Hierarchical Location Problem
Many facility systems are hierarchical in nature. These facilities are usually hierarchical in terms of the types of services they provide. For example, the health care delivery system consists of local clinics, hospitals and medical centers (Fig. 10.1).
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Hierarchical Location Problem Sara Bastani and Narges Kazemzadeh
In the basic models presented in previous chapters, it is assumed that there was only one type of facility being located. As the systems that provide services/products usually consist of two or more levels of facilities, we discuss hierarchical facility systems in this chapter. Many facility systems are hierarchical in nature. These facilities are usually hierarchical in terms of the types of services they provide. For example, the health care delivery system consists of local clinics, hospitals and medical centers (Fig. 10.1). In this system a local clinic provides basic health care and diagnostic services. A hospital provides out-patient surgery in addition to those provided by a local clinic; and a medical center provides out-patient surgery and a full range of in-patient services. As another example of a hierarchical system, consider a solid waste disposal system. The solid waste is collected from the source of solid waste and shipped to transfer stations or landfill stations by trucks. Other examples of a hierarchical system are: education system, postal system, banking system and production–distribution system (Narula 1986; Daskin 1995). In the examples above, facilities cannot be located independently at each level. Thus, there is a need to consider them as a hierarchical system. In this chapter, location-routing problem, which is confused with the hierarchical location problem, is not discussed. In the location-routing problem, the locations of the primary facilities and the demand points are fixed and given; the objective is to locate intermediate facilities and design tours originating at the primary facilities to serve the secondary facilities and tours emanating from secondary facilities to serve the demand points. The location-routing problem is presented in Chap. 18. This chapter is organized as follows. In Sect. 10.1, we give a definition about hierarchical location problem, its applications and classifications. In Sects. 10.2–10.5 mathematical models for the problem are given. We present solution methods in Sect. 10.3. We conclude the chapter with some case studies in Sect. 10.4.
R.Z. Farahani and M. Hekmatfar (eds.), Facility Location: Concepts, Models, Algorithms and Case Studies, Contributions to Management Science, c Physica-Verlag Heidelberg 2009 DOI 10.1007/978-3-7908-2151-2 10,
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S. Bastani and N. Kazemzadeh Customer 3
Hospital
Customer 2
Medical center
Customer 1
Local clinic
Level 3 service: a full range of in-patient services Level 2 service: out-patient surgery Level 1 service: basic health care and diagnostic services
Fig. 10.1 An example of a health care delivery system
10.1 Applications and Classifications Many applications of hierarchical location problem are: Health care systems are one of the most studied real-life applications of the hierarchical facility location problem. Such systems can consist of local clinics, hospitals and medical centers. Some works in this area are Calvo and Marks (1973
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