IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v39y2005i2p182-187.html
   My bibliography  Save this article

Complexity and Reducibility of the Skip Delivery Problem

Author

Listed:
  • C. Archetti

    (Department of Quantitative Methods, University of Brescia, C.da S. Chiara 50, I-25122 Brescia, Italy)

  • R. Mansini

    (Department of Electronics for Automation, University of Brescia, via Branze 38, I-25123 Brescia, Italy)

  • M. G. Speranza

    (Department of Quantitative Methods, University of Brescia, C.da S. Chiara 50, I-25122 Brescia, Italy)

Abstract

In the skip delivery problem (SDP), a fleet of vehicles must deliver skips to a set of customers. Each vehicle has a maximum capacity of two skips, and has to start and end its tour at a central depot. The demand of each customer can be greater than the capacity of the vehicles. The objective is to minimize the cost of the total distance traveled by the vehicles to serve all the customers. We show that the SDP is solvable in polynomial time, while its generalization to the case where all vehicles have a capacity greater than two, known as the split delivery vehicle routing problem (SDVRP), is shown to be NP-hard, even under restricted conditions on the costs. We also show that, if the costs are symmetrical and satisfy the triangle inequality, the SDP is reducible in polynomial time to a problem of possibly smaller size, where each customer has unitary demand. This property allows a remarkable simplification of the problem.

Suggested Citation

  • C. Archetti & R. Mansini & M. G. Speranza, 2005. "Complexity and Reducibility of the Skip Delivery Problem," Transportation Science, INFORMS, vol. 39(2), pages 182-187, May.
  • Handle: RePEc:inm:ortrsc:v:39:y:2005:i:2:p:182-187
    DOI: 10.1287/trsc.1030.0084
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/trsc.1030.0084
    Download Restriction: no

    File URL: https://libkey.io/10.1287/trsc.1030.0084?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
    ---><---

    References listed on IDEAS

    as
    1. Moshe Dror & Pierre Trudeau, 1989. "Savings by Split Delivery Routing," Transportation Science, INFORMS, vol. 23(2), pages 141-145, May.
    2. Éric Gourdin & Martine Labbé & Gilbert Laporte, 2000. "The Uncapacitated Facility Location Problem with Client Matching," Operations Research, INFORMS, vol. 48(5), pages 671-685, October.
    3. Lawrence Bodin & Aristide Mingozzi & Roberto Baldacci & Michael Ball, 2000. "The Rollon–Rolloff Vehicle Routing Problem," Transportation Science, INFORMS, vol. 34(3), pages 271-288, August.
    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. Fernanda Menezes & Oscar Porto & Marcelo L. Reis & Lorenza Moreno & Marcus Poggi de Aragão & Eduardo Uchoa & Hernán Abeledo & Nelci Carvalho do Nascimento, 2010. "Optimizing Helicopter Transport of Oil Rig Crews at Petrobras," Interfaces, INFORMS, vol. 40(5), pages 408-416, October.
    2. Claudia Archetti & Martin W. P. Savelsbergh & M. Grazia Speranza, 2006. "Worst-Case Analysis for Split Delivery Vehicle Routing Problems," Transportation Science, INFORMS, vol. 40(2), pages 226-234, May.
    3. C. Archetti & M. G. Speranza & A. Hertz, 2006. "A Tabu Search Algorithm for the Split Delivery Vehicle Routing Problem," Transportation Science, INFORMS, vol. 40(1), pages 64-73, February.
    4. Alberto Ceselli & Giovanni Righini & Matteo Salani, 2009. "A Column Generation Algorithm for a Rich Vehicle-Routing Problem," Transportation Science, INFORMS, vol. 43(1), pages 56-69, February.
    5. Fleming, Christopher L. & Griffis, Stanley E. & Bell, John E., 2013. "The effects of triangle inequality on the vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 224(1), pages 1-7.
    6. José-Manuel Belenguer & Enrique Benavent & Nacima Labadi & Christian Prins & Mohamed Reghioui, 2010. "Split-Delivery Capacitated Arc-Routing Problem: Lower Bound and Metaheuristic," Transportation Science, INFORMS, vol. 44(2), pages 206-220, May.
    7. Jan Pelikán & Jan Fábry, 2012. "Heuristics for routes generation in pickup and delivery problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(3), pages 463-472, September.
    8. Claudia Archetti & M. Grazia Speranza & Martin W. P. Savelsbergh, 2008. "An Optimization-Based Heuristic for the Split Delivery Vehicle Routing Problem," Transportation Science, INFORMS, vol. 42(1), pages 22-31, February.
    9. U Derigs & B Li & U Vogel, 2010. "Local search-based metaheuristics for the split delivery vehicle routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(9), pages 1356-1364, September.

    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. Huang, Sen & Liu, Kanglin & Zhang, Zhi-Hai, 2023. "Column-and-constraint-generation-based approach to a robust reverse logistic network design for bike sharing," Transportation Research Part B: Methodological, Elsevier, vol. 173(C), pages 90-118.
    2. Ling Gai & Ying Jin & Binyuan Zhang, 2022. "An integrated method for hybrid distribution with estimation of demand matching degree," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2782-2808, November.
    3. Weikang Fang & Zailin Guan & Peiyue Su & Dan Luo & Linshan Ding & Lei Yue, 2022. "Multi-Objective Material Logistics Planning with Discrete Split Deliveries Using a Hybrid NSGA-II Algorithm," Mathematics, MDPI, vol. 10(16), pages 1-30, August.
    4. Jiliu Li & Zhixing Luo & Roberto Baldacci & Hu Qin & Zhou Xu, 2023. "A New Exact Algorithm for Single-Commodity Vehicle Routing with Split Pickups and Deliveries," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 31-49, January.
    5. Lin, Yen-Hung & Batta, Rajan & Rogerson, Peter A. & Blatt, Alan & Flanigan, Marie, 2011. "A logistics model for emergency supply of critical items in the aftermath of a disaster," Socio-Economic Planning Sciences, Elsevier, vol. 45(4), pages 132-145, December.
    6. Sun, Yanshuo & Kirtonia, Sajeeb & Chen, Zhi-Long, 2021. "A survey of finished vehicle distribution and related problems from an optimization perspective," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 149(C).
    7. Nicola Bianchessi & Stefan Irnich, 2016. "Branch-and-Cut for the Split Delivery Vehicle Routing Problem with Time Windows," Working Papers 1620, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    8. Wei, Xiaoyang & Jia, Shuai & Meng, Qiang & Tan, Kok Choon, 2020. "Tugboat scheduling for container ports," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 142(C).
    9. Kjetil Fagerholt *, 2004. "Designing optimal routes in a liner shipping problem," Maritime Policy & Management, Taylor & Francis Journals, vol. 31(4), pages 259-268, October.
    10. Sophie N. Parragh & Jorge Pinho de Sousa & Bernardo Almada-Lobo, 2015. "The Dial-a-Ride Problem with Split Requests and Profits," Transportation Science, INFORMS, vol. 49(2), pages 311-334, May.
    11. Fatemeh Sabouhi & Ali Bozorgi-Amiri & Mohammad Moshref-Javadi & Mehdi Heydari, 2019. "An integrated routing and scheduling model for evacuation and commodity distribution in large-scale disaster relief operations: a case study," Annals of Operations Research, Springer, vol. 283(1), pages 643-677, December.
    12. Drexl, Andreas & Klose, Andreas, 2001. "Facility location models for distribution system design," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 546, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    13. Saman Eskandarzadeh & Reza Tavakkoli-Moghaddam & Amir Azaron, 2009. "An extension of the relaxation algorithm for solving a special case of capacitated arc routing problems," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 214-234, February.
    14. Jie, Wanchen & Yang, Jun & Zhang, Min & Huang, Yongxi, 2019. "The two-echelon capacitated electric vehicle routing problem with battery swapping stations: Formulation and efficient methodology," European Journal of Operational Research, Elsevier, vol. 272(3), pages 879-904.
    15. Pedro Munari & Martin Savelsbergh, 2020. "A Column Generation-Based Heuristic for the Split Delivery Vehicle Routing Problem with Time Windows," SN Operations Research Forum, Springer, vol. 1(4), pages 1-24, December.
    16. S Mitra, 2008. "A parallel clustering technique for the vehicle routing problem with split deliveries and pickups," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(11), pages 1532-1546, November.
    17. Belfiore, PatrI´cia & Yoshida Yoshizaki, Hugo Tsugunobu, 2009. "Scatter search for a real-life heterogeneous fleet vehicle routing problem with time windows and split deliveries in Brazil," European Journal of Operational Research, Elsevier, vol. 199(3), pages 750-758, December.
    18. Mingyue Shao & Dongxu Chen & Xiaolong Lu & Xuefei Liu & Zhongzhen Yang, 2023. "Does Drop and Pull Transport Have a Chance? The Case of China," Sustainability, MDPI, vol. 15(13), pages 1-20, June.
    19. Jing Chen & Pengfei Gui & Tao Ding & Sanggyun Na & Yingtang Zhou, 2019. "Optimization of Transportation Routing Problem for Fresh Food by Improved Ant Colony Algorithm Based on Tabu Search," Sustainability, MDPI, vol. 11(23), pages 1-22, November.
    20. Efraín Ruiz y Ruiz & Irma García-Calvillo & Samuel Nucamendi-Guillén, 2022. "Open vehicle routing problem with split deliveries: mathematical formulations and a cutting-plane method," Operational Research, Springer, vol. 22(2), pages 1017-1037, April.

    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:inm:ortrsc:v:39:y:2005:i:2:p:182-187. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.