Survey Covering problems in facility location: A review Reza Zanjirani Farahani a,⇑ , Nasrin Asgari b,1 , Nooshin Heidari c , Mahtab Hosseininia c , Mark Goh d,e a Department of Informatics and Operations Management, Kingston Business School, Kingston University, Kingston Hill, Kingston Upon Thames, Surrey KT2 7LB, UK b Centre for Maritime Studies, 12 Prince George’s Park, National University of Singapore, Singapore 118411, Singapore c Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran d School of Business, 15 Kent Ridge Drive, National University of Singapore, Singapore 119245, Singapore e School of Management, University of South Australia, Adelaide, Australia article info Article history: Received 16 August 2010 Received in revised form 25 August 2011 Accepted 27 August 2011 Available online 1 September 2011 Keywords: Facility location Covering problem Mathematical formulation Survey abstract In this study, we review the covering problems in facility location. Here, besides a number of reviews on covering problems, a comprehensive review of models, solutions and applications related to the covering problem is presented after Schilling, Jayaraman, and Barkhi (1993). This survey tries to review all aspects of the covering problems by stressing the works after Schilling, Jayaraman, and Barkhi (1993). We first present the covering problems and then investigate solutions and applications. A summary and future works conclude the paper. Crown Copyright Ó 2011 Published by Elsevier Ltd. All rights reserved. 1. Introduction Facility location is a critical component of strategic planning for a broad spectrum of public and private firms (Owen & Daskin, 1998). For this, it is necessary to consider many criteria such as cost or distance from demand points. Many models have been made to help decision making in this area. The readers who are interested in learning about facility location models are referred to the works of Francis and White (1974), Handler and Mirchandani (1979), Love, Morris, and Wesolowsky (1988), Francis, McGinnis, and White (1992), Mirchandani and Francis (1990), Daskin (1995), Drezner (1995), Drezner and Hamacher (2002), Nickel and Puerto (2005), Church and Murray (2009) and Farahani and Hekmatfar (2009). One of the most popular models among facility location models is covering problem. While covering models are not new they have always been very attractive for research. This is due to its applica- bility in real-world life, especially for service and emergency facil- ities. In some covering problems, a customer should be served by at least one facility within a given critical distance (not necessarily the nearest facility). In most of the covering problems, customers receive services by facilities depending on the distance between the customer and facilities. The customer can receive service from each facility which its distance from customer is equal or less than a predefined number. This critical predefined number is called coverage distance or coverage radius (Fallah, NaimiSadigh, & Aslanzadeh, 2009). Therefore, the concept of coverage is related to a satisfactory method rather than a best possible one. Many of the problems like determining the number and locations of public schools, police stations, libraries, hospitals, public buildings, post offices, parks, military vases, radar installations, branch banks, shopping centers and waste-disposal facilities can be formulated as covering problems (Francis & White, 1974). The scope of this survey is exclusively limited to the review of articles related to covering problem in facility location. Schilling, Jayaraman, and Barkhi (1993) present a literature re- view on covering problems in facility location. Since they present a very comprehensive review considering publications up to 1991, we have tried to consider covering researches after this time. How- ever, this paper also covers some older papers that are both very important and basic from classification point of view or have not been in the domain of Schilling et al. (1993). Schilling et al. (1993) classify models which use the concept of covering in two categories: (1) Set Covering Problem (SCP) where coverage is required and (2) Maximal Covering Location Problem (MCLP) where coverage is optimized. For each category, they provide taxonomy according to topological structure, nature of demand, characteristic of facility to be sited and application in public or private sectors. Also, based on solution methods – either optimal or heuristic – a classification is proposed. Owen and Daskin (1998) present an overview of facility location literature considerings stochastic or dynamic problem characteristics. Conforti, Cornuéjols, Kapoor, and VuŠkovic ´ (2001) study results and also open problems on perfect, ideal and balanced metrics related to set packing and set covering problem. Also Berman, 0360-8352/$ - see front matter Crown Copyright Ó 2011 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.cie.2011.08.020 ⇑ Corresponding author. Tel.: +44 (0)20 8417 5165; fax: +44 (0)20 8417 5024. E-mail addresses: Zanjiranireza@gmail.com (R.Z. Farahani), asgarin@gmail.com (N. Asgari), bizgohkh@nus.edu.sg (M. Goh). 1 Fax: +65 6775 6762. Computers & Industrial Engineering 62 (2012) 368–407 Contents lists available at SciVerse ScienceDirect Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie