Coordination in a two‐stage capacitated supply chain with multiple suppliers

The aim of this paper is to coordinate the inventory policies in a decentralized supply chain with stochastic demand by means of contracts. The system considered is a decentralized two‐stage supply chain consisting of multiple independent suppliers and a manufacturer with limited production capacities. The suppliers operate on a make‐to‐stock basis and apply base stock policy to manage their inventories. On the other hand, the manufacturer employs a make‐to‐order strategy. Under the necessary assumptions, each supplier is modeled as an M/M/1 make‐to‐stock queue; and the manufacturer is modeled as a GI/M/1 queue after deriving an approximate distribution for the interarrival times of the manufacturer. Once the supply chain is modeled as a queuing system, centralized and decentralized models are developed. Comparison of the optimal solutions to these models reveals that the supply chain needs coordination. Three different transfer payment contracts are examined in this paper. These are the backorder and holding cost subsidy contracts, the transfer payment contract based on Pareto improvement, and the cost sharing contract. Each contract is evaluated according to its coordination ability and whether it is Pareto improving or not. The results indicate that all three contracts can coordinate the supply chain. However, when the Pareto improvement is taken into account, the cost sharing contract seems to be the one that will be preferred by all parties.