Coordination of Closed-loop Supply Chains by a Contract: A Quantitative Analysis for Single-period Products

This paper aims at designing a supply contract to coordinate a closed-loop supply chain for a single-period product. The model addresses a supply chain wherein a supplier with infinite capacity serves a retailer facing a random demand. The retailer offers two purchasing options to the customers, who are assumed price-sensitive: to buy the product at (i) full price or (ii) discounted price but giving back the worn-out one. Depending on the nature of the returned item, the retailer can either sell it on a secondary market or transfer it to the supplier, still receiving money in return. Both the optimal order quantity and the optimal discount coefficient are analytically defined in two standard settings - named centralized and decentralized - and in four contract-based settings. The centralized setting aims at maximizing the overall utility regardless of how this is shared along the supply chain. Under the decentralized setting, actors make decision independently. The contract-based settings (which define diverse ways to share the salvage and recovery values between the actors) are based on two parameters, which make both actors benefit from the coordination: a wholesale price, which is agreed by the actors, and a sharing factor that establishes the quota of the retailer's revenue that is passed up to the supplier. Under the contract agreements, individual as well as supply chain expected profits are analytically defined and compared with those obtained under the other settings to prove the achievement of channel coordination and the win-win conditions.