Ordering, pricing and allocation in a service supply chain

In this paper, we study a two-stage game problem on pricing, ordering and allocation in a service supply chain, where one supplier sells a product with a fixed capacity to customers via two retailers under wholesale price contracts. The two retailers face random demands and order from the supplier. The supplier needs to allocate its capacity to retailers according to some allocation rule when its capacity cannot fit the retailers' order. We study two decentralized supply chains, where retail prices are determined by the supplier or the retailers. For each model, we derive and characterize the equilibrium by transforming the game problem into an optimization problem. We find that under the leader of the supplier the competition between the two retailers is eliminated and each retailer just orders its optimal quantity. So, the retailers' behavior in the game is not influenced by the supplier's allocation rule. Furthermore, with pricing power, the supplier can get higher profit but the retailers would not necessarily.