Economic order quantity of deteriorating drugs with new and redistributed demands in a closed-loop supply chain: from the viewpoint of a hospital pharmacy

Drug waste poses significant economic and environmental challenges as unused medicines are frequently discarded. This study develops an economic order quantity (EOQ)-based inventory control framework integrating new and recycled drugs while accounting for degradation effects and government incentive policies within a closed-loop pharmaceutical supply chain (CLPSC). The framework captures interactions among stakeholders, logistics and information flows, assuming a fixed deterioration rate. Pharmacies dispense medications via prescriptions and recycle unused drugs under government supervision; substandard items are incinerated while acceptable ones are resold at incentivised prices. Focusing on a hospital pharmacy's perspective, the model examines supply–demand scenarios to minimise total costs, including ordering, holding, recovery, inspection, incineration and deterioration costs. Optimal policies are analytically derived and verified for convexity via Hessian matrices. Numerical results show that, under the scenario of the supply rate of redistributed drugs exceeding their demand rate, the deteriorating drug inventory model affects the decisions on determining the optimal ordering quantity for new and redistributed drugs. Sensitivity analyses reveal that supply and demand rates are critical parameters for making ordering decisions. This research provides a practical reference for policymakers and pharmacy managers seeking cost-effective, sustainable drug recycling strategies that reduce pollution and support sustainable development goals (SDGs).