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Solving the Rectangular assignment problem and applications

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The rectangular assignment problem is a generalization of the linear assignment problem (LAP): one wants to assign a number of persons to a smaller number of jobs, minimizing the total corresponding costs. Applications are, e.g., in the fields of object recognition and scheduling. Further, we show how it can be used to solve variants of the LAP, such as the k-cardinality LAP and the LAP with outsourcing by transformation. We introduce a transformation to solve the machine replacement LAP. We describe improvements of a LAP-algorithm for the rectangular problem, in general and slightly adapted for these variants, based on the structure of the corresponding cost matrices. For these problem instances, we compared the best special codes from literature to our codes, which are more general and easier to implement. The improvements lead to more efficient and robust codes, making them competitive on all problem instances and often showing much shorter computing times. Copyright The Author(s) 2010

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  • J. Bijsterbosch & A. Volgenant, 2010. "Solving the Rectangular assignment problem and applications," Annals of Operations Research, Springer, vol. 181(1), pages 443-462, December.
    • Handle: RePEc:spr:annopr:v:181:y:2010:i:1:p:443-462:10.1007/s10479-010-0757-3
    DOI: 10.1007/s10479-010-0757-3
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    1. Mosheiov, Gur & Yovel, Uri, 2006. "Minimizing weighted earliness-tardiness and due-date cost with unit processing-time jobs," European Journal of Operational Research, Elsevier, vol. 172(2), pages 528-544, July.
    2. Robert E. Machol & Michael Wien, 1976. "Technical Note—A “Hard” Assignment Problem," Operations Research, INFORMS, vol. 24(1), pages 190-192, February.
    3. Volgenant, A., 2004. "Solving the k-cardinality assignment problem by transformation," European Journal of Operational Research, Elsevier, vol. 157(2), pages 322-331, September.
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    Cited by:

    1. Yuli Zhang & Zuo-Jun Max Shen & Shiji Song, 2018. "Exact Algorithms for Distributionally β -Robust Machine Scheduling with Uncertain Processing Times," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 662-676, November.

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