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Two-stage time minimizing assignment problem

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  • 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
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    References listed on IDEAS

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    1. Ming S. Hung & Walter O. Rom, 1980. "Solving the Assignment Problem by Relaxation," Operations Research, INFORMS, vol. 28(4), pages 969-982, August.
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    3. 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.
    4. 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.
    5. Martello, Silvano & Toth, Paolo, 1995. "The bottleneck generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 83(3), pages 621-638, June.
    6. 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.
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    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.

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