A Sustainable Closed-Loop Supply Chains Inventory Model Considering Optimal Number of Remanufacturing Times

The mathematical modeling of reverse logistics inventory systems ignores the fact that returned items may arrive out of sequence, i.e., with different number of remanufacturing times. Moreover, such modeling assumes that the retuned items may retain the same quality upon recovery regardless of how many times they have been previously remanufactured. This paper develops a new mathematical expression of the percentage of retuned items that can be remanufactured a finite number of times. The proposed expression is modeled as a function of the expected number of times an item can be remanufactured in its lifecycle and the number of times an item can be technologically (or optimally) remanufactured based on its quality upon recovery. The model developed in this paper considers joint production and remanufacturing options. The return rate is a varying demand-dependent rate, which is a decision variable with demand, product deterioration, manufacturing, and remanufacturing rates being arbitrary functions of time. The model considers the initial inventory of returned items in the mathematical formulation, which enables decision-makers to adjust all functions and input parameters for subsequent cycles. Illustrative examples indicate that dependent purchasing price of recovery items and the incorporation of remanufacturing investment cost significantly impact the optimal remanufacturing policy.