Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 320913, 19 pages
Research Article

Optimal Control of Production and Remanufacturing in a Reverse Logistics Model with Backlogging

1Department of Business Administration, University of Macedonia, 54006 Thessaloniki, Greece
2Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece

Received 24 June 2010; Revised 8 September 2010; Accepted 15 September 2010

Academic Editor: G. Rega

Copyright © 2010 I. Konstantaras. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Reverse logistics activities have received increasing attention within logistics and operations management during the last years, both from a theoretical and a practical point of view. The field of reverse logistics includes all logistics processes starting with the take-back of used products from customers up to the stage of making them reusable products or disposing them. In this paper, a single-product recovery system is studied. In such system, used products are collected from customers and are kept at the recoverable inventory warehouse in view to be recovered. The constant demand rate can be satisfied either by newly produced products or by recovered ones (serviceable inventory), which are regarded as perfectly as the new ones. Excess demand is completely backlogged. Following an exact analytical approach, the optimal set-up numbers and the optimal lot sizes for the production of new products and for the recovery of returned products are obtained. A numerical cost comparison of this model with the corresponding one without backordering is also performed.