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  • 1.
    Carling, Kenneth
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Han, Mengjie
    Dalarna University, School of Technology and Business Studies, Statistics.
    Håkansson, Johan
    Dalarna University, School of Technology and Business Studies, Human Geography.
    Rebreyend, Pascal
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    An empirical test of the gravity p-median model2012Report (Other academic)
    Abstract [en]

    A customer is presumed to gravitate to a facility by the distance to it and the attractiveness of it. However regarding the location of the facility, the presumption is that the customer opts for the shortest route to the nearest facility.This paradox was recently solved by the introduction of the gravity p-median model. The model is yet to be implemented and tested empirically. We implemented the model in an empirical problem of locating locksmiths, vehicle inspections, and retail stores ofv ehicle spare-parts, and we compared the solutions with those of the p-median model. We found 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.

  • 2.
    Carling, Kenneth
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Han, Mengjie
    Dalarna University, School of Technology and Business Studies, Statistics.
    Håkansson, Johan
    Dalarna University, School of Technology and Business Studies, Information Systems.
    Rebreyend, Pascal
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    Distance measure and the p-median problem in rural areas2015In: Annals of Operations Research, ISSN 0254-5330, E-ISSN 1572-9338, Vol. 226, no 1, p. 89-99Article in journal (Refereed)
    Abstract [en]

    The p-median model is used to locate P facilities to serve a geographically distributed population. Conventionally, it is assumed that the population patronize the nearest facility and that the distance between the resident and the facility may be measured by the Euclidean distance. Carling, Han, and Håkansson (2012) compared two network distances with the Euclidean in a rural region with a sparse, heterogeneous network and a non-symmetric distribution of the population. For a coarse network and P small, they found, in contrast to the literature, the Euclidean distance to be problematic. In this paper we extend their work by use of a refined network and study systematically the case when P is of varying size (1-100 facilities). We find that the network distance give as good a solution as the travel-time network. The Euclidean distance gives solutions some 4-10 per cent worse than the network distances, and the solutions tend to deteriorate with increasing P. Our conclusions extend to intra-urban location problems.

  • 3.
    Carling, Kenneth
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Han, Mengjie
    Dalarna University, School of Technology and Business Studies, Statistics.
    Håkansson, Johan
    Dalarna University, School of Technology and Business Studies, Human Geography.
    Rebreyend, Pascal
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    Distance measure and the p-median problem in rural areas2012Report (Other academic)
    Abstract [en]

    The p-median model is used to locate P facilities to serve a geographically distributed population. Conventionally, it is assumed that the population patronize the nearest facility and that the distance between the resident and the facility may be measured by the Euclidean distance. Carling, Han, and Håkansson (2012) compared two network distances with the Euclidean in a rural region witha sparse, heterogeneous network and a non-symmetric distribution of thepopulation. For a coarse network and P small, they found, in contrast to the literature, the Euclidean distance to be problematic. In this paper we extend their work by use of a refined network and study systematically the case when P is of varying size (2-100 facilities). We find that the network distance give as gooda solution as the travel-time network. The Euclidean distance gives solutions some 2-7 per cent worse than the network distances, and the solutions deteriorate with increasing P. Our conclusions extend to intra-urban location problems.

  • 4.
    Carling, Kenneth
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Han, Mengjie
    Dalarna University, School of Technology and Business Studies, Statistics.
    Håkansson, Johan
    Dalarna University, School of Technology and Business Studies, Information Systems.
    Rebreyend, Pascal
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    Testing the gravity p-median model empirically2015In: Operations Research Perspectives, ISSN 2214-7160, Vol. 2, no 124, article id 132Article in journal (Refereed)
    Abstract [en]

    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.

  • 5.
    Han, Mengjie
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Håkansson, Johan
    Dalarna University, School of Humanities and Media Studies, Cultural Studies.
    Rebreyend, Pascal
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    How do different densities in a network affect the optimal location of service centers?2013Report (Other academic)
    Abstract [en]

    The p-median problem is often used to locate p service centers by minimizing their distances to a geographically distributed demand (n). The optimal locations are sensitive to geographical context such as road network and demand points especially when they are asymmetrically distributed in the plane. Most studies focus on evaluating performances of the p-median model when p and n vary. To our knowledge this is not a very well-studied problem when the road network is alternated especially when it is applied in a real world context. The aim in this study is to analyze how the optimal location solutions vary, using the p-median model, when the density in the road network is alternated. The investigation is conducted by the means of a case study in a region in Sweden with an asymmetrically distributed population (15,000 weighted demand points), Dalecarlia. To locate 5 to 50 service centers we use the national transport administrations official road network (NVDB). The road network consists of 1.5 million nodes. To find the optimal location we start with 500 candidate nodes in the network and increase the number of candidate nodes in steps up to 67,000. To find the optimal solution we use a simulated annealing algorithm with adaptive tuning of the temperature. The results show that there is a limited improvement in the optimal solutions when nodes in the road network increase and p is low. When p is high the improvements are larger. The results also show that choice of the best network depends on p. The larger p the larger density of the network is needed. 

  • 6.
    Han, Mengjie
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Håkansson, Johan
    Dalarna University, School of Technology and Business Studies, Information Systems.
    Rebreyend, Pascal
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    How does data quality in a network affect heuristic solutions?2014Report (Other academic)
    Abstract [en]

    To have good data quality with high complexity is often seen to be important. Intuition says that the higher accuracy and complexity the data have the better the analytic solutions becomes if it is possible to handle the increasing computing time. However, for most of the practical computational problems, high complexity data means that computational times become too long or that heuristics used to solve the problem have difficulties to reach good solutions. This is even further stressed when the size of the combinatorial problem increases. Consequently, we often need a simplified data to deal with complex combinatorial problems. In this study we stress the question of how the complexity and accuracy in a network affect the quality of the heuristic solutions for different sizes of the combinatorial problem. We evaluate this question by applying the commonly used

    p-median model, which is used to find optimal locations in a network of p supply points that serve n demand points. To evaluate this, we vary both the accuracy (the number of nodes) of the network and the size of the combinatorial problem (p).

    The investigation is conducted by the means of a case study in a region in Sweden with an asymmetrically distributed population (15,000 weighted demand points), Dalecarlia. To locate 5 to 50 supply points we use the national transport administrations official road network (NVDB). The road network consists of 1.5 million nodes. To find the optimal location we start with 500 candidate nodes in the network and increase the number of candidate nodes in steps up to 67,000 (which is aggregated from the 1.5 million nodes). To find the optimal solution we use a simulated annealing algorithm with adaptive tuning of the temperature. The results show that there is a limited

    improvement in the optimal solutions when the accuracy in the road network increase and the combinatorial problem (low

    p) is simple. When the combinatorial problem is complex (large p) the improvements of increasing the accuracy in the road network are much larger. The results also show that choice of the best accuracy of the network depends on the complexity of the combinatorial (varying p) problem.

  • 7.
    Han, Mengjie
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Håkansson, Johan
    Dalarna University, School of Technology and Business Studies, Human Geography.
    Rebreyend, Pascal
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    How does the use of different road networks effect the optimal location of facilities in rural areas?2012Report (Other academic)
    Abstract [en]

    The p-median problem is often used to locate P service facilities in a geographically distributed population. Important for the performance of such a model is the distance measure.

    Distance measure can vary if the accuracy of the road network varies. The rst aim in this study is to analyze how the optimal location solutions vary, using the p-median model, when the road network is alternated. It is hard to nd an exact optimal solution for p-median problems. Therefore, in this study two heuristic solutions are applied, simulating annealing and a classic heuristic. The secondary aim is to compare the optimal location solutions using dierent algorithms for large p-median problem. The investigation is conducted by the means of a case study in a rural region with an asymmetrically distributed population, Dalecarlia.

    The study shows that the use of more accurate road networks gives better solutions for optimal location, regardless what algorithm that is used and regardless how many service facilities that is optimized for. It is also shown that the simulated annealing algorithm not just is much faster than the classic heuristic used here, but also in most cases gives better location solutions.

  • 8. Meng, Xiangli
    et al.
    Carling, Kenneth
    Dalarna University, School of Technology and Business Studies, Microdata Analysis.
    Håkansson, Johan
    Dalarna University, School of Technology and Business Studies, Microdata Analysis.
    Rebreyend, Pascal
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    How do administrative borders affect accessibility to hospitals? The case of Sweden2018In: International Journal of Health Planning and Management, ISSN 0749-6753, E-ISSN 1099-1751, Vol. 33, no 3Article in journal (Refereed)
    Abstract [en]

    An administrative border might hinder the optimal allocation of a given set of resources by restricting the flow of goods, services, and people. In this paper, we address the question: Do administrative borders lead to poor accessibility to public service? In answering the question, we have examined the case of Sweden and its regional administrative borders and hospital accessibility. We have used detailed data on the Swedish road network, its hospitals, and its geo-coded population. We have assessed the population's spatial accessibility to Swedish hospitals by computing the inhabitants' distance to the nearest hospital. We have also elaborated several scenarios ranging from strongly confining regional borders to no confinements of borders and recomputed the accessibility. Our findings imply that administrative borders are only marginally worsening the accessibility.

  • 9.
    Meng, Xiangli
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Carling, Kenneth
    Dalarna University, School of Technology and Business Studies, Statistics.
    Håkansson, Johan
    Dalarna University, School of Technology and Business Studies, Information Systems. Dalarna University, School of Technology and Business Studies, Human Geography.
    Rebreyend, Pascal
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    On administrative borders and accessibility to public services:: The case of hospitals in Sweden.2014Report (Other academic)
    Abstract [en]

    An administrative border might hinder the optimal allocation of a given set of resources by restricting the flow of goods, services, and people. In this paper we address the question: Do administrative borders lead to poor accessibility to public service such as hospitals? In answering the question, we have examined the case of Sweden and its regional borders. We have used detailed data on the Swedish road network, its hospitals, and its geo-coded population. We have assessed the population’s spatial accessibility to Swedish hospitals by computing the inhabitants’ distance to the nearest hospital. We have also elaborated several scenarios ranging from strongly confining regional borders to no confinements of borders and recomputed the accessibility. Our findings imply that administrative borders are only marginally worsening the accessibility.

  • 10.
    Meng, Xiangli
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Rebreyend, Pascal
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    From the road network database to a graph for localization purposes2014Report (Other academic)
    Abstract [en]

    The problems of finding best facility locations require complete and accurate road network with the corresponding population data in a specific area. However the data obtained in road network databases usually do not fit in this usage. In this paper we propose our procedure of converting the road network database to a road graph which could be used in localization problems. The road network data come from the National road data base in Sweden. The graph derived is cleaned, and reduced to a suitable level for localization problems. The population points are also processed in ordered to match with that graph. The reduction of the graph is done maintaining most of the accuracy for distance measures in the network.

  • 11.
    Meng, Xiangli
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Rebreyend, Pascal
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    On transforming a road network database to a graph for localization purpose2016In: International Journal of Web Services Research, ISSN 1545-7362, E-ISSN 1546-5004, Vol. 13, no 2, p. 46-55Article in journal (Refereed)
    Abstract [en]

    The problems of finding best facility locations require complete and accurate road networks with the corresponding population data in a specific area. However the data obtained from road network databases usually do not fit in this usage. In this paper we propose a procedure of converting the road network database to a road graph which could be used for localization problems. Several challenging problems exist in the transformation process which are commonly met also in other data bases. The procedure of dealing with those challenges are proposed. The data come from the National road data base in Sweden. The graph derived is cleaned, and reduced to a suitable level for localization problems. The residential points are also processed in ordered to match the graph. The reduction of the graph is done maintaining the accuracy of distance measures in the network.

  • 12.
    Rebreyend, Pascal
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    A dispatching tool for railway Transportation2006In: PATAT 06, BRNO, 2006Conference paper (Other academic)
    Abstract [en]

    Railway transportations becomes again to be seen as an efficient and environmentally friendly mean of transportation. To develop it, users (both passengers and compagnies) want to have reliability and especially trains which follow timetables. If to reduce causes leading to delay or cancel a train is a difficult task, we may put some effort to minimize consequences of this problem to other tra ins. This chain effect tends to be worse and worse since the traffic is increasing while the infrastructure remains almost the same for ecomomical reasons. Train Dispatching (i.e to route train in real-time) is an important key to reduce delays and other effects in case of problems. The dispatcher chooses for each train on which track it should run and can ask a rain to stop. A typical example is the single-track connection where only in few places trains in opposite directions can meet. If the preliminary schedule is built in order to have crossing done without let some trains waiting for the other, the dispatcher should in case of an unexpected delay of one train choose either to move the crossing to another place or to stop the on-time train and keep the crossin g at the same place. When the network consists of dual or several tracks, the main problem is not the crossing but the difference in speed of different t rains (freight, long-distance passengers, suburban) and where and how a train can overtake another one.

  • 13.
    Rebreyend, Pascal
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    DisTrain: a simulation tool for train dispatching2005In: Proceedings 2005 IEEE Intelligent Transportation Systems Conference (ITSC), Vienna, Austria: IEEE , 2005Conference paper (Refereed)
    Abstract [en]

    This paper introduces main motivations and ideas of the tool called DisTrain whioch is an on-going work. The purpose of thistool is to provide a library to work and solve the Train Dispatching (or re-scheduling) problem. This paper is organized as follow: The first section introduce the briefly the problem and give a small litterature survey around this problem. The second section describes the main motivations and goals of this tool. Section III explain how the problem is represented and the interface between data and the library. Section IV explain how the library works and explain how different algorithms can solve this problem and why they should be tried. The fifth section targets practical issues. Then, section VI, VII conclude this paper and point out the future of DisTrain. This paper describes an on-going research work on the train dispatching problem. This dispatching or re-scheduling problem (which is NP-complete in general cases) lacks a benchmark or a library to test different algorithms. Therefore, we present a modelisation of the problem, on which our future tool is based. The tool is decomposed into a simulation engine (event driven) which may use different algorithms to solve the problem. Different algorithms may be used and tried

  • 14.
    Rebreyend, Pascal
    et al.
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    Clugery, Cedric
    Hily, Emmanuel
    A Heuristic-Based Bee Colonyt Algorthm for the Multiprocessor Scheduling Problem2010In: Nature Inspired Cooperative Strategies for Optimization (NICSO 2010), Heidelberg: Springer Berlin , 2010, Vol. 284, p. 295-304Chapter in book (Other academic)
    Abstract [en]

    The multiprocessor scheduling is one of the NP-complete scheduling problems. This problem comes when a known parallel program must be executed on a parallel computer. Different methods and algorithms have been tested for this scheduling problem. This paper presents and tests a hybrid bee algorithm. In this approach, the bee algorithm is combined with a heuristic in order to produce quickly good solutions. The choosen heuristic is a greedy approach and hybridization is done using the indirect representation. The heuristic is a list heuristic and the bee algorithm has to find the best order for the ordered list of tasks used by the heuristic. Experimental results on different benchmarks will be presented and analized, as well as a comparison with other hybrid approaches.

  • 15.
    Rebreyend, Pascal
    et al.
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    Dougherty, Mark
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    Yella, Siril
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    International Master Programme: two intakes per year for a better peer group support2005In: LMD Informatique en Europe et Emploi, Montpellier, France, 2005Conference paper (Other academic)
  • 16.
    Rebreyend, Pascal
    et al.
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    Han, Mengjie
    Dalarna University, School of Technology and Business Studies, Statistics.
    Håkansson, Johan
    Dalarna University, School of Technology and Business Studies, Human Geography.
    How does different algorithm work when applied on the different road networks when optimal location of facilities is searched for in rural areas?2014In: Web Information Systems Engineering – WISE 2013 Workshops: WISE 2013 International Workshops BigWebData, MBC, PCS, STeH, QUAT, SCEH, and STSC 2013, Nanjing, China, October 13-15, 2013, Revised Selected Papers / [ed] Zhisheng Huang, Chengfei Liu, Jing He, Guangyan Huang, Berlin: Springer Berlin/Heidelberg, 2014, Vol. 8182, p. 284-291Conference paper (Refereed)
    Abstract [en]

    The p-median problem is often used to locate P service facilities in a geographically distributed population. Important for the performance of such a model is the distance measure. The first aim in this study is to analyze how the optimal location solutions vary, using the p-median model, when the road network is alternated. It is hard to find an exact optimal solution for p-median problems. Therefore, in this study two heuristic solutions are applied, simulating annealing and a classic heuristic. The secondary aim is to compare the optimal location solutions using different algorithms for large p-median problem. The investigation is conducted by the means of a case study in a rural region with a. asymmetrically distributed population, Dalecarlia. The study shows that the use of more accurate road networks gives better solutions for optimal location, regardless what algorithm that is used and regardless how many service facilities that is opt for. It is also shown that the Simulating annealing algorithm not just is much faster than the classic heuristic used here, but also in most cases gives better solutions.

  • 17.
    Rebreyend, Pascal
    et al.
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    Lemarchand, Laurent
    Euler, Reinhardt
    A computational comparison of different algorithms for very large p-median problems2015In: Evolutionary Computation in Combinatorial Optimization: 15th European Conference, EvoCOP 2015, Copenhagen, Denmark, April 8-10, 2015, Proceedings / [ed] Gabriela Ochoa, Francisco Chicano, Springer, 2015, Vol. 9026, p. 13-24Conference paper (Refereed)
    Abstract [en]

    In this paper, we propose a new method for solving large scale p-median problem instances based on real data. We compare different approaches in terms of runtime, memory footprint and quality of solutions obtained. In order to test the different methods on real data, we introduce a new benchmark for the p-median problem based on real Swedish data. Because of the size of the problem addressed, up to 1938 candidate nodes, a number of algorithms, both exact and heuristic, are considered. We also propose an improved hybrid version of a genetic algorithm called impGA. Experiments show that impGA behaves as well as other methods for the standard set of medium-size problems taken from Beasley’s benchmark, but produces comparatively good results in terms of quality, runtime and memory footprint on our specific benchmark based on real Swedish data.

  • 18.
    Rebreyend, Pascal
    et al.
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    Lemarchand, Laurent
    Massé, Damien
    Håkansson, Johan
    Dalarna University, School of Technology and Business Studies, Microdata Analysis.
    Multiobjective Optimization for Multimode Transportation Problems2018In: Advances in Operations Research, ISSN 1687-9147, E-ISSN 1687-9155, article id 8720643Article in journal (Refereed)
    Abstract [en]

    We propose modelling for a facilities localization problem in the context of multimode transportation. The applicative goal is to locate service facilities such as schools or hospitals while optimizing the different transportation modes to these facilities. We formalize the School Problem and solve it first exactly using an adapted -constraint multiobjective method. Because of the size of the instances considered, we have also explored the use of heuristic methods based on evolutionary multiobjective frameworks, namely, NSGA2 and a modified version of PAES. Those methods are mixed with an original local search technique to provide better results. Numerical comparisons of solutions sets quality are made using the hypervolume metric. Based on the results for test-cases that can be solved exactly, efficient implementation for PAES and NSGA2 allows execution times comparison for large instances. Results show good performances for the heuristic approaches as compared to the exact algorithm for small test-cases. Approximate methods present a scalable behavior on largest problem instances. A master/slave parallelization scheme also helps to reduce execution times significantly for the modified PAES approach.

  • 19.
    Rönnegård, Lars
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Rebreyend, Pascal
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    Håkansson, Johan
    Dalarna University, School of Technology and Business Studies, Statistics.
    Vinterkonferens i rumslig statistik i Dalarna2011In: Qvintensen, ISSN 2000-1819, Vol. 2011, no 4Article in journal (Other academic)
  • 20.
    Shaik, Asif ur Rahman
    et al.
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    Vlad, Stefan
    Rebreyend, Pascal
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    Yella, Siril
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    Multi-agent simulation of sawmill yard operations2012In: ASM-ASC 2012 - Applied Simulation and Modelling - Artificial Intelligence and Soft Computing / [ed] A. Bruzzone, M.H. Hamza, 2012Conference paper (Refereed)
    Abstract [en]

    This paper reports the findings of using multi-agent based simulation model to evaluate the sawmill yard operations within a large privately owned sawmill in Sweden, Bergkvist Insjön AB in the current case. Conventional working routines within sawmill yard threaten the overall efficiency and thereby limit the profit margin of sawmill. Deploying dynamic work routines within the sawmill yard is not readily feasible in real time, so discrete event simulation model has been investigated to be able to report optimal work order depending on the situations. Preliminary investigations indicate that the results achieved by simulation model are promising. It is expected that the results achieved in the current case will support Bergkvist-Insjön AB in making optimal decisions by deploying efficient work order in sawmill yard.

  • 21.
    Zhao, Xiaoyun
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Rebreyend, Pascal
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    Håkansson, Johan
    Dalarna University, School of Technology and Business Studies, Information Systems. Dalarna University, School of Technology and Business Studies, Human Geography.
    Does road network density matter in optimally locating facilities?2015Report (Other (popular science, discussion, etc.))
    Abstract [en]

    Optimal location on the transport infrastructure is the preferable requirement for many decision making processes. Most studies have focused on evaluating performances of optimally locate p facilities by minimizing their distances to a geographically distributed demand (n) when p and n vary. The optimal locations are also sensitive to geographical context such as road network, especially when they are asymmetrically distributed in the plane. The influence of alternating road network density is however not a very well-studied problem especially when it is applied in a real world context. This paper aims to investigate how the density level of the road network affects finding optimal location by solving the specific case of p-median location problem. A denser network is found needed when a higher number of facilities are to locate. The best solution will not always be obtained in the most detailed network but in a middle density level. The solutions do not further improve or improve insignificantly as the density exceeds 12,000 nodes, some solutions even deteriorate. The hierarchy of the different densities of network can be used according to location and transportation purposes and increase the efficiency of heuristic methods. The method in this study can be applied to other location-allocation problem in transportation analysis where the road network density can be differentiated. 

  • 22.
    Zhao, Xiaoyun
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Rebreyend, Pascal
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    Håkansson, Johan
    Dalarna University, School of Technology and Business Studies, Information Systems. Dalarna University, School of Technology and Business Studies, Human Geography.
    How does the complexity of a road network affect optimal facility locations?2015Report (Other academic)
    Abstract [en]

    The road network is a necessary component in transportation. It facilitiesspatial movements of people and goods, and it also influences the optimal locations of facilities that usually serve as destinations of the movements. To fulfill the transportation needs and to adapt to the facility development, the road network is often organized hierarchically and asymmetrically with various road levels and spatial structures. The complexity of the road network increases along with the increase of road levels and spatial structures. However, location models locate facilities on a given road network, usually the most complex one, and the influence from the complexity of road network in finding optimal locations is not well-studied. This paper aims to investigate how the complexity of a road network affects the optimal facility locations by applying the widely-applied p-median model. The main result indicates that an increase in road network complexity, up to a certain level, can obviously improve the solution, and the complexity beyond that level does not always lead to better solutions. Furthermore, the result is not sensitive to the choice of algorithms. In a specific case study, a detailed sensitivity analysis of algorithm and facility number further provides insight into computation complexity and location problems from intra-urban to inter-urban.

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