| 1. |
- Carling, Kenneth, et al.
(författare)
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Testing the gravity p-median model empirically
- 2015
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Ingår i: Operations Research Perspectives. - : Elsevier. - 2214-7160. ; 2:124
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Tidskriftsartikel (refereegranskat)abstract
- Regarding the location of a facility, the presumption in the widely used p-median model is that the customer opts for the shortest route to the nearest facility. However, this assumption is problematic on free markets since the customer is presumed to gravitate to a facility by the distance to and the attractiveness of it. The recently introduced gravity p-median model offers an extension to the p-median model that account for this. The model is therefore potentially interesting, although it has not yet been implemented and tested empirically. In this paper, we have implemented the model in an empirical problem of locating vehicle inspections, locksmiths, and retail stores of vehicle spare-parts for the purpose of investigating its superiority to the p-median model. We found, however, the gravity p-median model to be of limited use for the problem of locating facilities as it either gives solutions similar to the p-median model, or it gives unstable solutions due to a non-concave objective function.
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| 2. |
- Carling, Kenneth, et al.
(författare)
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Confidence in heuristic solutions?
- 2015
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Ingår i: Journal of Global Optimization. - : Springer Science and Business Media LLC. - 0925-5001 .- 1573-2916. ; 63:2, s. 381-399
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Tidskriftsartikel (refereegranskat)abstract
- Solutions to combinatorial optimization problems frequently rely on heuristics to minimize an objective function. The optimum is sought iteratively and pre-setting the number of iterations dominates in operations research applications, which implies that the quality of the solution cannot be ascertained. Deterministic bounds offer a mean of ascertaining the quality, but such bounds are available for only a limited number of heuristics and the length of the interval may be difficult to control in an application. A small, almost dormant, branch of the literature suggests using statistical principles to derive statistical bounds for the optimum. We discuss alternative approaches to derive statistical bounds. We also assess their performance by testing them on 40 test p-median problems on facility location, taken from Beasley’s OR-library, for which the optimum is known. We consider three popular heuristics for solving such location problems; simulated annealing, vertex substitution, and Lagrangian relaxation where only the last offers deterministic bounds. Moreover, we illustrate statistical bounds in the location of 71 regional delivery points of the Swedish Post. We find statistical bounds reliable and much more efficient than deterministic bounds provided that the heuristic solutions are sampled close to the optimum. Statistical bounds are also found computationally affordable.
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| 3. |
- Carling, Kenneth, et al.
(författare)
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On statistical bounds of heuristic solutions to location problems
- 2014
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Solutions to combinatorial optimization problems, such as problems of locating facilities, frequently rely on heuristics to minimize the objective function. The optimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. Pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small, almost dormant, branch of the literature suggests using statistical principles to estimate the minimum and its bounds as a tool to decide upon stopping and evaluating the quality of the solution. In this paper we examine the functioning of statistical bounds obtained from four different estimators by using simulated annealing on p-median test problems taken from Beasley’s OR-library. We find the Weibull estimator and the 2nd order Jackknife estimator preferable and the requirement of sample size to be about 10 being much less than the current recommendation. However, reliable statistical bounds are found to depend critically on a sample of heuristic solutions of high quality and we give a simple statistic useful for checking the quality. We end the paper with an illustration on using statistical bounds in a problem of locating some 70 distribution centers of the Swedish Post in one Swedish region.
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| 4. |
- Zhao, Xiaoyun, et al.
(författare)
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Network density and the p-median solution
- 2013
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The p-medianmodel is commonly used to find optimal locations of facilities for geographically distributed demands. So far, there are few studies that have considered the importance of the road network in the model. However, Han, Håkansson, and Rebreyend (2013) examined the solutions of the p-median model with densities of the road network varying from 500 to 70,000 nodes. They found as the density went beyond some 10,000 nodes, solutions have no further improvements but gradually worsen. The aim of this study is to check their findings by using an alternative heuristic being vertex substitution, as a complement to their using simulated annealing. We reject the findings in Han et al (2013). The solutions do not further improve as the nodes exceed 10,000, but neither do the solutions deteriorate.
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| 5. |
- Carling, Kenneth, et al.
(författare)
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On statistical bounds of heuristic solutions to location problems
- 2016
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Ingår i: Journal of combinatorial optimization. - : Springer Science and Business Media LLC. - 1382-6905 .- 1573-2886. ; 31:4, s. 1518-1549
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Tidskriftsartikel (refereegranskat)abstract
- Solutions to combinatorial optimization problems, such as problems of locating facilities, frequently rely on heuristics to minimize the objective function. The optimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. Pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small, almost dormant, branch of the literature suggests using statistical principles to estimate the minimum and its bounds as a tool to decide upon stopping and evaluating the quality of the solution. In this paper we examine the functioning of statistical bounds obtained from four different estimators by using simulated annealing on p-median test problems taken from Beasley’s OR-library. We find the Weibull estimator and the 2nd order Jackknife estimator preferable and the requirement of sample size to be about 10 being much less than the current recommendation. However, reliable statistical bounds are found to depend critically on a sample of heuristic solutions of high quality and we give a simple statistic useful for checking the quality. We end the paper with an illustration on using statistical bounds in a problem of locating some 70 distribution centers of the Swedish Post in one Swedish region.
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