IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v39y1992i4p447-469.html
   My bibliography  Save this article

A squared‐euclidean distance location‐allocation problem

Author

Listed:
  • Hanif D. Sherali
  • Cihan H. Tuncbilek

Abstract

This article is concerned with the analysis of a squared‐Euclidean distance location‐allocation problem with balanced transportation constraints, where the costs are directly proportional to distances and the amount shipped. The problem is shown to be equivalent to maximizing a convex quadratic function subject to transportation constraints. A branch‐and‐bound algorithm is developed that utilizes a specialized, tight, linear programming representation to compute strong upper bounds via a Lagrangian relaxation scheme. These bounds are shown to substantially dominate several other upper bounds that are derived using standard techniques as problem size increases. The special structure of the transportation constraints is used to derive a partitioning scheme, and this structure is further exploited to devise suitable logical tests that tighten the bounds implied by the branching restrictions on the transportation flows. The transportation structure is also used to generate additional cut‐set inequalities based on a cycle prevention method which preserves a forest graph for any partial solution. Results of the computational experiments, and a discussion on possible extensions, are also presented.

Suggested Citation

  • Hanif D. Sherali & Cihan H. Tuncbilek, 1992. "A squared‐euclidean distance location‐allocation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(4), pages 447-469, June.
  • Handle: RePEc:wly:navres:v:39:y:1992:i:4:p:447-469
    DOI: 10.1002/1520-6750(199206)39:43.0.CO;2-O
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(199206)39:43.0.CO;2-O
    Download Restriction: no

    File URL: https://libkey.io/10.1002/1520-6750(199206)39:43.0.CO;2-O?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. A. Charnes & W. W. Cooper, 1962. "Programming with linear fractional functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(3‐4), pages 181-186, September.
    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. M. Akyüz & İ. Altınel & Temel Öncan, 2014. "Location and allocation based branch and bound algorithms for the capacitated multi-facility Weber problem," Annals of Operations Research, Springer, vol. 222(1), pages 45-71, November.
    2. Necati Aras & İ. Kuban Altınel & Metin Orbay, 2007. "New heuristic methods for the capacitated multi‐facility Weber problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(1), pages 21-32, February.
    3. M. Hakan Akyüz & Temel Öncan & İ. Kuban Altınel, 2019. "Branch and bound algorithms for solving the multi-commodity capacitated multi-facility Weber problem," Annals of Operations Research, Springer, vol. 279(1), pages 1-42, August.

    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. Azarnoosh Kafi & Behrouz Daneshian & Mohsen Rostamy-Malkhalifeh, 2021. "Forecasting the confidence interval of efficiency in fuzzy DEA," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(1), pages 41-59.
    2. Tunjo Perić & Josip Matejaš & Zoran Babić, 2023. "Advantages, sensitivity and application efficiency of the new iterative method to solve multi-objective linear fractional programming 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. 31(3), pages 751-767, September.
    3. Kristiaan Kerstens & Jafar Sadeghi & Ignace Van de Woestyne, 2020. "Plant capacity notions in a non-parametric framework: a brief review and new graph or non-oriented plant capacities," Annals of Operations Research, Springer, vol. 288(2), pages 837-860, May.
    4. Yande Gong & Joe Zhu & Ya Chen & Wade D. Cook, 2018. "DEA as a tool for auditing: application to Chinese manufacturing industry with parallel network structures," Annals of Operations Research, Springer, vol. 263(1), pages 247-269, April.
    5. Zhang, Yanfang & Wei, Jinpeng & Gao, Qi & Shi, Xunpeng & Zhou, Dequn, 2022. "Coordination between the energy-consumption permit trading scheme and carbon emissions trading: Evidence from China," Energy Economics, Elsevier, vol. 116(C).
    6. Johannes König & Carsten Schröder, 2018. "Inequality-minimization with a given public budget," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 16(4), pages 607-629, December.
    7. Bao-Ngoc Tong & Cheng-Ping Cheng & Lien-Wen Liang & Yi-Jun Liu, 2023. "Using Network DEA to Explore the Effect of Mobile Payment on Taiwanese Bank Efficiency," Sustainability, MDPI, vol. 15(8), pages 1-18, April.
    8. Georg Bechler & Claudius Steinhardt & Jochen Mackert, 2021. "On the Linear Integration of Attraction Choice Models in Business Optimization Problems," SN Operations Research Forum, Springer, vol. 2(1), pages 1-13, March.
    9. Harald Dyckhoff & Katrin Allen, 1999. "Theoretische Begründung einer Effizienzanalyse mittels Data Envelopment Analysis (DEA)," Schmalenbach Journal of Business Research, Springer, vol. 51(5), pages 411-436, May.
    10. Changyu Zhou & Guohe Huang & Jiapei Chen, 2019. "A Type-2 Fuzzy Chance-Constrained Fractional Integrated Modeling Method for Energy System Management of Uncertainties and Risks," Energies, MDPI, vol. 12(13), pages 1-21, June.
    11. Yu, Shasha & Lei, Ming & Deng, Honghui, 2023. "Evaluation to fixed-sum-outputs DMUs by non-oriented equilibrium efficient frontier DEA approach with Nash bargaining-based selection," Omega, Elsevier, vol. 115(C).
    12. Phung, Manh-Trung & Cheng, Cheng-Ping & Guo, Chuanyin & Kao, Chen-Yu, 2020. "Mixed Network DEA with Shared Resources: A Case of Measuring Performance for Banking Industry," Operations Research Perspectives, Elsevier, vol. 7(C).
    13. Chen, Kuan-Chen & Lin, Sun-Yuan & Yu, Ming-Miin, 2022. "Exploring the efficiency of hospital and pharmacy utilizations in Taiwan: An application of dynamic network data envelopment analysis," Socio-Economic Planning Sciences, Elsevier, vol. 84(C).
    14. Yangxue Ning & Yan Zhang & Guoqiang Wang, 2023. "An Improved DEA Prospect Cross-Efficiency Evaluation Method and Its Application in Fund Performance Analysis," Mathematics, MDPI, vol. 11(3), pages 1-15, January.
    15. Richard S. Barr & Kory A. Killgo & Thomas F. Siems & Sheri Zimmel, 1999. "Evaluating the productive efficiency and performance of U.S. commercial banks," Financial Industry Studies Working Paper 99-3, Federal Reserve Bank of Dallas.
    16. Maziar Sahamkhadam, 2021. "Dynamic copula-based expectile portfolios," Journal of Asset Management, Palgrave Macmillan, vol. 22(3), pages 209-223, May.
    17. Mehdi Toloo & Rouhollah Khodabandelou & Amar Oukil, 2022. "A Comprehensive Bibliometric Analysis of Fractional Programming (1965–2020)," Mathematics, MDPI, vol. 10(11), pages 1-21, May.
    18. W D Cook & J Zhu, 2011. "Output-specific input-assurance regions in DEA," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(10), pages 1881-1887, October.
    19. Fijałkowska Justyna & Sačer Ivana Mamić & Zyznarska-Dworczak Beata & Sandulescu Maria-Silvia & Garsztka Przemysław & Mokošova Daša, 2023. "The Efficiency of Sustainability Engagement Reported by Banks in Poland, Croatia and Romania," Journal of Intercultural Management, Sciendo, vol. 15(1), pages 94-123, March.
    20. Kao, Chiang & Liu, Shiang-Tai, 2020. "A slacks-based measure model for calculating cross efficiency in data envelopment analysis," Omega, Elsevier, vol. 95(C).

    More about this item

    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:wly:navres:v:39:y:1992:i:4:p:447-469. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.