, there are new aspects when applying these concepts to retail outlets and supermarkets, because they usually face inventory replenishment problems. This makes the joint inventory replenishment and revenue management problem imperative. [Methodology] We adopt the mechanism design and dynamic programming approaches. [Results] We establish the optimality of cyclic intertemporal price discrimination, even if the customers are endowed with homogeneous valuations. Under the optimal policy, the replenishments and price promotions are synchronized, and the seller adopts the highest selling price when the inventory level is the lowest and plans discontinuous price discount at the replenishment point when the inventory is the highest. We also show that, under inventory-based pricing there is a direct mapping between deterministic and stochastic arrivals scenarios, and randomness on the arrivals per se does not alter the structure of the optimal policy. [Managerial Implications] This cyclic pricing scheme offers a stark contrast to the "low-price-every-day" scheme and achieves overall higher profit because customer strategic behavior offers additional flexibility to the seller in managing his inventory. Furthermore, because strategic customers are willingly backlogged, this creates opportunities for the seller to work with the customers to achieve a lower operational cost and a higher overall profit.