A delay-in-payment contract for Pareto improvement of a supply chain with stochastic demand

• We consider supply chain coordination with stochastic demand for infinite horizon.
• We propose a delay-in-payment contract to coordinate the supply chain.
• The system is formulated as a stochastic dynamic programming problem.
• Compared with the traditional wholesale-price contract, the system can achieve Pareto improvement with the delay-in-payment contract.

We consider a supply chain consisting of a single supplier and a single retailer with stochastic customer demand, which is operated over an infinite horizon. We propose a delay-in-payment contract to coordinate the supply chain. With this contract, the supplier allows the retailer to pay partial order cost at the ordering epoch, and to pay the remaining portion after a permissible number of periods. The system is formulated as a stochastic dynamic programming problem. It is shown that there exists a base-stock policy to be optimal. Compared with the traditional wholesale-price contract, the delay-in-payment contract with appropriate parameters can achieve a Pareto improvement (i.e., the performances of both the supplier and the retailer using the delay-in-payment contract are better than those using the wholesale-price contract). Numerical studies are performed to investigate both the effectiveness of the Pareto improvement, and the impact of the major parameters of the delay-in-payment contract on the system performance.