Abstract: This paper studied a two-level supply chain with one supplier and one retailer. The retailer sources products from the supplier and sells them to the end customers, and customer demand is uncertain. Due to the long lead time, the supplier needs to build capacity before receiving orders from the retailer. If the supplier assumes all the cost of building enough capacity to meet demand while the retailer assumes no cost, it is not clear that the supplier will build enough capacity. Motivated by the observations, we consider two types of contract relationship between the supplier and the retailer: wholesale price only contract and capacity cost sharing contracts. We first characterize the optimal decisions of the supplier’s and the retailer’s under two cases. We then show that the supplier is willing to build more capacity under the cost sharing contract and such a contract increases the expected profits of the supplier and the retailer. Finally, through a numerical study, we demonstrate how the retailer’s and the supplier’s optimal decisions and their resulting expected profits are affected by the specific terms of the cost sharing contracts.

Key words: supply chain contracting, stochastic demand, capacity investment, costsharing