The economic lot-sizing problem with remanufacturing and inspection for grading heterogeneous returns

Abstract

We address an extension of the economic lot-sizing problem with remanufacturing in which returns are assumed dissimilar and an inspection activity is required in order to grade them into a finite number of pre-established nominal qualities of either remanufacturable or non-remanufacturable returns. There are set-up costs related to the production activities, including inspection. Separate inventories are assumed for incoming returns, inspected-and-graded returns and serviceable (new or remanufactured) products. Remanufacturing, discarding and inventory holding costs depend on the quality of the returns. The objective is to determine when and how much to inspect, remanufacture, discard and produce in order to meet the demand requirements on time, minimizing the sum of all the involved costs. For this problem we provide a mathematical programming formulation and suggest several lot-sizing rules based on different inspection and remanufacturing decisions. We also show the problem is NP-hard and provide a property about the form of its optimal solutions. An extensive numerical experimentation is conducted in order to analyse the behaviour of the lot-sizing rules suggested, considering different values for the problem parameters. The results obtained show that remanufacturing can offer economic benefits even in the case of an independent and relatively expensive inspection. In addition, we can conclude that the inspection of all incoming returns is in general the most cost-effective decision, even if not all of them are remanufactured.