The competitive location problem is one of the key problems for the research areas of spatial economy, regional development, combinatorial optimization and system engineering. Generally speaking, competitive location problems tend to maximize the market share as the final goal without considering the sustainable operation capability, which leads to the deviation of the actual operating results from the original intention of decision. To tackle this problem, the ability of continuing operations is considered, the constraints of the probability of sustainable operation probability are given and a nonlinear integer programming model for competitive location is established. In this paper, an effective Real Coded Genetic Algorithm (RCGA) is presented for the competitive location problem to maximize the market share with the constraints of the sustainable operation probability. Genetic algorithm is a widely used random search algorithm and has very good performance in solving nonlinear programming and combinational optimization problems. First, it is assumed that the operating costs are the function of the size of the competitive facility and the constraints of the sustainable operation probability are formulated. Then a nonlinear mixed integer programming model for the facility location-design problem is built based on the gravity attractive model. Second, a RCGA is presented regarding the value types of the location variables and the scale variables. The numerical results show that RCGA can get high quality solutions in very short time, and the gap between feasible and optimal solutions is less than 0.5%. Related issues are also discussed by comparison to other algorithms to further demonstrate the success and practicability of the proposed approach, which provides an alternative way and an effective algorithm for the competitive location problem.
ZHU Hua-gui
. Research on Competitive Facility Location Under the Operation-sustainable Chance Constraint——An Efficient Real Coded Genetic Algorithm[J]. Chinese Journal of Management Science, 2016
, 24(12)
: 158
-165
.
DOI: 10.16381/j.cnki.issn1003-207x.2016.12.018
[1] Hotelling H. Stability in competition[J]. Economic Journal, 1929,39(153): 41-57.
[2] Eiselt H A, Laporte G. Sequential location problems[J]. European Journal of Operational Research, 1997, 96(2): 217-231.
[3] ReVelle C S, Eiselt H A. Location analysis: A synthesis and survey-Invited review[J]. European Journal of Operational Research, 2005,165(1): 1-19.
[4] Kress D, Pesch E. Sequential competitive location on networks[J]. European Journal of Operational Research, 2012, 217(3): 483-499.
[5] Huff D L. Defining and estimating a trading area[J]. Journal of Marketing, 1964, 28(3): 34-38.
[6] Nakanish M, Cooper L G. Parameter estimation for a multiplicative competitive interaction model-least squares approach[J]. Journal of Marketing Research, 1974, 11(3): 303-311.
[7] Plastria F. Static competitive facility location: An overview of optimisation approaches[J]. European Journal of Operational Research, 2001, 129(3): 461-470.
[8] Drezner T.Optimal continuous location of a retail facility, facility attractiveness, and market share: An interactive model[J]. Journal of Retailing, 1994, 70(1): 49-64.
[9] Drezner T. Locating a single new facility among existing unequally attractive facilities[J]. Journal of Regional Science, 1994, 34(2): 237-252.
[10] Drezner T, Drezner Z. Competitive facilities: Market share and location with random utility[J]. Journal of Regional Science, 1996, 36(1): 1-15.
[11] Plastria F, Carrizosa E. Optimal location and design of a competitive facility[J]. Mathematical Programming, 2004, 100(2): 247-265.
[12] Drezner T, Drezner Z, Kalczynski P. A cover-based competitive location model[J]. Journal of the Operational Research Society, 2011, 62(1): 100-113.
[13] Aboolian R, Berman O, Krass D. Competitive facility location and design problem[J]. European Journal of Operational Research, 2007, 182(1): 40-62.
[14] Drezner T, Drezner Z, Kalczynski P. Strategic competitive location: Improving existing and establishing new facilities[J]. Journal of the Operational Research Society, 2012, 63(12): 1720-1730.
[15] Serra D, ReVelle C, Rosing K. Surviving in a competitive spatial market: The threshold capture model[J]. Journal of Regional Science, 1999, 39(4): 637-652.
[16] Poularakis K, Tassiulas L, Ieee. Surviving in a competitive market of information providers[C]//Proceedings of 2013 IEEE Conforence on Computer Communications Workshops, April 14-19,2013.
[17] Zarrinpoor N, Seifbarghy M. A competitive location model to obtain a specific market share while ranking facilities by shorter travel time[J]. The International Journal of Advanced Manufacturing Technology, 2010, 55(5-8): 807-816.
[18] Lee J M, Lee Y H. Facility location and scale decision problem with customer preference[J]. Computers & Industrial Engineering, 2012, 63(1): 184-191.
[19] Fernández J, Hendrix E M T. Recent insights in Huff-like competitive facility location and design[J]. European Journal of Operational Research, 2013, 227(3): 581-584.
[20] 刘全,王晓燕,傅启明,等. 双精英协同进化遗传算法[J]. 软件学报, 2012, 23(4): 765-775.
[21] 马祖军,周愉峰. 考虑设施中断风险和防御的分销网络选址_库存问题[J]. 系统工程,2015, 33(12): 48-54.
[22] Deep K, Thakur M. A new crossover operator for real coded genetic algorithms[J]. Applied Mathematics and Computation, 2007, 188(1): 895-911.
[23] Deep K, Thakur M. A new mutation operator for real coded genetic algorithms[J]. Applied Mathematics and Computation, 2007, 193(1): 211-230.
[24] Thakur M, Meghwani S S, Jalota H. A modified real coded genetic algorithm for constrained optimization[J]. Applied Mathematics and Computation, 2014, 235: 292-317.
[25] 杨珺,冯鹏祥,孙昊,等.电动汽车物流配送系统的换电站选址与路径优化问题[J]. 中国管理科学, 2015, 23(9): 87-96.
[26] 杨珺,卢巍.低碳政策下多容量等级选址与配送问题研究[J]. 中国管理科学, 2014, 22(5): 51-60.
[27] 唐金环,戢守峰,朱宝琳.考虑碳配额差值的选址_路径_库存集成问题优化模型与算法[J].中国管理科学, 2014, 22(9): 114-122.
