An Uncertain Programming Model for Competitive Logistics Distribution Center Location Problem

Affiliation(s)

^{1}
College of Mathematics and Sciences, Shanghai Normal University, Shanghai, China.

^{2}
Institute of Uncertain Systems, Huanggang Normal University, Hubei, China.

^{3}
Institute of Systems Engineering, Tianjin University, Tianjin, China.

ABSTRACT

We employ uncertain programming to investigate the competitive logistics distribution center location problem in uncertain environment, in which the demands of customers and the setup costs of new distribution centers are uncertain variables. This research was studied with the assumption that customers patronize the nearest distribution center to satisfy their full demands. Within the framework of uncertainty theory, we construct the expected value model to maximize the expected profit of the new distribution center. In order to seek for the optimal solution, this model can be transformed into its deterministic form by taking advantage of the operational law of uncertain variables. Then we can use mathematical software to obtain the optimal location. In addition, a numerical example is presented to illustrate the effectiveness of the presented model.

KEYWORDS

Competitive Location, Logistics Distribution Center, Uncertain Programming, Uncertainty Theory

Competitive Location, Logistics Distribution Center, Uncertain Programming, Uncertainty Theory

Cite this paper

Lan, B. , Peng, J. and Chen, L. (2015) An Uncertain Programming Model for Competitive Logistics Distribution Center Location Problem.*American Journal of Operations Research*, **5**, 536-547. doi: 10.4236/ajor.2015.56042.

Lan, B. , Peng, J. and Chen, L. (2015) An Uncertain Programming Model for Competitive Logistics Distribution Center Location Problem.

References

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http://dx.doi.org/10.1016/j.cor.2005.03.002

[2] Klose, Z. and Drexl, A. (2005) Facility Location Models for Distribution System Design. European Journal of Operational Research, 162, 4-29.

http://dx.doi.org/10.1016/j.ejor.2003.10.031

[3] Hotelling, H. (1929) Stability in Competition. Economic Journal, 39, 41-57. http://dx.doi.org/10.2307/2224214

[4] Drezner, Z. (1982) Competitive Location Strategies for Two Facilities. Regional Science and Urban Economics, 12, 485-493.

http://dx.doi.org/10.1016/0166-0462(82)90003-5

[5] Hakimi, S. (1983) On Locating New Facilities in a Competitive Environment. European Journal of Operational Research, 12, 29-35.

http://dx.doi.org/10.1016/0377-2217(83)90180-7

[6] Plastria, F. (2001) Static Competitive Facility Location: An Overview of Optimisation Approaches. European Journal of Operational Research, 129, 461-470.

http://dx.doi.org/10.1016/S0377-2217(00)00169-7

[7] Wong, S. and Yang, H. (1999) Determining Market Areas Captured by Competitive Facilities: A Continuous Equilibrium Modeling Approach. Journal of Regional Science, 39, 51-72.

http://dx.doi.org/10.1111/1467-9787.00123

[8] Yang, H. and Wong, S. (2000) A Continuous Equilibrium Model for Estimating Market Areas of Competitive Facilities with Elastic Demand and Market Externality. Transportation Science, 34, 216-227.

http://dx.doi.org/10.1287/trsc.34.2.216.12307

[9] Plastria, F. and Vanhaverbeke, L. (2008) Discrete Models for Competitive Location with Foresight. Computers & Operations Research, 35, 683-700.

http://dx.doi.org/10.1016/j.cor.2006.05.006

[10] Küçükaydin, H., Aras, N. and Altnel, I. (2012) A Leader-Follower Game in Competitive Facility Location. Computers & Operations Research, 39, 437-448.

http://dx.doi.org/10.1016/j.cor.2011.05.007

[11] Sasaki, M., Campbell, J., Krishnamoorthy, M. and Ernst, A. (2015) A Stackelberg Hub Arc Location Model for a Competitive Environment. Computers & Operations Research, 47, 27-41.

http://dx.doi.org/10.1016/j.cor.2014.01.009

[12] Drezner, T. (1994) Locating a Single New Facility among Existing Unequally Attractive Facilities. Journal of Regional Science, 34, 237-252.

http://dx.doi.org/10.1111/j.1467-9787.1994.tb00865.x

[13] Drezner, T., Drezner, Z. and Kalczynski, P. (2011) A Cover-Based Competitive Location Model. Journal of the Operational Research Society, 62, 100-113.

http://dx.doi.org/10.1057/jors.2009.153

[14] Huff, D. (1966) A Programmed Solution for Approximating an Optimum Retail Location. Land Economics, 42, 293-303.

http://dx.doi.org/10.2307/3145346

[15] Drezner, T. (2014) A Review of Competitive Facility Location in the Plane. Logistics Research, 7, 114-126.

http://dx.doi.org/10.1007/s12159-014-0114-z

[16] Leonardi, G. and Tadei, R. (1984) Random Utility Demand Models and Service Location. Regional Science and Urban Economics, 14, 399-431.

http://dx.doi.org/10.1016/0166-0462(84)90009-7

[17] Drezner, T. and Drezner, Z. (1996) Competitive Facilities: Market Share and Location with Random Utility. Journal of Regional Science, 36, 1-15.

http://dx.doi.org/10.1111/j.1467-9787.1996.tb01098.x

[18] Drezner, T., Drezner, Z. and Wesolowsky, G. (1998) On the Logit Approach to Competitive Facility Location. Journal of Regional Science, 38, 313-327.

http://dx.doi.org/10.1111/1467-9787.00094

[19] Shiode, S. and Drezner, Z. (2003) A Competitive Facility Location Problem on a Tree Network with Stochastic Weights. European Journal of Operational Research, 149, 47-52.

http://dx.doi.org/10.1016/S0377-2217(02)00459-9

[20] Drezner, Z. and Wesolowsky, G. (1981) Optimal Location Probabilities in the Distance Weber Problem. Transportation Science, 15, 85-97.

http://dx.doi.org/10.1287/trsc.15.2.85

[21] Shiode, S. and Ishii, H. (1991) A Single Facility Stochastic Location Problem under a Distance. Annals of Operations Research, 31, 469-478.

http://dx.doi.org/10.1007/BF02204864

[22] Wesolowsky, G. (1977) Probabilistic Weights in the One Dimensional Facility Location Problem. Management Science, 24, 224-229.

http://dx.doi.org/10.1287/mnsc.24.2.224

[23] Liu, B. (2007) Uncertainty Theory. Spinger-Verlag, Berlin.

http://dx.doi.org/10.1007/978-3-540-73165-8_5

[24] Gao, Y. (2012) Uncertain Models for Single Facility Location Problems on Networks. Applied Mathematical Modelling, 36, 2592-2599.

http://dx.doi.org/10.1016/j.apm.2011.09.042

[25] Wen, M., Qin, Z. and Kang, R. (2014) The α-Cost Minimization Model for Capacitated Facility Location-Allocation Problem with Uncertain Demands. Fuzzy Optimization and Decision Making, 13, 345-356.

http://dx.doi.org/10.1007/s10700-014-9179-z

[26] Wang, K. and Yang, Q. (2014) Hierarchical Facility Location for the Reverse Logistics Network Design under Uncertainty. Journal of Uncertain Systems, 8, 255-270.

[27] Wu, Z. and Peng, J. (2014) A Chance-Constrained Model of Logistics Distribution Center Location under Uncertain Environment. Advances in Information Sciences and Service Sciences, 6, 33-42.

[28] Revelle, C. (1986) The Maximum Capture or Sphere of Influence Location Problem: Hotelling Revisited on a Network. Journal of Regional Science, 26, 343-358.

http://dx.doi.org/10.1111/j.1467-9787.1986.tb00824.x

[29] Liu, B. (2010) Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty. Spinger-Verlag, Berlin.

http://dx.doi.org/10.1007/978-3-642-13959-8

[30] Liu, B. (2009) Some Research Problems in Uncertainty Theory. Journal of Uncertain Systems, 3, 3-10.

[31] Liu, B. (2009) Theory and Practice of Uncertain Programming. Spinger-Verlag, Berlin.

[1] Lu, A. and Bostel, N. (2007) A Facility Location Model for Logistics Systems including Reverse Flows: The Case of Remanufacturing Activities. Computers & Operations Research, 34, 299-323.

http://dx.doi.org/10.1016/j.cor.2005.03.002

[2] Klose, Z. and Drexl, A. (2005) Facility Location Models for Distribution System Design. European Journal of Operational Research, 162, 4-29.

http://dx.doi.org/10.1016/j.ejor.2003.10.031

[3] Hotelling, H. (1929) Stability in Competition. Economic Journal, 39, 41-57. http://dx.doi.org/10.2307/2224214

[4] Drezner, Z. (1982) Competitive Location Strategies for Two Facilities. Regional Science and Urban Economics, 12, 485-493.

http://dx.doi.org/10.1016/0166-0462(82)90003-5

[5] Hakimi, S. (1983) On Locating New Facilities in a Competitive Environment. European Journal of Operational Research, 12, 29-35.

http://dx.doi.org/10.1016/0377-2217(83)90180-7

[6] Plastria, F. (2001) Static Competitive Facility Location: An Overview of Optimisation Approaches. European Journal of Operational Research, 129, 461-470.

http://dx.doi.org/10.1016/S0377-2217(00)00169-7

[7] Wong, S. and Yang, H. (1999) Determining Market Areas Captured by Competitive Facilities: A Continuous Equilibrium Modeling Approach. Journal of Regional Science, 39, 51-72.

http://dx.doi.org/10.1111/1467-9787.00123

[8] Yang, H. and Wong, S. (2000) A Continuous Equilibrium Model for Estimating Market Areas of Competitive Facilities with Elastic Demand and Market Externality. Transportation Science, 34, 216-227.

http://dx.doi.org/10.1287/trsc.34.2.216.12307

[9] Plastria, F. and Vanhaverbeke, L. (2008) Discrete Models for Competitive Location with Foresight. Computers & Operations Research, 35, 683-700.

http://dx.doi.org/10.1016/j.cor.2006.05.006

[10] Küçükaydin, H., Aras, N. and Altnel, I. (2012) A Leader-Follower Game in Competitive Facility Location. Computers & Operations Research, 39, 437-448.

http://dx.doi.org/10.1016/j.cor.2011.05.007

[11] Sasaki, M., Campbell, J., Krishnamoorthy, M. and Ernst, A. (2015) A Stackelberg Hub Arc Location Model for a Competitive Environment. Computers & Operations Research, 47, 27-41.

http://dx.doi.org/10.1016/j.cor.2014.01.009

[12] Drezner, T. (1994) Locating a Single New Facility among Existing Unequally Attractive Facilities. Journal of Regional Science, 34, 237-252.

http://dx.doi.org/10.1111/j.1467-9787.1994.tb00865.x

[13] Drezner, T., Drezner, Z. and Kalczynski, P. (2011) A Cover-Based Competitive Location Model. Journal of the Operational Research Society, 62, 100-113.

http://dx.doi.org/10.1057/jors.2009.153

[14] Huff, D. (1966) A Programmed Solution for Approximating an Optimum Retail Location. Land Economics, 42, 293-303.

http://dx.doi.org/10.2307/3145346

[15] Drezner, T. (2014) A Review of Competitive Facility Location in the Plane. Logistics Research, 7, 114-126.

http://dx.doi.org/10.1007/s12159-014-0114-z

[16] Leonardi, G. and Tadei, R. (1984) Random Utility Demand Models and Service Location. Regional Science and Urban Economics, 14, 399-431.

http://dx.doi.org/10.1016/0166-0462(84)90009-7

[17] Drezner, T. and Drezner, Z. (1996) Competitive Facilities: Market Share and Location with Random Utility. Journal of Regional Science, 36, 1-15.

http://dx.doi.org/10.1111/j.1467-9787.1996.tb01098.x

[18] Drezner, T., Drezner, Z. and Wesolowsky, G. (1998) On the Logit Approach to Competitive Facility Location. Journal of Regional Science, 38, 313-327.

http://dx.doi.org/10.1111/1467-9787.00094

[19] Shiode, S. and Drezner, Z. (2003) A Competitive Facility Location Problem on a Tree Network with Stochastic Weights. European Journal of Operational Research, 149, 47-52.

http://dx.doi.org/10.1016/S0377-2217(02)00459-9

[20] Drezner, Z. and Wesolowsky, G. (1981) Optimal Location Probabilities in the Distance Weber Problem. Transportation Science, 15, 85-97.

http://dx.doi.org/10.1287/trsc.15.2.85

[21] Shiode, S. and Ishii, H. (1991) A Single Facility Stochastic Location Problem under a Distance. Annals of Operations Research, 31, 469-478.

http://dx.doi.org/10.1007/BF02204864

[22] Wesolowsky, G. (1977) Probabilistic Weights in the One Dimensional Facility Location Problem. Management Science, 24, 224-229.

http://dx.doi.org/10.1287/mnsc.24.2.224

[23] Liu, B. (2007) Uncertainty Theory. Spinger-Verlag, Berlin.

http://dx.doi.org/10.1007/978-3-540-73165-8_5

[24] Gao, Y. (2012) Uncertain Models for Single Facility Location Problems on Networks. Applied Mathematical Modelling, 36, 2592-2599.

http://dx.doi.org/10.1016/j.apm.2011.09.042

[25] Wen, M., Qin, Z. and Kang, R. (2014) The α-Cost Minimization Model for Capacitated Facility Location-Allocation Problem with Uncertain Demands. Fuzzy Optimization and Decision Making, 13, 345-356.

http://dx.doi.org/10.1007/s10700-014-9179-z

[26] Wang, K. and Yang, Q. (2014) Hierarchical Facility Location for the Reverse Logistics Network Design under Uncertainty. Journal of Uncertain Systems, 8, 255-270.

[27] Wu, Z. and Peng, J. (2014) A Chance-Constrained Model of Logistics Distribution Center Location under Uncertain Environment. Advances in Information Sciences and Service Sciences, 6, 33-42.

[28] Revelle, C. (1986) The Maximum Capture or Sphere of Influence Location Problem: Hotelling Revisited on a Network. Journal of Regional Science, 26, 343-358.

http://dx.doi.org/10.1111/j.1467-9787.1986.tb00824.x

[29] Liu, B. (2010) Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty. Spinger-Verlag, Berlin.

http://dx.doi.org/10.1007/978-3-642-13959-8

[30] Liu, B. (2009) Some Research Problems in Uncertainty Theory. Journal of Uncertain Systems, 3, 3-10.

[31] Liu, B. (2009) Theory and Practice of Uncertain Programming. Spinger-Verlag, Berlin.