Pricing, replenishment, and timing of selling in a market with heterogeneous customers

We consider a deterministic pricing and replenishment model in which the retailer advertises a fixed price and the selling schedule, and customers can advance or delay their time of purchase incurring holding or shortage costs. We investigate the impact of heterogeneity in the customers' reservation prices. We show that the resulting optimal solution may be very different from that obtained when customers are homogeneous. We identify nine types of possible optimal sales strategies, and compute their profits. In particular, the solution may contain sales at several discrete points of time between consecutive replenishment epochs with no sales between them.