Purchasing and remanufacturing decisions with different quality returned material and finished goods

To transition from a linear to a circular value chain, an effective refurbishment policy is crucial to preserve material value and functionality at the end of a product's life-cycle. This study examines a refurbisher that processes first- and second-quality returned materials to produce first- and second-quality products in a make-to-stock system. The refurbisher makes purchasing decisions for the returned materials and determines whether to refurbish or remain idle, and if refurbishing, how to convert them into finished goods of varying quality. There are five refurbishment decisions (converting first-quality to first- or second-quality, second-quality to first- or second-quality, or no production) and two purchasing decisions for the materials. With production and arrival times modelled as exponential random variables, the optimal control problem is formulated as a Markovian Decision Process, using a long-run average profit criterion to identify optimal decisions. A linear programming approach is employed for numerical optimisation. Results show that the most profitable option based solely on sales prices, purchasing, and conversion costs may not be optimal. Instead, the optimal policy is influenced by per-unit profit differences, returned material availability, demand rates, and production times across various refurbishment scenarios.