Optimal acquisition and refurbishing policies with quality-based cost

Motivated by the remanufacturing industry practice, a refurbishing system, composed of a collection center and a refurbishing center, is studied, where the refurbishing and inspecting costs are dependent on the quality of returned items. First a stochastic profit model is formulated, to make decisions on how many returned items are collected and what quality levels of the returned items are refurbished, so as to maximize the total expected profit. Then we prove the existence and uniqueness of the optimal solution of the acquisition quantity and derive the formulation of the optimal solution. Finally, numerical examples are provided to validate the results and show the impact of quality on acquisition policy.