The implications of contract timing on a supply chain with random yield

We investigate the impact of contract timing on a random yield supply chain consisting of a single buyer and multiple unreliable suppliers. In this supply chain, the buyer decides the order quantity and the suppliers decide the capacity levels which depend on the random yield rates. According to the sequence of these two decisions, we consider two contracts. If the buyer places the order prior to the supplier's capacity decision, we call it EA (ex-ante) contract. On the other hand, if the supplier's capacity decision comes first, we call it EP (ex-post) contract. Two different effects, the Ex-ante Ordering Effect and the Risk Pooling Effect are identified. The Ex-ante Ordering Effect represents that the buyer will increase the order quantity compared to the benchmark case with no random yield in both one-supplier and multiple-supplier settings under EA contract. The Risk Pooling Effect indicates that the buyer will increase the total order quantity as the number of unreliable suppliers increases in the multiple-supplier setting under both EA and EP contracts. As the number of unreliable suppliers increases, the reduction of supply uncertainty from suppliers will induce the buyer to increase the total order quantity. Furthermore, we show that the supplier prefers EA contract only if the number of suppliers is small, whereas the buyer unambiguously prefers EA contract because of the first-move advantage in the game. That is, both the buyer and supplier are better off from the buyer's ordering decision prior to the supplier's capacity decision in the one-supplier setting. However, in case of multiple suppliers, the buyer still prefers to order first, whereas the suppliers should decide the capacity investment first if the number of competitive suppliers is large.