Efficient Median and Center Problems: a Bi-Objective Mixed Integer Programming Approach
الموضوعات : مجله بین المللی ریاضیات صنعتی
T. Sayyar
1
(Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.)
J. Fathali
2
(Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.)
M. Ghiyasi
3
(Faculty of Industrial Engineering and Management Sciences, Shahrood University of Technology, Shahrood, Iran.)
الکلمات المفتاحية: Median problem, Center problem, Efficiency, Data envelopment analysis,
ملخص المقالة :
This paper proposes a novel problem on the efficiency in the location problem. We consider the problem of finding optimal location of an efficient facility in the plane. This yields to a novel combination of the location problem and efficiency measurement. We describe the difference between our model and the principle existing models in the literature. We then present a bi-objective programming models for the efficient median and center problems.
[1] A. Charnes, W. Cooper, J. Rousseau, J. Semple, Data Envelopment Analysis and Axiomatic Notions of Efficiency and Reference Sets, Retrieved from (1987).
[2] S. A. Darestani, S. Mohammadreza, A fuzzy data envelopment analysis approach for multi-objective covering facility location problem using NSGA-II, International Journal of Industrial and Systems Engineering 24 (2016) 1-31.
[3] H. Eiselt, M. Gendreau, G. Laporte, Arc routing problems, part II: The rural postman problem, Operations research 43 (1995) 399-414.
[4] L. Fang, H. Li, Multi-criteria decision analysis for efficient location-allocation problem combining DEA and goal programming, RAIRO-Operations Research 49 (2015) 753-772.
[5] S. Georgantzinos, I. Giannikos, A modeling framework for incorporating DEA efficiency into set covering, packing and partitioning formulations, International Transactions in Operational Research (2017).
[6] P. Guo, Fuzzy data envelopment analysis and its application to location problems, Information Sciences 179 (2009) 820-829.
[7] S. Khodaparasti, H. Maleki, M. E. Bruni, S. Jahedi, P. Beraldi, D. Conforti, Balancing efficiency and equity in location-allocation models with an application to strategic EMS design, Optimization Letters 10 (2016) 1053-1070.
[8] R. K. Klimberg, S. J. Ratick, Modeling data envelopment analysis (DEA) efficient location/allocation decisions, Computers & Operations Research 35 (2008) 457-474.
[9] P. Mitropoulos, I. Mitropoulos, I. Giannikos, Combining DEA with location analysis for the effective consolidation of services in the health sector, Computers & Operations Research 40 (2013) 2241-2250.
[10] H. Moheb-Alizadeh, S. Rasouli, R. Tavakkoli-Moghaddam, The use of multi-criteria data envelopment analysis (MCDEA) for location allocation problems in a fuzzy environment, Expert Systems with Applications 38 (2011) 5687-5695.
[11] R. Ramanathan, Estimating relative attractiveness of locations using data envelopment analysis, International Journal of Business Performance and Supply Chain Modelling 1 (2009) 99-113.
[12] M. Salahi, A. Jamalian, A bi- objective model for combined deta envelopment analysis and incapacicitatedsingle- source multiproduct facility location problem, Journal of Operational Research and Applications 12 (2015) 79-93.
[13] P. Thomas, Y. Chan, L. Lehmkuhl, W. Nixon, Obnoxious-facility location and dataenvelopment analysis: A combined distancebased formulation, European journal of operational research 141 (2002) 495-514.
