A proposed mathematical model for closed-loop network configuration based on product life cycle

Products may be returned over their life cycle. Industrial experiences show that there are three main return-recovery pairs. Commercial returns are repaired. End-of-use returns often are remanufactured. In addition, end-of-life returns are recycled. However, up to now, no optimization model is proposed for closed-loop configuration based on three return-recovery pairs. The repaired and remanufactured products can be sold in the same or secondary market. In this paper, we design and configure a general closed-loop supply chain network based on product life cycle. The network includes a manufacturer, collection, repair, disassembly, recycling, and disposal sites. The returned products are collected in a collection site. Commercial returns go to a repair site. End-of-use and end-of-life returns are disassembled. Then, end-of-life returns are recycled. The manufacturer uses recycled and end-of-use parts and new parts to manufacture new products. The new parts are purchased from external suppliers. A mixed-integer linear programming model is proposed to configure the network. The objective is to maximize profit by determining quantity of parts and products in the network. We also extend the model for the condition that the remanufactured products are sent to the secondary market. The mathematical models are validated through computational testing and sensitivity analysis.