Capacitated location allocation problem with stochastic location and fuzzy demand: a hybrid algorithm.

*(English)*Zbl 1426.90180Summary: 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.

##### MSC:

90B80 | Discrete location and assignment |

90C59 | Approximation methods and heuristics in mathematical programming |

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

##### Keywords:

location allocation problem; fuzzy programming; fuzzy simulation; hybrid intelligent algorithm; evaluating expected distance
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\textit{S. M. Mousavi} and \textit{S. T. A. Niaki}, Appl. Math. Modelling 37, No. 7, 5109--5119 (2013; Zbl 1426.90180)

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