Heuristic approaches for solid transportation-p-facility location problem

  • Soumen Kumar Das
  • Sankar Kumar RoyEmail author
  • Gerhard Wilhelm Weber
Original Paper


Determining optimum places for the facilities and optimum transportation from existing sites to the facilities belongs to the main problems in supply chain management. The solid transportation-p-facility location problem (ST-p-FLP) is an integration between the facility location problem and the solid transportation problem (STP). This paper delineates the ST-p-FLP, a generalization of the classical STP in which location of p-potential facility sites are sought so that the total transportation cost by means of conveyances from existing facility sites to potential facility sites will be minimized. This is one of the most important problems in the transportation systems and the location research areas. Two heuristic approaches are developed to solve such type of problem: a locate-allocate heuristic and an approximate heuristic. Thereafter, the performance of the proposed model and the heuristics are evaluated by an application example, and the obtained results are compared. Moreover, a sensitivity analysis is introduced to investigate the resiliency of the proposed model. Finally, conclusions and an outlook to future research works are provided.


Facility location problem Solid transportation problem Solid transportation-p-facility location Optimization Heuristic approaches 



The author Soumen Kumar Das is very thankful to the Department of Science & Technology (DST) of India for providing financial support to continue this research work under [JRF-P (DST-INSPIRE Program)] scheme: Sanctioned letter number DST/INSPIRE Fellowship/2015/IF150209 dated 01/10/2015. The research of Sankar Kumar Roy and Gerhard-Wilhelm Weber is partially supported by the Portuguese Foundation for Science and Technology (“FCT-Fundação para a Ciência e a Tecnologia”), through the CIDMA-Center for Research and Development in Mathematics and Applications, University of Aveiro, Portugal, within project UID/MAT/04106/2013. The authors express the gratitude to the anonymous reviewers for their valuable criticisms, and to the Editor-in-Chief, Prof. Dr. Ulrike Leopold-Wildburger for her great support.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied Mathematics with Oceanology and Computer ProgrammingVidyasagar UniversityMidnaporeIndia
  2. 2.Chair of Marketing and Economic Engineering, Faculty of Engineering ManagementPoznan University of TechnologyPoznanPoland
  3. 3.Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey

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