zbMATH — the first resource for mathematics

Capacitated location allocation problem with stochastic location and fuzzy demand: a hybrid algorithm. (English) Zbl 1426.90180
Summary: In this article, a capacitated location allocation problem is considered in which the demands and the locations of the customers are uncertain. The demands are assumed fuzzy, the locations follow a normal probability distribution, and the distances between the locations and the customers are taken Euclidean and squared Euclidean. The fuzzy expected cost programming, the fuzzy \({\beta}\)-cost minimization model, and the credibility maximization model are three types of fuzzy programming that are developed to model the problem. Moreover, two closed-form Euclidean and squared Euclidean expressions are used to evaluate the expected distance between customers and facilities. In order to solve the problem at hand, a hybrid intelligent algorithm is applied in which the simplex algorithm, fuzzy simulation, and a modified genetic algorithm are integrated. Finally, in order to illustrate the efficiency of the proposed hybrid algorithm, some numerical examples are presented.

90B80 Discrete location and assignment
90C59 Approximation methods and heuristics in mathematical programming
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
Full Text: DOI
[1] Cooper, L., Location-allocation problems, Oper. Res., 11, 331-344, (1963) · Zbl 0113.14201
[2] Hakimi, S., Optimum distribution of switching centers in a communication network and some related graph theoretic problems, Oper. Res., 13, 462-475, (1964) · Zbl 0135.20501
[3] Gen, M.; Cheng, R., Genetic algorithms and engineering design, (1997), Wiley New York
[4] Badri, M. A., Combining the analytic hierarchy process and goal programming for global facility location-allocation problem, Int. J. Prod. Econ., 62, 237-248, (1999)
[5] Lee, S.; Green, G.; Kim, C., A multiple criteria models for the location-allocation problem, Comput. Oper. Res., 8, 1-8, (1981)
[6] Logendran, R.; Terrell, M. P., Uncapacitated plant location-allocation problems with price sensitive stochastic demands, Comput. Oper. Res., 15, 189-198, (1988)
[7] Sherali, H. D.; Rizzo, T. P., Unbalanced, capacitated p-Median problems on a chain graph with a continuum of link demands, Networks, 21, 133-163, (1991) · Zbl 0725.90049
[8] Carrizosa, E.; Conde, E.; Munoz-Marquez, M.; Puerto, J., The generalized Weber problem with expected distances, Oper. Res., 29, 35-57, (1995) · Zbl 0835.90040
[9] Carrizosa, E.; Munoz-Marquez, M.; Puerto, J., A note on the optimal positioning of service units, Oper. Res., 46, 155-156, (1998) · Zbl 0979.90086
[10] Zhou, J. (2000). Uncapacitated facility layout problem with stochastic demands. Proceedings of the Sixth National Conference of Operations Research Society of China, 904-911.
[11] Mousavi, S.M., Niaki, S.T.A., Mehdizadeh, E., Tavarroth, M.R. (2012). The capacitated multi-facility location-allocation problem with probabilistic customer location and demand: two hybrid meta-heuristic algorithms. International Journal of Systems Sciencehttp://dx.doi.org/10.1080/00207721.2012.670301. · Zbl 1307.93383
[12] Zhou, J.; Liu, B., New stochastic models for capacitated location- allocation problem, Comput. Ind. Eng., 45, 111-126, (2003)
[13] Zhou, J.; Liu, B., Modeling capacitated location-allocation problem with fuzzy demands, Comput. Ind. Eng., 53, 454-468, (2007)
[14] Wen, M.; Iwamura, K., Facility location-allocation problem in random fuzzy environment: using (α, β)-cost minimization model under the hurwicz criterion, Comput. Math., 55, 704-713, (2008) · Zbl 1137.90595
[15] Wen, M.; Iwamura, K., Fuzzy facility location-allocation problem under the hurwicz criterion, Eur. J. Oper. Res., 184, 627-635, (2008) · Zbl 1149.90366
[16] Abiri, M. B.; Yousefli, A., An application of probabilistic programming to the fuzzy location-allocation problems, Int. J. Adv. Manuf. Technol., 52, 1-7, (2010)
[17] Durmaz, E.; Aras, N.; Altnel, I. K., Discrete approximation heuristics for the capacitated continuous location-allocation problem with probabilistic customer locations, Comput. Oper. Res., 36, 2139-2148, (2009) · Zbl 1158.90374
[18] Carter, R. L.; Morris, R.; Roger, K., On the partitioning of squared Euclidean distance and its applications in cluster analysis, Psychometrika, 54, 1, 9-23, (1989)
[19] Aly, A. A.; White, J. A., Probabilistic formulation of the multifacility Weber problem, Naval Res. Logist. Quart., 25, 531-547, (1978) · Zbl 0393.90056
[20] Megiddo, N.; Supowit, K. J., On the complexity of some common geometric location problems, SIAM J. Comput., 13, 182-196, (1984) · Zbl 0534.68032
[21] Liu, Y.K., Zhu, X.L. (2006). Fuzzy capacitated location allocation problem with minimum risk criteria. IEE, Proceedings of the First International Conference on Innovative Computing, Information and Control (ICICIC’06).
[22] Phadke, M. S., Quality engineering using robust design, (1989), Prentice-Hall Upper Saddle River
[23] Amanna, A. E.; Ali, D.; Gadhiok, M.; Price, M.; Reed, J. H., Cognitive radio engine parametric optimization utilizing Taguchi analysis, EURASIP J. Wireless Commun. Network., 1, 5, (2012)
[24] S.M. Mousavi, V. Hajipour, S.T.A. Niaki, N. Alikar, Optimizing multi-item multi-period inventory control system with discounted cash flow and inflation: Two calibrated meta-heuristic algorithms. Appl. Math. Model, 2012 http://dx.doi.org/10.1016/j.apm.2012.05.019. · Zbl 1349.90038
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.