The yield rate paradox in closed-loop supply chains

We investigate the dynamics of a closed-loop make-to-stock supply chain consisting of a remanufacturer and a manufacturer with a first-order vector auto-regressive demand and return process. Remanufactured products, considered as-good-as-new, partially satisfy market demand; newly manufactured products fill the remainder. The manufacturer and the remanufacturer cooperate to minimize the sum of the 1) capacity costs at the remanufacturing and manufacturing processes, 2) finished goods inventory holding and backlog cost, 3) cost to dispose of returned items not re-manufactured and 4) collection cost. The remanufacturer inspects returned products in a triage process. Only a predetermined fraction (the triage yield rate) of the returns are re-manufactured. We investigate the impact of the triage yield on the system-wide cost. In a cost-sensitive setting, when the unit cost of remanufacturing is lower than the unit cost of manufacturing, it seems reasonable to conjecture that higher triage yields lead to lower system-wide costs. We show the system-wide cost is always convex in the triage yield rate, suggesting system-wide costs could actually increase in the triage yield rate, even when the unit remanufacturing cost is lower than the manufacturing cost. This yield rate paradox originates from the increased yields creating additional variability in the manufacturing activities. By investigating boundary conditions we find the minimal disposal penalty required to entice the remanufacturer to process all returns.