Dynamic facility location: The progressive p-median problem (original) (raw)
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A Genetic Algorithm for the P-Median Facility Location Problem
The p-median problem is one of the most well-known facility location problem and have several applications in transportation, distribution, location of public, warehouses etc. The objective is to locate p facilities (medians) such that the sum of the distances from each demand point to its nearest facility is minimized. The p-median problem is well known to be NP-hard and several heuristics have been developed in the literature, but there are few applications of genetic algorithms for this problem. In this study, a new genetic algorithm approach to solve uncapacitated p-median problem is proposed. The parameters of the genetic algorithm are tuned using design of experiments approach. The proposed algorithm is tested on several instances of benchmark data set and evaluated with optimal solutions of the problems.
A branch-and-price approach to p-median location problems
2005
This paper describes a branch-and-price algorithm for the p-median location problem. The objective is to locate p facilities (medians) such as the sum of the distances from each demand point to its nearest facility is minimized. The traditional column generation process is compared with a stabilized approach that combines the column generation and Lagrangean/surrogate relaxation. The Lagrangean/surrogate multiplier modies the reduced cost criterion, providing the selection of new productive columns at the search tree. Computational experiments are conducted considering especially dicult instances to the traditional column generation and also with some large-scale instances.
Solving a Capacitated p-Median Location Allocation Problem Using Genetic Algorithm: A case study
2014
Facility location-allocation problems have various applications in private and public sectors. A capacitated p-median problem is considered in this work which is computationally NP-Hard. The primary goal of this paper was to determine a set of p-facilities location in which all demand points are allocated and its average distance traveled from the customers' location to the selected p-facilities is minimized. In addition, the model also considered supplier's allocation for p facilities. A real world case study has been addressed, and genetic algorithm which consists of crossover and mutation operators was proposed in order to solve the problem. Computational results for different values of p were generated, and finally the optimum solution based on minimum cost was reported.
Journal of Automation, Mobile Robotics and Intelligent Systems, 2014
The paper introduces the bi-partial version of the well known p-median or p-center facility location problem. The bi-partial approach, developed by the author, primarily to deal with the clustering problems, is shown here to work for a problem that does not possess some of the essential properties, inherent to the bi-partial formulations. It is demonstrated that the classical objective function of the problem can be correctly interpreted in terms of the bi-partial approach, that it possesses the essential properties that are at the core of the bi-partial approach, and, finally, that the general algorithmic precepts of the bi-partial approach can also be applied to this problem. It is proposed that the use of bi-partial approach for similar problems can be beneficial from the point of view of flexibility and interpretation.
Results of a New Approach to Solving the p-Median Problem with Maximum Distance Constraints
Geographical Analysis, 2010
Results of a New Approach to Solving the p-Median Problem with Maximum Distance Constraints Considerable interest has been directed in the past to developing approaches for solving the p-median problem with maximum distance Constraints. All culrent solution techniques consider potential facilities to be located only at nodes of the network. This paper deals with the solution of this problem under the condition where facility placement is not restricted to nodes. The examples given show that improvement in weighted distance can be obtained by solving the unrestricted site problem. In addition, feasible solutions can be obtained for smaller numbers of facilities than possible by all nodal facility placement.
The p-median problem under uncertainty
European Journal of Operational Research, 2008
Consider the need to currently locate p facilities but it is possible that up to q additional facilities will have to be located in the future. There are known probabilities that 0 6 r 6 q facilities will need to be located. The p-median problem under uncertainty is to find the location of p facilities such that the expected value of the objective function in the future is minimized. The problem is formulated on a graph, properties of it are proven, an integer programming formulation is constructed, and heuristic algorithms are suggested for its solution. The heuristic algorithms are modified to reduce the run time by about two orders of magnitude with minimal effect on the quality of the solution. Optimal solutions for many problems are found effectively by CPLEX. Computational results using the heuristic algorithms are presented.
A Fast and Deterministic Approach to a Near Optimal Solution for the p-Median Problem
International Journal of Operations Research and Information Systems, 2012
Finding solutions for the p-median problem is one of the primary research issues in the field of location theory. Since the p-median problem has proved to be a NP-hard problem, several heuristic and approximation methods have been proposed to find near optimal solutions with acceptable computational time. This study introduces a computationally efficient and deterministic algorithm whose objective is to return a near optimal solution for the p-median problem. The merit of the proposed approach, called Relocation Median (RLM), lies in solving the p-median problem in superior computational time with a tiny percentage deviation from the optimal solution. This approach is especially relevant when the problem is enormous where, even when a heuristic method is applied, the computational time is quite high. RLM consists of two parts: The first part uses a greedy search method to find an initial solution; the second part sequentially substitutes medians in the initial solution with addition...
International Journal of Operations & Production Management, 1991
The performance of Ardalan′s heuristic is compared with that of Teitz and Bart for the location of service facilities, where performance is assessed in terms of the accuracy of solutions. The comparison is made considering two kinds of location problem: p‐median and p‐median with maximum distance constraints. The results indicate that the Teitz and Bart method generally produces a better solution than the Ardalan method for both problems.
A Comparative Study of Different Techniques for P-Median Problem : A review
2011
P-median problem refers to decrease the average distances in facility location problem. It is the burning issue in facility location problem, the prominent area of research in present scenario. Through this paper, efforts are made to highlight the different aspects of p-median solving techniques. Different techniques are analyzed and compared to reveal the best results.
The p-median problem: A survey of metaheuristic approaches
European Journal of Operational Research, 2007
The p-median problem, like most location problems, is classified as N P -hard, and so, heuristic methods are usually used for solving it. The pmedian problem is a basic discrete location problem with real application that have been widely used to test heuristics. Metaheuristics are frameworks for building heuristics. In this survey, we examine the p-median, with the aim of providing an overview on advances in solving it using recent procedures based on metaheuristic rules.