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A branching algorithm to solve binary problem in uncertain environment: an application in machine allocation problem

Author

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  • Sujeet Kumar Singh

    (National University of Singapore)

  • Deepika Rani

    (Dr. B. R. Ambedkar National Institute of Technology)

Abstract

This paper studies a new algorithm to solve the uncertain generalized assignment problem. The presented technique is based on the concept of branch and bound rather than the usual simplex based techniques. At first, the problem is relaxed to the transportation model which is easy to handle and work with. The model, so obtained is solved by the conventional transportation technique. The obtained solution serves as starting solution for further sub problems. The ambiguity in parameters is represented by triangular fuzzy numbers. We propose a linear ranking function, called the grade function which is based on the centroid method. The grade function is used to rank the triangular fuzzy numbers. The proposed approach is justified numerically by showing its application in generalized machine allocation problem.

Suggested Citation

  • Sujeet Kumar Singh & Deepika Rani, 2019. "A branching algorithm to solve binary problem in uncertain environment: an application in machine allocation problem," OPSEARCH, Springer;Operational Research Society of India, vol. 56(3), pages 1007-1023, September.
    • Handle: RePEc:spr:opsear:v:56:y:2019:i:3:d:10.1007_s12597-019-00378-z
    DOI: 10.1007/s12597-019-00378-z
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    References listed on IDEAS

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    1. Yagiura, Mutsunori & Ibaraki, Toshihide & Glover, Fred, 2006. "A path relinking approach with ejection chains for the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 169(2), pages 548-569, March.
    2. Jeet, V. & Kutanoglu, E., 2007. "Lagrangian relaxation guided problem space search heuristics for generalized assignment problems," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1039-1056, November.
    3. Cattrysse, Dirk G. & Van Wassenhove, Luk N., 1992. "A survey of algorithms for the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 60(3), pages 260-272, August.
    4. Mutsunori Yagiura & Toshihide Ibaraki & Fred Glover, 2004. "An Ejection Chain Approach for the Generalized Assignment Problem," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 133-151, May.
    5. Karsak, E. Ertugrul & Kuzgunkaya, Onur, 2002. "A fuzzy multiple objective programming approach for the selection of a flexible manufacturing system," International Journal of Production Economics, Elsevier, vol. 79(2), pages 101-111, September.
    6. Majumdar, J. & Bhunia, A.K., 2007. "Elitist genetic algorithm for assignment problem with imprecise goal," European Journal of Operational Research, Elsevier, vol. 177(2), pages 684-692, March.
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    Cited by:

    1. Helena Gaspars-Wieloch, 2021. "The Assignment Problem in Human Resource Project Management under Uncertainty," Risks, MDPI, vol. 9(1), pages 1-17, January.

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