IDEAS home Printed from https://ideas.repec.org/a/eee/oprepe/v5y2018icp319-333.html

Multi-index constrained transportation problem with bounds on availabilities, requirements and commodities

Author

Listed:
  • Khurana, Archana
  • Adlakha, Veena
  • Lev, Benjamin

Abstract

In this paper, we consider a multi-index constrained transportation problem (CTP) of axial constraints with bounds on destination requirements, source availabilities, and multiple types of commodities. The specified problem is converted into a related transportation problem by adding a source, a destination, and a commodity, making it equivalent to a standard axial sum problem. This related problem is transformed into a multi-index transportation problem that can be solved easily. The provided solution method is very useful for transporting heterogeneous commodities. A transportation model may sometimes have various capacity constraints on the flow between pairs of origins and destinations. Moreover, budgetary, political, and emergency situations may impair or enhance the flow between origins and destinations, making it critical for a manager to reevaluate allocations. These considerations have motivated us to explore the multi-index CTP with impaired and enhanced flow. We present several numerical examples to demonstrate the proposed algorithms.

Suggested Citation

  • Khurana, Archana & Adlakha, Veena & Lev, Benjamin, 2018. "Multi-index constrained transportation problem with bounds on availabilities, requirements and commodities," Operations Research Perspectives, Elsevier, vol. 5(C), pages 319-333.
    • Handle: RePEc:eee:oprepe:v:5:y:2018:i:c:p:319-333
    DOI: 10.1016/j.orp.2018.10.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S2214716018300666
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.orp.2018.10.001?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

    for a different version of it.

    References listed on IDEAS

    as
    1. A. Charnes & Darwin Klingman, 1970. "Note--The Distribution Problem with Upper and Lower Bounds on the Node Requirements," Management Science, INFORMS, vol. 16(9), pages 638-642, May.
    2. Dahiya, Kalpana & Verma, Vanita, 2007. "Capacitated transportation problem with bounds on RIM conditions," European Journal of Operational Research, Elsevier, vol. 178(3), pages 718-737, May.
    3. Pradip Kundu & Samarjit Kar & Manoranjan Maiti, 2014. "Multi-objective solid transportation problems with budget constraint in uncertain environment," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(8), pages 1668-1682, August.
    4. K. B. Haley, 1963. "The Multi-Index Problem," Operations Research, INFORMS, vol. 11(3), pages 368-379, June.
    5. Harvey M. Wagner, 1959. "On a Class of Capacitated Transportation Problems," Management Science, INFORMS, vol. 5(3), pages 304-318, April.
    6. Kowalski, Krzysztof & Lev, Benjamin & Shen, Wenjing & Tu, Yan, 2014. "A fast and simple branching algorithm for solving small scale fixed-charge transportation problem," Operations Research Perspectives, Elsevier, vol. 1(1), pages 1-5.
    7. Hu, Qian & Zhang, Zhenzhen & Lim, Andrew, 2016. "Transportation service procurement problem with transit time," Transportation Research Part B: Methodological, Elsevier, vol. 86(C), pages 19-36.
    8. Di, Zhen & Yang, Lixing & Qi, Jianguo & Gao, Ziyou, 2018. "Transportation network design for maximizing flow-based accessibility," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 209-238.
    9. Dangalchev, Chavdar A., 2000. "Optimization of the transportation expense of a firm with contractual supplies," Transportation Research Part B: Methodological, Elsevier, vol. 34(3), pages 203-217, April.
    10. D. Klingman & R. Russell, 1975. "Solving Constrained Transportation Problems," Operations Research, INFORMS, vol. 23(1), pages 91-106, February.
    11. Adlakha, Veena & Kowalski, Krzysztof & Lev, Benjamin, 2010. "A branching method for the fixed charge transportation problem," Omega, Elsevier, vol. 38(5), pages 393-397, October.
    12. Archana Khurana & Tripti Verma, 2015. "On a class of capacitated transshipment problems with bounds on rim conditions," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 7(3), pages 251-280.
    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. Singh, Bikramjit & Singh, Amarinder, 2023. "Hybrid particle swarm optimization for pure integer linear solid transportation problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 243-266.
    2. Abd Elazeem M. Abd Elazeem & Abd Allah A. Mousa & Mohammed A. El-Shorbagy & Sayed K. Elagan & Yousria Abo-Elnaga, 2021. "Detecting All Non-Dominated Points for Multi-Objective Multi-Index Transportation Problems," Sustainability, MDPI, vol. 13(3), pages 1-18, January.

    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. Gourav Gupta & Shivani & Deepika Rani, 2024. "Neutrosophic goal programming approach for multi-objective fixed-charge transportation problem with neutrosophic parameters," OPSEARCH, Springer;Operational Research Society of India, vol. 61(3), pages 1274-1300, September.
    2. Wang, Gang, 2024. "Order assignment and two-stage integrated scheduling in fruit and vegetable supply chains," Omega, Elsevier, vol. 124(C).
    3. Sharma, Anuj & Verma, Vanita & Kaur, Prabhjot & Dahiya, Kalpana, 2015. "An iterative algorithm for two level hierarchical time minimization transportation problem," European Journal of Operational Research, Elsevier, vol. 246(3), pages 700-707.
    4. Bertazzi, Luca & Maggioni, Francesca, 2018. "A stochastic multi-stage fixed charge transportation problem: Worst-case analysis of the rolling horizon approach," European Journal of Operational Research, Elsevier, vol. 267(2), pages 555-569.
    5. Qu, Kai & Fan, Xiangyi & Xu, Xiangdong & Hanasusanto, Grani A. & Chen, Anthony, 2025. "Improving transportation network redundancy under uncertain disruptions via retrofitting critical components," Transportation Research Part B: Methodological, Elsevier, vol. 194(C).
    6. Raúl Pérez-Fernández & Bernard De Baets, 2017. "Recursive Monotonicity of the Scorix: Borda Meets Condorcet," Group Decision and Negotiation, Springer, vol. 26(4), pages 793-813, July.
    7. Supinder Kaur & Ekta Jain & Kalpana Dahiya, 2025. "Two-level solid transportation problem," OPSEARCH, Springer;Operational Research Society of India, vol. 62(1), pages 423-447, March.
    8. Pankaj Gupta & Mukesh Mehlawat, 2007. "An algorithm for a fuzzy transportation problem to select a new type of coal for a steel manufacturing unit," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 114-137, July.
    9. Sullivan, James L. & Novak, David C., 2024. "A method for evaluating accessibility in transportation problems considering social vulnerability," European Journal of Operational Research, Elsevier, vol. 317(3), pages 646-659.
    10. Jimenez, F. & Verdegay, J. L., 1999. "Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach," European Journal of Operational Research, Elsevier, vol. 117(3), pages 485-510, September.
    11. J R Montoya-Torres & A Aponte & P Rosas, 2011. "Applying GRASP to solve the multi-item three-echelon uncapacitated facility location problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(2), pages 397-406, February.
    12. Zhang, Li-Hao & Liu, Chunxiao & Zhang, Cheng & Wang, Shanshan, 2023. "Upstream encroachment and downstream outsourcing in competing shipping supply chains," International Journal of Production Economics, Elsevier, vol. 255(C).
    13. Zhang, Honggang & Wang, Yuyan & Jiang, Mengyu & Huang, Zefan & Pang, King-Wah & Liu, Zhiyuan, 2025. "Optimizing land-air collaborative operations with environmental considerations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 202(C).
    14. Qiang Tu & Han He & Xiaomin Lai & Chuan Jiang & Zhanji Zheng, 2024. "Identifying Critical Links in Degradable Road Networks Using a Traffic Demand-Based Indicator," Sustainability, MDPI, vol. 16(18), pages 1-20, September.
    15. Huang, Shan-Huen & Lin, Pei-Chun, 2015. "Vehicle routing–scheduling for municipal waste collection system under the “Keep Trash off the Ground” policy," Omega, Elsevier, vol. 55(C), pages 24-37.
    16. Gaudioso, Manlio & Monaco, Maria Flavia & Sammarra, Marcello, 2021. "A Lagrangian heuristics for the truck scheduling problem in multi-door, multi-product Cross-Docking with constant processing time," Omega, Elsevier, vol. 101(C).
    17. ÇalIskan, Cenk, 2011. "A specialized network simplex algorithm for the constrained maximum flow problem," European Journal of Operational Research, Elsevier, vol. 210(2), pages 137-147, April.
    18. Awdhesh Kumar Bind & Deepika Rani & Ali Ebrahimnejad, 2025. "A cost-effective and sustainable multi-objective 4D product blending transportation solution with all unit discounts in an intuitionistic fuzzy environment," Operational Research, Springer, vol. 25(4), pages 1-51, December.
    19. Zhou, Guanyu & Dong, Qianyu & Zhao, Yuming & Wang, Han & Jian, Linni & Jia, Youwei, 2023. "Bilevel optimization approach to fast charging station planning in electrified transportation networks," Applied Energy, Elsevier, vol. 350(C).
    20. Wang, Shuliang & Chen, Chen & Zhang, Jianhua & Gu, Xifeng & Huang, Xiaodi, 2022. "Vulnerability assessment of urban road traffic systems based on traffic flow," International Journal of Critical Infrastructure Protection, Elsevier, vol. 38(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:oprepe:v:5:y:2018:i:c:p:319-333. 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.journals.elsevier.com/operations-research-perspectives .

    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.