NP-Hard, capacitated, balanced p-median problems on a chain graph with a continuum of link demands
Mathematics of Operations Research
Asymptotic behavior of the Weber location problem on the plane
Annals of Operations Research - Special issue on locational decisions
Discrete Applied Mathematics - Special volume: viewpoints on optimization
Algorithmic approaches for solving the euclidean distance location and location-allocation problems
Algorithmic approaches for solving the euclidean distance location and location-allocation problems
Heuristic solution of the multisource Weber problem as a p-median problem
Operations Research Letters
Solving the stochastic capacitated location-allocation problem by using a new hybrid algorithm
MATH'10 Proceedings of the 15th WSEAS international conference on Applied mathematics
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The capacitated continuous location-allocation problem, also called capacitated multisource Weber problem (CMWP), is concerned with locating m facilities in the Euclidean plane, and allocating their capacity to n customers at minimum total cost. The deterministic version of the problem, which assumes that customer locations and demands are known with certainty, is a nonconvex optimization problem. In this work, we focus on a probabilistic extension referred to as the probabilistic CMWP (PCMWP), and consider the situation in which customer locations are randomly distributed according to a bivariate probability distribution. We first formulate the discrete approximation of the problem as a mixed-integer linear programming model in which facilities can be located on a set of candidate points. Then we present three heuristics to solve the problem. Since optimal solutions cannot be found, we assess the performance of the heuristics using the results obtained by an alternate location-allocation heuristic that is originally developed for the deterministic version of the problem and tailored by us for the PCMWP. The new heuristics depend on the evaluation of the expected distances between facilities and customers, which is possible only for a few number of distance function and probability distribution combinations. We therefore propose approximation methods which make the heuristics applicable for any distance function and probability distribution of customer coordinates.