Theory and methodology on the global optimal solution to a General Reverse Logistics Inventory Model for deteriorating items and time-varying rates

In this paper, we present a unified general inventory model for integrated production of new items and remanufacturing of returned items for an infinite planning horizon. Our model considers a production environment that consists of three shops. The first shop is for remanufacturing returned items, the second shop is for manufacturing new items, while the third shop is for collecting returned items to be remanufactured in the first shop. The system is subject to joint production and remanufacturing options, the first one is to produce new items while the second one is to reproduce/recycle the returned items “as-good-as new”. Items deteriorate while they are in storage, and production, remanufacturing, demand, return, and deterioration rates are arbitrary functions of time. A closed form for the total relevant costs as well as a rigorous mathematical proof, which shows the global optimality of the solution to the underlying inventory system are introduced. Illustrative examples, which explain the application of the theoretical results as well as their numerical verifications, are also given.