Efficient Median and Center Problems: a Bi-Objective Mixed Integer Programming Approach
محورهای موضوعی : مجله بین المللی ریاضیات صنعتیT. Sayyar 1 , J. Fathali 2 , M. Ghiyasi 3
1 - Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.
2 - Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.
3 - Faculty of Industrial Engineering and Management Sciences, Shahrood University of Technology, Shahrood, Iran.
کلید واژه: Median problem, Center problem, Efficiency, Data envelopment analysis,
چکیده مقاله :
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.
در این مقاله ما یک مساله جدید از ادغام مساله مکانیابی و کارایی را ارائه می کنیم. هدف ما در این مساله، پیدا کردن یک مکان کارا در صفحه است. در نهایت به یک ترکیب جدید از ادغام مساله مکانیابی و تحلیل پوششی داده ها دست می یابیم. در این مقاله ما تفاوت کارخود را با سایر کارهایی که در این زمینه انجام شده است را شرح می دهیم. سپس یک مدل برنامه ریزی دو هدفه را برای مساله یک میانه کارا و یک مرکز کارا ارائه می دهیم.
[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.