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A multi-objective chance-constrained network optimal model with random fuzzy coefficients and its application to logistics distribution center location problem. (English) Zbl 1219.90092
Summary: The problem of the distribution center is concerned with how to select distribution centers from a potential set in order to minimize the total relevant cost comprising of fixed costs of the distribution center and transport costs, and minimize the transportation time. In this paper, we propose a multi-objective network optimal model with random fuzzy coefficients for the logistics distribution center location problem. Furthermore, we convert the uncertain model into a deterministic one by the probability and possibility measure. Then the spanning tree-based genetic algorithm (st-GA) by the Prüfer number representation is introduced to solve the crisp multiobjective programming. At last, the proposed model and algorithm are applied to the Xinxi Dairy Holdings Limited Company to show the efficiency.
MSC:
90B80Discrete location and assignment
90C29Multi-objective programming; goal programming
90C70Fuzzy programming
90C59Approximation methods and heuristics
Software:
Genocop
References:
[1]Barahona F., Jensen D. (1998) Plant location with minimum inventory. Mathematical Programming 83: 101–111
[2]Buckley, J. J. (2006). Fuzzy Probability and Statistics. StudFuzz 196.
[3]Chankong V., Haimes Y.Y. (1983) Multiobjective decision making: Theory and methodology. North-Holland, Amsterdam
[4]Charnes A., Cooper W. W. (1963) Deterministic equivalents for optimizing and satisficing under chance constraints. Operational Research 11: 18–39 · Zbl 0117.15403 · doi:10.1287/opre.11.1.18
[5]Chen C. (2001) A fuzzy approach to select the location of the distribution center. Fuzzy Sets and Systems 118: 65–73 · Zbl 1151.90453 · doi:10.1016/S0165-0114(98)00459-X
[6]Davis M. M., Maggard M. J. (1990) An analysis of customer satisfaction with waiting times in a two-stage service process. Journal of Operations Management 9(3): 324–334 · doi:10.1016/0272-6963(90)90158-A
[7]Dubois D., Prade H. (1978) Operations on fuzzy numbers. International Journal of System Sciences 9: 613–626 · Zbl 0383.94045 · doi:10.1080/00207727808941724
[8]Dubois D., Prade H. (1980) Fuzzy sets and systems: Theory and applications. Academic Press, New York
[9]Gen M., Cheng R. (2000) Genetic algorithms and engineering optimization. Wiley, New York
[10]Harkness J. (2003) Facility location with increasing production costs. Operational Research 145: 1–13 · Zbl 1012.90024 · doi:10.1016/S0377-2217(02)00176-5
[11]Itoh T., Ishii H. (2005) One machine scheduling problem with fuzzy random due-dates. Fuzzy Optimization and Decision Making 4: 71–78 · Zbl 1079.90054 · doi:10.1007/s10700-004-5571-4
[12]Karabuk S. (2007) Modeling and optimizing transportation decisions in a manufacturing supply chain. Transportation Research Part E 43: 321–337 · doi:10.1016/j.tre.2006.01.003
[13]Klement, E. P., Puri, M. L., Ralescu, D. A. (1986). Limit theorems for fuzzy random variables. Proceedings of the Royal Society of Lodon A 407, pp. 171–182
[14]Kwakemaak H. (1978) Fuzzy random variables-I. Definitions and theorems. Information Sciences 15(1): 1–29 · Zbl 0438.60004 · doi:10.1016/0020-0255(78)90019-1
[15]Klose A., Drexl A. (2005) Facility location models for distribution system design. Operational Research 102: 4–29
[16]Li J., Xu J., Gen M. (2006) A class of multiobjective linear programming model with fuzzy random coefficients. Mathematical and Computer Modelling 44: 1097–1113 · Zbl 1165.90701 · doi:10.1016/j.mcm.2006.03.013
[17]Liu B. (2002) Theory and practice of uncertain programming. Physica-berlag, New York
[18]Lodwick W., Bachman K. (2005) Solving large-scale fuzzy and possibilistic optimization problems. Fuzzy Optimization and Decision Making 4: 257–278 · Zbl 1117.90079 · doi:10.1007/s10700-005-3663-4
[19]Michalewicz Z. (1994) Genetic algorithms + data structures = Evolution programs, 2nd edn. Springer, New York
[20]Mittal V., Kamakura W. A. (2001) Satisfaction, repurchase intent, and repurchase behavior: Investigation the moderating effect of customer characteristics. Journal of Marketing Research 38: 131–142 · doi:10.1509/jmkr.38.1.131.18832
[21]Moreno J., Moreno-Vega J., Verdegay J. (2004) Fuzzy location problems on networks. Fuzzy Sets and Systems 142: 393–405 · Zbl 1045.90039 · doi:10.1016/S0165-0114(03)00091-5
[22]Nahmias S. (1979) Fuzzy variables. Fuzzy Sets and Systems 1: 97–110 · Zbl 0383.03038 · doi:10.1016/0165-0114(78)90011-8
[23]Näther W. (2000) On random fuzzy variables of second order and their application to linear statistical inference with fuzzy data. Metrika 51: 201–221 · doi:10.1007/s001840000047
[24]Okada S., Soper T. (2000) A shortest path problem on a network with fuzzy arc lengths. Fuzzy Sets and Systems 109: 129–140 · Zbl 0956.90070 · doi:10.1016/S0165-0114(98)00054-2
[25]Puri M. L., Ralescu D. A. (1986) Fuzzy random variables. Journal of Mathematical Analysis and Applications 114: 409–422 · Zbl 0592.60004 · doi:10.1016/0022-247X(86)90093-4
[26]Shen Q., Zhao R., Tang W. (2009) Random fuzzy alternating renewal processes. Soft Computing 13: 139–147 · Zbl 1170.60031 · doi:10.1007/s00500-008-0307-y
[27]Sheu J. (2004) A hybrid fuzzy-based approach for identifying global logistics strategies. Transportation Research Part E 40: 39–61 · doi:10.1016/j.tre.2003.08.002
[28]Stalk G. Jr (1988) Time-The next source of competitive advantage. Harvard Business Review 66(4): 41–51
[29]Syam S. (2002) A model and methodologies for the location problem with logistical components. Comput. Oper. Res. 29: 1173–1193 · Zbl 0994.90089 · doi:10.1016/S0305-0548(01)00023-5
[30]Syarif A., Yun Y. S., Gen M. (2002) Study on multi-stage logistic chain network: A spanning tree-based genetic algorithm approach. Computer and Industrial Engineering 43: 299–314 · doi:10.1016/S0360-8352(02)00076-1
[31]Tan M., Tang X. (2006) The further study of safety stock under uncertain environment. Fuzzy Optimization and Decision Making 5: 193–202 · Zbl 1163.91424 · doi:10.1007/s10700-006-7337-7
[32]Tragantalerngsak S., Holt J., Ronnqvist M. (2000) An exact method for the two-echelon, single-source, capacitated facility location problem. Operational Research 123: 473–489 · Zbl 0991.90083 · doi:10.1016/S0377-2217(99)00105-8
[33]Wang X., Tang W., Zhao R. (2007) Random fuzzy EOQ model with imperfect quality items. Fuzzy Optimization and Decision Making 6: 139–153 · Zbl 1154.90317 · doi:10.1007/s10700-007-9002-1
[34]Xu J., Liu Q., Wang R. (2008) A class of multi-objective supply chain networks optimal model under random fuzzy environment and its application to the industry of Chinese liquor. Information Sciences 178: 2022–2043 · Zbl 1161.90016 · doi:10.1016/j.ins.2007.11.025
[35]Yang L. et al (2007) Logistics distribution centers location problem and algorithm under fuzzy environment. Computational and applied mathematics 208: 303–315 · Zbl 1119.90003 · doi:10.1016/j.cam.2006.09.015
[36]Zadeh L. (1965) Fuzzy sets. Information and Control 8: 338–353 · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X
[37]Zadeh L. (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1: 3–28 · Zbl 0377.04002 · doi:10.1016/0165-0114(78)90029-5
[38]Zhou G., Min H., Gen M. (2002) The balanced allocation of customers to multiple distribution centers in the supply chain network: A genetic algorithm approach. Computational and Industrial Engineering 43: 251–261 · doi:10.1016/S0360-8352(02)00067-0