IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v261y2017i2p549-562.html
   My bibliography  Save this article

The directed profitable rural postman problem with incompatibility constraints

Author

Listed:
  • Colombi, Marco
  • Corberán, Ángel
  • Mansini, Renata
  • Plana, Isaac
  • Sanchis, José M.

Abstract

In this paper, we study a variant of the directed rural postman problem (RPP) where profits are associated with arcs to be served, and incompatibility constraints may exist between nodes and profitable arcs leaving them. If convenient, some of the incompatibilities can be removed provided that penalties are paid. The problem looks for a tour starting and ending at the depot that maximizes the difference between collected profits and total cost as sum of traveling costs and paid penalties, while satisfying remaining incompatibilities. The problem finds application in the domain of road transportation service, and in particular in the context of horizontal collaboration among carriers and shippers. We call this problem the directed profitable rural postman problem with incompatibility constraints. We propose two problem formulations and introduce a matheuristic procedure exploiting the presence of a variant of the generalized independent set problem (GISP) and of the directed rural postman problem (DRPP) as subproblems. Computational results show how the matheuristic is effective outperforming in many cases the result obtained in one hour computing time by a straightforward branch-and-cut approach implemented with IBM CPLEX 12.6.2 on instances with up to 500 nodes, 1535 arcs, 1132 profitable arcs, and 10,743 incompatibilities.

Suggested Citation

  • Colombi, Marco & Corberán, Ángel & Mansini, Renata & Plana, Isaac & Sanchis, José M., 2017. "The directed profitable rural postman problem with incompatibility constraints," European Journal of Operational Research, Elsevier, vol. 261(2), pages 549-562.
  • Handle: RePEc:eee:ejores:v:261:y:2017:i:2:p:549-562
    DOI: 10.1016/j.ejor.2017.02.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221717301078
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2017.02.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Cruijssen, Frans & Cools, Martine & Dullaert, Wout, 2007. "Horizontal cooperation in logistics: Opportunities and impediments," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 43(2), pages 129-142, March.
    2. Souffriau, Wouter & Vansteenwegen, Pieter & Vanden Berghe, Greet & Van Oudheusden, Dirk, 2011. "The planning of cycle trips in the province of East Flanders," Omega, Elsevier, vol. 39(2), pages 209-213, April.
    3. Ávila, Thais & Corberán, Ángel & Plana, Isaac & Sanchis, José M., 2016. "A branch-and-cut algorithm for the profitable windy rural postman problem," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1092-1101.
    4. Ángel Corberán & Elena Fernández & Carles Franquesa & José María Sanchis, 2011. "The Windy Clustered Prize-Collecting Arc-Routing Problem," Transportation Science, INFORMS, vol. 45(3), pages 317-334, August.
    5. Julián Aráoz & Elena Fernández & Carles Franquesa, 2009. "The Clustered Prize-Collecting Arc Routing Problem," Transportation Science, INFORMS, vol. 43(3), pages 287-300, August.
    6. Gendreau, Michel & Manerba, Daniele & Mansini, Renata, 2016. "The multi-vehicle traveling purchaser problem with pairwise incompatibility constraints and unitary demands: A branch-and-price approach," European Journal of Operational Research, Elsevier, vol. 248(1), pages 59-71.
    7. Deitch, Ray & Ladany, Shaul P., 2000. "The one-period bus touring problem: Solved by an effective heuristic for the orienteering tour problem and improvement algorithm," European Journal of Operational Research, Elsevier, vol. 127(1), pages 69-77, November.
    8. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    9. Malandraki, Chryssi & Daskin, Mark S., 1993. "The maximum benefit Chinese postman problem and the maximum benefit traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 65(2), pages 218-234, March.
    10. Aráoz, Julián & Fernández, Elena & Meza, Oscar, 2009. "Solving the Prize-collecting Rural Postman Problem," European Journal of Operational Research, Elsevier, vol. 196(3), pages 886-896, August.
    11. Marco Colombi & Ángel Corberán & Renata Mansini & Isaac Plana & José M. Sanchis, 2017. "The Hierarchical Mixed Rural Postman Problem," Transportation Science, INFORMS, vol. 51(2), pages 755-770, May.
    12. Moshe Dror & André Langevin, 1997. "A Generalized Traveling Salesman Problem Approach to the Directed Clustered Rural Postman Problem," Transportation Science, INFORMS, vol. 31(2), pages 187-192, May.
    13. Dominique Feillet & Pierre Dejax & Michel Gendreau, 2005. "The Profitable Arc Tour Problem: Solution with a Branch-and-Price Algorithm," Transportation Science, INFORMS, vol. 39(4), pages 539-552, November.
    14. Pearn, W. L. & Wang, K. H., 2003. "On the Maximum Benefit Chinese Postman Problem," Omega, Elsevier, vol. 31(4), pages 269-273, August.
    15. Colombi, Marco & Corberán, Ángel & Mansini, Renata & Plana, Isaac & Sanchis, José M., 2017. "The Hierarchical Mixed Rural Postman Problem: Polyhedral analysis and a branch-and-cut algorithm," European Journal of Operational Research, Elsevier, vol. 257(1), pages 1-12.
    16. Colombi, Marco & Mansini, Renata, 2014. "New results for the Directed Profitable Rural Postman Problem," European Journal of Operational Research, Elsevier, vol. 238(3), pages 760-773.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gajda, Mikele & Trivella, Alessio & Mansini, Renata & Pisinger, David, 2022. "An optimization approach for a complex real-life container loading problem," Omega, Elsevier, vol. 107(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Archetti, Claudia & Bertazzi, Luca & Laganà, Demetrio & Vocaturo, Francesca, 2017. "The Undirected Capacitated General Routing Problem with Profits," European Journal of Operational Research, Elsevier, vol. 257(3), pages 822-833.
    2. Ávila, Thais & Corberán, Ángel & Plana, Isaac & Sanchis, José M., 2016. "A branch-and-cut algorithm for the profitable windy rural postman problem," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1092-1101.
    3. Enrique Benavent & Ángel Corberán & Luís Gouveia & Maria Mourão & Leonor Pinto, 2015. "Profitable mixed capacitated arc routing and related problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 244-274, April.
    4. Colombi, Marco & Mansini, Renata, 2014. "New results for the Directed Profitable Rural Postman Problem," European Journal of Operational Research, Elsevier, vol. 238(3), pages 760-773.
    5. Claudia Archetti & M. Grazia Speranza & Ángel Corberán & José M. Sanchis & Isaac Plana, 2014. "The Team Orienteering Arc Routing Problem," Transportation Science, INFORMS, vol. 48(3), pages 442-457, August.
    6. Ángel Corberán & Elena Fernández & Carles Franquesa & José María Sanchis, 2011. "The Windy Clustered Prize-Collecting Arc-Routing Problem," Transportation Science, INFORMS, vol. 45(3), pages 317-334, August.
    7. Kasaei, Maziar & Salman, F. Sibel, 2016. "Arc routing problems to restore connectivity of a road network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 95(C), pages 177-206.
    8. Summerfield, Nichalin S. & Dror, Moshe & Cohen, Morris A., 2015. "City streets parking enforcement inspection decisions: The Chinese postman’s perspective," European Journal of Operational Research, Elsevier, vol. 242(1), pages 149-160.
    9. Xiaoguang Bao & Xinhao Ni, 2024. "Approximation algorithms for two clustered arc routing problems," Journal of Combinatorial Optimization, Springer, vol. 47(5), pages 1-12, July.
    10. Jessica Rodríguez-Pereira & Gilbert Laporte, 2022. "The target visitation arc routing problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 60-76, April.
    11. Aráoz, Julián & Fernández, Elena & Meza, Oscar, 2009. "Solving the Prize-collecting Rural Postman Problem," European Journal of Operational Research, Elsevier, vol. 196(3), pages 886-896, August.
    12. Oruc, Buse Eylul & Kara, Bahar Yetis, 2018. "Post-disaster assessment routing problem," Transportation Research Part B: Methodological, Elsevier, vol. 116(C), pages 76-102.
    13. Fernández, Elena & Roca-Riu, Mireia & Speranza, M. Grazia, 2018. "The Shared Customer Collaboration Vehicle Routing Problem," European Journal of Operational Research, Elsevier, vol. 265(3), pages 1078-1093.
    14. Elena Fernández & Jessica Rodríguez-Pereira, 2017. "Multi-depot rural postman problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 340-372, July.
    15. Arbib, Claudio & Servilio, Mara & Archetti, Claudia & Speranza, M. Grazia, 2014. "The directed profitable location Rural Postman Problem," European Journal of Operational Research, Elsevier, vol. 236(3), pages 811-819.
    16. Orlis, Christos & Laganá, Demetrio & Dullaert, Wout & Vigo, Daniele, 2020. "Distribution with Quality of Service Considerations: The Capacitated Routing Problem with Profits and Service Level Requirements," Omega, Elsevier, vol. 93(C).
    17. Nicola Bianchessi & Stefan Irnich & Christian Tilk, 2020. "A Branch-Price-and-Cut Algorithm for the Capacitated Multiple Vehicle Traveling Purchaser Problem with Unitary Demand," Working Papers 2003, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    18. Rodríguez-Pereira, Jessica & Fernández, Elena & Laporte, Gilbert & Benavent, Enrique & Martínez-Sykora, Antonio, 2019. "The Steiner Traveling Salesman Problem and its extensions," European Journal of Operational Research, Elsevier, vol. 278(2), pages 615-628.
    19. Julián Aráoz & Elena Fernández & Carles Franquesa, 2009. "The Clustered Prize-Collecting Arc Routing Problem," Transportation Science, INFORMS, vol. 43(3), pages 287-300, August.
    20. Ruiz-Meza, José & Montoya-Torres, Jairo R., 2022. "A systematic literature review for the tourist trip design problem: Extensions, solution techniques and future research lines," Operations Research Perspectives, Elsevier, vol. 9(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:261:y:2017:i:2:p:549-562. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.