International Journal of Strategic Decision Sciences, 4(4), 55-71, October-December 2013 55 Copyright © 2013, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. ABSTRACT In this paper, the authors address the problem of network design for a closed-loop supply chain. The prob- lem is formulated as a mixed zero-one bi-level optimization model, with the manufacturer as the leader who minimizes his costs at the upper level, and a forwarding agent dealt with as the follower. The leader decides on the locations of the facilities, and the forwarding agent builds the forward and reverse transportation plans so as to minimize the total transportation cost. A genetic algorithm solution method is used to obtain the Stackelberg solution. Furthermore, the algorithm uses penalty functions to handle the constraints. The solution algorithm is implemented in Matlab, utilizing LINGO 11.0 (2008) to solve each lower level problem instance. Finally, the accuracy of the model is tested on a set of numerical experiments. Multi-Level Programming Approach to a Closed-Loop Supply Chain Network Design Sima Ghayebloo, Department of Industrial Engineering, K. N. Toosi University of Technology, Tehran, Iran Mohammad Jafar Tarok, Department of Industrial Engineering, K. N. Toosi University of Technology, Tehran, Iran Mostafa Abedzadeh, Department of Industrial Engineering, K. N. Toosi University of Technology, Tehran, Iran Claver Diallo, Department of Industrial Engineering, Dalhousie University, Halifax, Canada Keywords: Closed-Loop Supply Chain, Multi-Level Programming, Network Design, Reverse Logistics, Stackelberg Solution 1. INTRODUCTION The managing of end-of-life products is called reverse logistics (Gupta, 2007). Reverse lo- gistics (RL) is the process of planning, imple- menting, and controlling the flow of unused materials from markets or usage areas to a point of recovery or proper disposal. More precisely, RL is the process of moving goods from their typical final destination for the purpose of capturing value, or proper disposal (Rogers, 1998). Fleischmann et al. (Fleischmann, 2000) state that product recovery not only reverses the product stream with the consequence that there are many supply sources and few demand points, but that the design is severely complicated by the high uncertainty levels in many factors. DOI: 10.4018/ijsds.2013100104