A review of network location theory and models

Cataloged from PDF version of article.In this study, we review the existing literature on network location problems. The study has a broad scope that includes problems featuring desirable and undesirable facilities, point facilities and extensive facilities, monopolistic and competitive markets, and single or multiple objectives. Deterministic and stochastic models as well as robust models are covered. Demand data aggregation is also discussed. More than 500 papers in this area are reviewed and critical issues, research directions, and problem extensions are emphasized.Erdoğan, Damla SelinM.S

Improvements and comparison of heuristics for solving the uncapacitated multisource Weber problem

Copyright @ 2000 INFORMSThe multisource Weber problem is to locate simultaneously m facilities in the Euclidean plane to minimize the total transportation cost for satisfying the demand of n fixed users, each supplied from its closest facility. Many heuristics have been proposed for this problem, as well as a few exact algorithms. Heuristics are needed to solve quickly large problems and to provide good initial solutions for exact algorithms. We compare various heuristics, i.e., alternative location-allocation (Cooper 1964), projection (Bongartz et al. 1994), Tabu search (Brimberg and Mladenovic 1996a), p-Median plus Weber (Hansen ct al. 1996), Genetic search and several versions of Variable Neighbourhood search. Based on empirical tests that are reported, it is found that most traditional and some recent heuristics give poor results when the number of facilities to locate is large and that Variable Neighbourhood search gives consistently best results, on average, in moderate computing time.This study was supported by the Department of National Defence (Canada) Academic Research; Office of Naval Research Grant N00014-92-J-1194, Natural Sciences and Engineering Research Council of Canada Grant GPO 105574 and Fonds pour la Formation des Chercheurs et l’Aide a la Recherche Grant 32EQ 1048; and by an International Postdoctoral Fellowship of the Natural Sciences and Engineering Research Council of Canada, Grant OGPOO 39682

Hybrid Meta-heuristics with VNS and Exact Methods: Application to Large Unconditional and Conditional Vertex p-Centre Problems

Large-scale unconditional and conditional vertex p-centre problems are solved using two meta-heuristics. One is based on a three-stage approach whereas the other relies on a guided multi-start principle. Both methods incorporate Variable Neighbourhood Search, exact method, and aggregation techniques. The methods are assessed on the TSP dataset which consist of up to 71,009 demand points with p varying from 5 to 100. To the best of our knowledge, these are the largest instances solved for unconditional and conditional vertex p-centre problems. The two proposed meta-heuristics yield competitive results for both classes of problems

Dynamic temporary blood facility location-allocation during and post-disaster periods

The key objective of this study is to develop a tool (hybridization or integration of different techniques) for locating the temporary blood banks during and post-disaster conditions that could serve the hospitals with minimum response time. We have used temporary blood centers, which must be located in such a way that it is able to serve the demand of hospitals in nearby region within a shorter duration. We are locating the temporary blood centres for which we are minimizing the maximum distance with hospitals. We have used Tabu search heuristic method to calculate the optimal number of temporary blood centres considering cost components. In addition, we employ Bayesian belief network to prioritize the factors for locating the temporary blood facilities. Workability of our model and methodology is illustrated using a case study including blood centres and hospitals surrounding Jamshedpur city. Our results shows that at-least 6 temporary blood facilities are required to satisfy the demand of blood during and post-disaster periods in Jamshedpur. The results also show that that past disaster conditions, response time and convenience for access are the most important factors for locating the temporary blood facilities during and post-disaster periods

Solving the conditional and unconditional p-center problem with modified harmony search: A real case study

AbstractIn this paper, we solve the well-known conditional and unconditional p-center problem using a modified harmony search algorithm. This music inspired algorithm is a simple meta-heuristic that was proposed recently for solving combinatorial and large-scale engineering and optimization problems. This algorithm is applicable to both discrete and continuous search spaces. We have tested the present algorithm on ORLIB and TSP test problems and compared the results of the classic harmony search approach to those of the modified harmony search method. We also present some results for other meta-heuristic algorithms including the variable neighborhood search, the Tabu search, and the scatter search. Finally, we utilize this location model to locate bicycle stations in the historic city of Isfahan in Iran

Speeding up the optimal method of Drezner for the p-centre problem in the plane

This paper revisits an early but interesting optimal algorithm first proposed by Drezner to solve the continuous p-centre problem. The original algorithm is reexamined and efficient neighbourhood reductions which are mathematically supported are proposed to improve its overall computational performance. The revised algorithm yields a considerably high reduction in computational time reaching, in some cases, a decrease of 96%. This new algorithm is now able to find proven optimal solutions for large data sets with over 1300 demand points and various values of p for the first time

Neighbourhood Reduction in Global and Combinatorial Optimization: The Case of the p-Centre Problem

Neighbourhood reductions for a class of location problems known as the vertex (or discrete) and planar (or continuous) p-centre problems are presented. A brief review of these two forms of the p-centre problem is first provided followed by those respective reduction schemes that have shown to be promising. These reduction schemes have the power of transforming optimal or near optimal methods such as metaheuristics or relaxation-based procedures, which were considered relatively slow, into efficient and exciting ones that are now able to find optimal solutions or tight lower/upper bounds for larger instances. Research highlights of neighbourhood reduction for global and combinatorial optimisation problems in general and for related location problems in particular are also given

Robustness in facility location

Facility location concerns the placement of facilities, for various objectives, by use of mathematical models and solution procedures. Almost all facility location models that can be found in literature are based on minimizing costs or maximizing cover, to cover as much demand as possible. These models are quite efficient for finding an optimal location for a new facility for a particular data set, which is considered to be constant and known in advance. In a real world situation, input data like demand and travelling costs are not fixed, nor known in advance. This uncertainty and uncontrollability can lead to unacceptable losses or even bankruptcy. A way of dealing with these factors is robustness modelling. A robust facility location model aims to locate a facility that stays within predefined limits for all expectable circumstances as good as possible. The deviation robustness concept is used as basis to develop a new competitive deviation robustness model. The competition is modelled with a Huff based model, which calculates the market share of the new facility. Robustness in this model is defined as the ability of a facility location to capture a minimum market share, despite variations in demand. A test case is developed by which algorithms can be tested on their ability to solve robust facility location models. Four stochastic optimization algorithms are considered from which Simulated Annealing turned out to be the most appropriate. The test case is slightly modified for a competitive market situation. With the Simulated Annealing algorithm, the developed competitive deviation model is solved, for three considered norms of deviation. At the end, also a grid search is performed to illustrate the landscape of the objective function of the competitive deviation model. The model appears to be multimodal and seems to be challenging for further research