O.R. Applications Combination of MCDM and covering techniques in a hierarchical model for facility location: A case study Reza Zanjirani Farahani a, * , Nasrin Asgari b a Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran b Supply Chain Management Research Group, Tehran, Iran Received 27 July 2004; accepted 27 October 2005 Available online 19 January 2006 Abstract In this paper, locating some warehouses as distribution centers (DCs) in a real-world military logistics system will be investigated. There are two objectives: finding the least number of DCs and locating them in the best possible locations. The first objective implies the minimum cost of locating the facilities and the latter expresses the quality of the DCs locations, which is evaluated by studying the value of appropriate attributes affecting the quality of a location. Quality of a location depends on a number of attributes; so the value of each location is determined by using Multi Attribute Decision Making models, by considering the feasible alternatives, the related attributes and their weights according to decision maker’s (DM) point of view. Then, regarding the obtained values and the minimum number of DCs, the two objective functions are formed. Constraints imposed on these two objectives cover all centers, which must be supported by the DCs. Using Multiple Objective Decision Making techniques, the locations of DCs are determined. In the final phase, we use a simple set partitioning model to assign each supported center to only one of the located DCs. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Location; MADM; Set covering; MODM; Set partitioning 1. Introduction In this paper, a real-world case study about locating supportive centers in a military logistics system will be investigated. First, we give a summary of the functions of this system; then the scope of the problem will be presented. 0377-2217/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2005.10.039 * Corresponding author. Tel.: +98 21 66413034/66497; fax: +98 21 66413025. E-mail address: farahan@aut.ac.ir (R.Z. Farahani). European Journal of Operational Research 176 (2007) 1839–1858 www.elsevier.com/locate/ejor