Socially concerned periodic review replenishment system with customer service level and supply chain contracting

This study contributes to the periodic review inventory system literature by: (1) investigating customer service level (CSL) as a social responsibility in pharmaceutical supply chains (PSCs) and (2) proposing supply chain contracting to achieve win–win coordination and guarantee a satisfied CSL. Specifically, considering the demand uncertainty as one of the main challenges faced by pharmacies, we analyze how applying contracts to coordinate the inventory policy of a pharmacy with that of its supplier can affect their profits and the CSL offered to society. Having shown the advantages of the centralization compared to the decentralization, we design a coordination scheme based on the quantity discount contract to encourage the players move towards centralization. Under the proposed scheme, we first obtain the minimum and maximum acceptable amounts of discount from each actor’s viewpoint. Then, we propose a benefit-sharing strategy in order to make the plan interesting to both sides. The proposed discount contract and benefit-sharing strategy distribute the extra profits equitably between the two participants according to their bargaining power, which can make a win–win condition for two actors. Our results suggest that coordinating review period and order-up-to-level of the retailer and replenishment multiplier of the supplier will be of benefit in terms of both economic profitability and social responsibility.