Journal of Manufacturing Systems 40 (2016) 1–8 Contents lists available at ScienceDirect Journal of Manufacturing Systems j ourna l h omepage: www.elsevier.com/locate/jmansys A closed-loop supply chain management problem: Reformulation and piecewise linearization Mohammed Al-Salem a , Ali Diabat b,∗ , Doraid Dalalah c , Mahmoud Alrefaei d a Department of Mechanical and Industrial Engineering, Qatar University, Doha, Qatar b Department of Engineering Systems & Management, Masdar Institute of Science & Technology, Abu Dhabi, United Arab Emirates c Department of Industrial Engineering, Jordan University of Science and Technology, Irbid, Jordan d Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan a r t i c l e i n f o Article history: Received 27 April 2014 Received in revised form 11 April 2016 Accepted 13 April 2016 Keywords: Reverse logistics Inventory management Warehouse location Closed-loop supply chains a b s t r a c t Recent environmental considerations as well as advancements in the field of logistics have promoted the integration of the forward and reverse supply chains, in order to increase operational efficiency and sup- port sustainable operations. In light of this, we formulate a mixed integer non-linear program (MINLP) that describes both the forward and reverse flow of a single type of product, through a set of warehouses whose location is determined based on whether they serve as forward, reverse or joint warehouses deal- ing with products from both directions. The objective of the model is to minimize the total costs, which include fixed location, fixed ordering, inventory holding, transportation as well as re-processing costs, the latter referring to returned products. In order to overcome the non-linearity of the formulation, the respective constraints are linearized, while for the non-linear terms of the objective function a piecewise linearization is proposed. The computational analysis focuses on comparing the results obtained by solv- ing the MINLP in commercial software with the results obtained from implementing the linearization for a different number of adopted segments for the piecewise linearization. In addition, both integrated approaches are compared to the sequential approach, according to which the location, ordering and transportation problems are initially solved, producing an output that is subsequently used as an input to solve the inventory problem. Results demonstrate the benefits of integration as well as the cost savings that can be achieved due to the closed loop consideration of the supply chain. A discussion of these results produces useful insights for supply chain operators. © 2016 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved. 1. Introduction Companies are constantly aiming to improve the design of their supply chains amid accelerated growth and fierce competition of contemporary global markets. Conventional supply chain prac- tices are being constantly re-evaluated as companies find ways of increasing the efficiency and accuracy of their operations. One of the traditional practices that is changing in a supply chain is the flow of products, which in no longer only in the forward direction. In order to make use of returned products companies are adopting reverse logistics in addition to forward logistics, forming what is known as a closed-loop supply chain. One of the reasons for this is the growing interest in product recovery and material recycling, which has expanded the scope of traditional supply chains to include final-users, collection centers, de-manufacturers or ∗ Corresponding author. Tel.: +971 2 810 9101; fax: +971 2 810 9901. E-mail address: adiabat@masdar.ac.ae (A. Diabat). remanufacturers. This growing interest is also reflected in recent research streams. Alshamsi and Diabat [1] address one reverse logistics network which takes into account the optimal selection of sites, the capacities of inspection centers and remanufacturing facilities. Aside from redesigning the supply chain network, Govin- dan et al. [2] focus on reviewing the coordination by contracts of the forward and reverse supply chains, and the authors provide the contract classification based on the criteria of transfer payment contractual incentives and inventory risk sharing. Another traditional approach that is changing is that decisions at different levels of the supply chain are now being considered simultaneously rather than sequentially. With regards to decision making levels, supply chain management can be categorized into strategic, tactical and operational level decisions, depending on the frequency of making them or the time-frame of impact. For exam- ple, decisions on the strategic level have a long-term impact of the company; examples include the location of warehouses, which is a decision usually made once or twice over the life of the com- pany. Tactical level decisions occur at the frequency of several times http://dx.doi.org/10.1016/j.jmsy.2016.04.001 0278-6125/© 2016 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.