IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v36y2008i5p730-740.html
   My bibliography  Save this article

Two-stage time minimizing assignment problem

Author

Listed:
  • Sonia
  • Puri, M.C.

Abstract

This paper deals with the optimal selection of m out of n facilities to first perform m given primary jobs in Stage-I followed by the remaining (n-m) facilities performing optimally the (n-m) secondary jobs in Stage-II. It is assumed that in both the stages facilities perform in parallel. The aim of the proposed study is to find that set of m facilities performing the primary jobs in Stage-I for which the sum of the overall completion times of jobs in Stage-I and the corresponding optimal completion time of the secondary jobs in Stage-II by the remaining (n-m) facilities is the minimum. The developed solution methodology involves solving the standard time minimizing and cost minimizing assignment problems alternately after forbidding some facility-job pairings and suggests a polynomially bound algorithm. This proposed algorithm has been implemented and tested on a variety of test problems and its performance is found to be quite satisfactory.

Suggested Citation

  • Sonia & Puri, M.C., 2008. "Two-stage time minimizing assignment problem," Omega, Elsevier, vol. 36(5), pages 730-740, October.
    • Handle: RePEc:eee:jomega:v:36:y:2008:i:5:p:730-740
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305-0483(06)00025-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Martello, Silvano & Toth, Paolo, 1995. "The bottleneck generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 83(3), pages 621-638, June.
    2. Ming S. Hung & Walter O. Rom, 1980. "Solving the Assignment Problem by Relaxation," Operations Research, INFORMS, vol. 28(4), pages 969-982, August.
    3. N.V. Thoai, 2002. "Convergence and Application of a Decomposition Method Using Duality Bounds for Nonconvex Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 165-193, April.
    4. Sherali, Hanif D., 1982. "Equivalent weights for lexicographic multi-objective programs: Characterizations and computations," European Journal of Operational Research, Elsevier, vol. 11(4), pages 367-379, December.
    5. Toth, Paolo, 2000. "Optimization engineering techniques for the exact solution of NP-hard combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 125(2), pages 222-238, September.
    6. Martello, Silvano & Toth, Paolo, 1995. "A note on exact algorithms for the bottleneck generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 83(3), pages 711-712, June.
    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. Arsham, Hossein & Adlakha, Veena & Lev, Benjamin, 2009. "A simplified algebraic method for system of linear inequalities with LP applications," Omega, Elsevier, vol. 37(4), pages 876-882, August.
    2. Cevahir Uzkurt & Rachna Kumar & Halil Semih Kimzan & Hanife Sert, 2012. "THE IMPACT OF ENVIRONMENTAL UNCERTAINTY DIMENSIONS ON ORGANISATIONAL INNOVATIVENESS: AN EMPIRICAL STUDY ON SMEs," International Journal of Innovation Management (ijim), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 1-23.
    3. Ekta Jain & Kalpana Dahiya & Anuj Sharma & Vanita Verma, 2019. "An improved algorithm for two stage time minimization assignment problem," Journal of Combinatorial Optimization, Springer, vol. 37(2), pages 713-736, February.
    4. Stephanie C. Schleimer & Arthur D. Shulman, 2011. "When Intra-Firm And Inter-Firm Collaborations Co-Occur: Comparing Their Impact Across New Services Versus New Product Innovations," International Journal of Innovation Management (ijim), World Scientific Publishing Co. Pte. Ltd., vol. 15(05), pages 869-898.
    5. Ekta Jain & Kalpana Dahiya & Vanita Verma, 2020. "A priority based unbalanced time minimization assignment problem," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 13-45, March.
    6. Fanrong Xie & Anuj Sharma & Zuoan Li, 2022. "An alternate approach to solve two-level priority based assignment problem," Computational Optimization and Applications, Springer, vol. 81(2), pages 613-656, March.

    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. Christian Billing & Florian Jaehn & Thomas Wensing, 2020. "Fair task allocation problem," Annals of Operations Research, Springer, vol. 284(1), pages 131-146, January.
    2. Boccia, Maurizio & Masone, Adriano & Sterle, Claudio & Murino, Teresa, 2023. "The parallel AGV scheduling problem with battery constraints: A new formulation and a matheuristic approach," European Journal of Operational Research, Elsevier, vol. 307(2), pages 590-603.
    3. Yelin Fu & Jianshan Sun & K. Lai & John Leung, 2015. "A robust optimization solution to bottleneck generalized assignment problem under uncertainty," Annals of Operations Research, Springer, vol. 233(1), pages 123-133, October.
    4. Özlem Karsu & Meral Azizoğlu, 2014. "Bicriteria multiresource generalized assignment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(8), pages 621-636, December.
    5. Liles, Joseph M. & Robbins, Matthew J. & Lunday, Brian J., 2023. "Improving defensive air battle management by solving a stochastic dynamic assignment problem via approximate dynamic programming," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1435-1449.
    6. Joseph B. Mazzola & Alan W. Neebe, 2012. "A generalized assignment model for dynamic supply chain capacity planning," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(6), pages 470-485, September.
    7. Arora, Shalini & Puri, M. C., 1998. "A variant of time minimizing assignment problem," European Journal of Operational Research, Elsevier, vol. 110(2), pages 314-325, October.
    8. Pentico, David W., 2007. "Assignment problems: A golden anniversary survey," European Journal of Operational Research, Elsevier, vol. 176(2), pages 774-793, January.
    9. Lamghari, Amina & Ferland, Jacques A., 2011. "Assigning judges to competitions of several rounds using Tabu search," European Journal of Operational Research, Elsevier, vol. 210(3), pages 694-705, May.
    10. Nguyen Thoai, 2012. "Criteria and dimension reduction of linear multiple criteria optimization problems," Journal of Global Optimization, Springer, vol. 52(3), pages 499-508, March.
    11. Fanrong Xie & Anuj Sharma & Zuoan Li, 2022. "An alternate approach to solve two-level priority based assignment problem," Computational Optimization and Applications, Springer, vol. 81(2), pages 613-656, March.
    12. Sherali, Hanif D. & Narayanan, Arvind & Sivanandan, R., 2003. "Estimation of origin-destination trip-tables based on a partial set of traffic link volumes," Transportation Research Part B: Methodological, Elsevier, vol. 37(9), pages 815-836, November.
    13. Laura Laguna-Salvadó & Matthieu Lauras & Uche Okongwu & Tina Comes, 2019. "A multicriteria Master Planning DSS for a sustainable humanitarian supply chain," Annals of Operations Research, Springer, vol. 283(1), pages 1303-1343, December.
    14. Amir Akbari & Paul I. Barton, 2018. "An Improved Multi-parametric Programming Algorithm for Flux Balance Analysis of Metabolic Networks," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 502-537, August.
    15. Lorenzo Ros-McDonnell & M. de-la-Fuente-Aragon & Marija Bogataj, 2012. "An approximate algorithm for optimal logistics of heavy and variable size items," 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(1), pages 1-17, March.
    16. Zheng, Feifeng & Cheng, Yongxi & Xu, Yinfeng & Liu, Ming, 2013. "Competitive strategies for an online generalized assignment problem with a service consecution constraint," European Journal of Operational Research, Elsevier, vol. 229(1), pages 59-66.
    17. Marcel Turkensteen & Dmitry Malyshev & Boris Goldengorin & Panos M. Pardalos, 2017. "The reduction of computation times of upper and lower tolerances for selected combinatorial optimization problems," Journal of Global Optimization, Springer, vol. 68(3), pages 601-622, July.
    18. P. Senthil Kumar, 2020. "Developing a New Approach to Solve Solid Assignment Problems Under Intuitionistic Fuzzy Environment," International Journal of Fuzzy System Applications (IJFSA), IGI Global, vol. 9(1), pages 1-34, January.
    19. Sherali, Hanif D. & Van Goubergen, Dirk & Van Landeghem, Hendrik, 2008. "A quantitative approach for scheduling activities to reduce set-up in multiple machine lines," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1224-1237, June.
    20. 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.

    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:jomega:v:36:y:2008:i:5:p:730-740. 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/wps/find/journaldescription.cws_home/375/description#description .

    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.