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Proceedings of GO 2005, pp. 153 – 158.Obtaining the globe optimization of set-covering basedp-center problemsFuh-Hwa Franklin Liu, Chi-Wei ShihDepartment of Industrial Engineering and Management, National Chiao Tung University, Hsin Chu, Taiwan 300,fliu@mail.nctu.edu.twAbstractKeywords:In this paper we introduce a procedure with polynomial complexity for solving the set-coveringbasedp-center problem that is inspired from BsearchEx (Elloumi et al., 2004). We present our newformulation (PC-SC2) and our new efficient exact procedure, slim bisecting search, SBsearch. Furthermore,we show how to simplify the continuous problem with the same distance matrix andincreasing p value. The computational results for SBsearch are compared with other existing procedures.p-center problem, Network flow, Mathematical programming, Minimax problem, Set covering problem.1. IntroductionLocating fixed facilities throughout the logistics network is an important decision problemthat gives form, structure and shape to the entire logistics system. Location decisions involvedetermining the number, location and size of the facilities to be used. Facility location modelscan be classified under four main topics p-center problem, p-median problem, location setcovering problem, maximum covering location problem, see Owen and Daskin (1998). Thelocation of emergency service facilities such as hospitals or fire stations is frequently modeledby the p-center problem. The p-center problem is NP-hard; see Kariv and Hakimi (1979) andMasuyama et al. (1981).Let N be the number of clients, M be the number of potential sites or facilities, and d ij bethe distance from client i to facility j. The p-center problem consists of locating p facilities andassigning each client to its closest facility so as to minimize the maximum distance betweena client and the facility it is assigned to. Many authors consider the particular case wherethe facilities are identical to the clients, i.e., N = M, and distances are symmetric and satisfytriangle inequalities. We call this particular case the symmetric p-center problem.Main mathematical location methods may be categorized as heuristic and exact. Exactmethods refer to those procedures with the capability to guarantee either a mathematicallyglobe optimum solution to the location problem or at least a solution of known accuracy; seeDrezner (1984), Handler (1990) and Daskin (1995). In many respects, this is an ideal approachto the location problem; however, the approach can result in long computer running times,huge memory requirements, and a compromised problem definition when applied to practicalproblems.In this paper we introduce a procedure with polynomial complexity for solving the setcovering-basedp-center problem that is inspired from BsearchEx (Elloumi et al., 2004). In Section2, we present our new formulation (PC-SC2) and our new efficient exact procedure, slimbisecting search, SBsearch. Furthermore, we show how to simplify the continuous problem