Payment schemes for a two-level consignment stock supply chain system

•Two-level supply chain with consignment stock agreement.•Different payment schemes were considered.•Equal payments at equal intervals scheme was shown to be the most profitable.•Profit sharing scenarios were also considered.

Inventories account for almost 50% of the total logistics costs of a supply chain. Therefore, managing inventories helps organizations to reduce costs, increase profits, and satisfy customers’ demand. Different inventory models have been developed to solve transportation and warehousing issues. These models help in optimizing different supply chain systems and maximizing their total profits. Coordinating orders between players has been shown to be profitable. A Consignment Stock (CS) agreement as a coordination mechanism has been receiving attention from practitioners and academicians. This paper reflects one reality of CS agreements and investigates the effects of four different payment schemes on the total profit of the system when a consignment stock agreement is adopted between a vendor and a buyer. The results showed that adopting a scheme that makes frequent and equal payments is often better than the other payment schemes compared in this paper. It was also shown in the paper that finding the optimum number and size of payments enhances the performance of the supply chain system and its total profit.