The integrated production-inventory-routing problem in the context of reverse logistics: The case of collecting and remanufacturing of EOL products

Production-planning, inventory control with returns management, and vehicle routing are critical and highly related problems in the design of closed-loop supply chain networks. In this paper, we address an extension of the Integrated Production-Inventory-Routing Problem (IPIRP) since we consider recovery and remanufacturing of End-Of-Life (EOL) products as a sustainable aspect. A mathematical programming formulation is proposed for the considered problem. The objective is to determine both the optimal amounts of goods (lot-sizes) to be manufactured, remanufactured and stored while meeting customers' requests (deliveries and pick-ups) with a minimum total cost due to the integrated operations considered. The originality of our study lies in the fact of jointly treating the capacited dynamic lot-sizing with remanufacturing problem and the vehicle routing problem with simultaneous pick-up and delivery. Some numerical examples to illustrate the relevance of our proposed model are given.