Production-Inventory Control in an EOQ-Type Reverse Logistics System

Abstract

In this paper a general reverse logistics system to satisfy a steady demand for one product by production and recycling is studied. The model incorporates the two extreme policies of production (the pure production model) and of recycling (the pure recycling model) only. This general model, which has been introduced recently by the authors and is therefore called RD-model, examines the possibility of repurchasing and recycling or disposing used items. Since the total cost of the model contains both EOQ-related (setup cost and holding cost) and non-EOQ-related costs (waste disposal, recycling, production and repurchasing costs), first the optimal lot sizes for the EOQ-related cost function are presented. Then, the transformation of the RD-model into a special fractional optimization program follows. The optimization program for the RD-model, let us call it RD-program, includes other known EOQ recovery models as special cases and, in this sense, it can be regarded as a meta program for all of them. An analysis of the material flow in various models will be provided, and a classification of the models is suggested. Moreover, cost-minimal repurchasing rates and use rates of used items are determined. The analysis shows — as it is known for other models — that the mixed strategies of combining production and recycling are dominated by the pure strategies (either production or recycling), i. e. — if technologically feasible — either pure production or recycling is optimal.