Supply commitment contract in capacity allocation games

This paper considers a supply chain with one supplier and two retailers. The supplier has limited normal capacity. When the orders of two retailers exceed the capacity, the supplier can satisfy the retailers with the limited normal capacity, or he can start an emergent production to increase his capacity in a short time with a high unit production cost. When the cost of quickly expanding capacity is lower than the market price, it is profitable for the whole system to start the emergent production. But the supplier has no incentives to do additional production if his cost is higher than the wholesale price. To resolve this issue, we propose a supply commitment contract that the supplier will fully fill a retailer’s order if the retailer pays a premium to the supplier. We consider a practical setting that each retailer has private information on her average demand. Two contracting scenarios of the supplier are compared: contracting with the two retailers simultaneously (the simultaneous scenario) and sequentially (the sequential scenario). It is shown that the retailers will adopt the threshold strategy based on their private demand information to pay the premium. By numerically studies, we further illustrate the supplier’s optimal contract choices and the consequent system performance. First, the suppliers always prefer the retailers to move simultaneous although the supplier’s profit is only slightly higher than that of the sequential scenario; second, the supplier sets a lower wholesale price and a higher commitment fee in the sequential scenario than those of simultaneous scenario; finally, the sequential scenario is a better choice from the perspectives of both the whole supply chain system and the retailers. Our research recommends the sequential moving in the supply commitment contract that it benefits the whole supply chain system with only slightly less efficient for the supplier.