A model for a production-repair system under a time-varying demand process

In this study, we consider a production system that satisfies a continuous time-varying demand for a finished product over a known and finite planning horizon by supplying either new products or repaired used products. Our model assumes that new products are fabricated from a single type of raw material procured from external suppliers, while used products are collected from the customers and then repaired to an 'as new' condition before being sold again. However, we assume that there is no further collection of used products during the period when they are being repaired or shipped. The problem is to determine a joint policy for raw materials procurement, new products production and used products repair such that the total relevant cost of the system is minimized. We propose a numerical solution procedure based on Microsoft Excel Solver's nonlinear mathematical programming function. Then, the procedure is illustrated with a numerical example.