A Single-Supplier, Multiple-Retailer Model with Single-Season, Multiple-Ordering Opportunities, and Fixed Ordering Cost

In this paper, we discuss the replenishment decision of seasonal products in a two-echelon distribution system consisting of a supplier and multiple retailers. Due to long manufacturing lead time, the supplier orders its entire stock for the season well in advance. The retailers, on the other hand, can replenish their inventory from the supplier throughout the season as demand realizes. Demand at each retailer follows a Poisson process. Each retailer order incurs a fixed cost, and the usual understocking and overstocking costs occur. When retailer lead time is negligible, we show that it is optimal for the retailer to follow a time-based, order-up-to policy and order only when inventory is depleted. We also characterize the structure of the optimal policy and propose a number of heuristics for easier computation. For the supplier, we express the distribution of total demand. This allows the supplier to solve a classic newsvendor problem to determine the total stock for the season. We find that the optimal retailer policy can sometimes cause large demand variation for the supplier, resulting in lower supplier profit. In centralized settings, this may even result in lower system profit than some naïve retailer heuristics, creating inefficiency in the supply chain. We offer insights on potential causes and managerial implications.