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An improved algorithm for two stage time minimization assignment problem

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Abstract

The paper develops a technique to solve two stage time minimization assignment problem dealing with the allocation of n jobs to n persons in two stages where \(n_1\) out of n jobs are primary jobs and constitute Stage-I and rest of the jobs are secondary jobs constituting Stage-II. It is assumed that each person can be assigned to one job only and each job is to be done by exactly one person. Further, in a particular stage, all the jobs are commenced simultaneously. Stage-II jobs are commenced only after Stage-I jobs are finished and the objective is to find an assignment which minimizes the total completion time of Stage-I and Stage-II jobs. Numerical examples are provided to support the theory. The proposed algorithm has been coded in MATLAB and tested on different problems with n varying from 10 to 100.

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Acknowledgements

We would like to thank the Editor-In-Chief for his support during the review process, and also the anonymous reviewers for their valuable suggestions and comments which helped in improving the manuscript considerably. The first author is thankful to Council of Scientific and Industrial Research, India (Sanction No. 09/135/(0724)/2015-EMR-I) for providing financial support for carrying out this research.

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Authors and Affiliations

  1. Department of Mathematics, Panjab University, Chandigarh, India

    Ekta Jain & Vanita Verma

  2. University Institute of Engineering and Technology, Panjab University, Chandigarh, India

    Kalpana Dahiya

  3. Department of Computer Science and Applications, Panjab University, Chandigarh, India

    Anuj Sharma

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  1. Ekta Jain
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  2. Kalpana Dahiya
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  3. Anuj Sharma
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  4. Vanita Verma
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Correspondence to Kalpana Dahiya.

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Jain, E., Dahiya, K., Sharma, A. et al. An improved algorithm for two stage time minimization assignment problem. J Comb Optim 37, 713–736 (2019). https://doi.org/10.1007/s10878-018-0318-2

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  • DOI: https://doi.org/10.1007/s10878-018-0318-2

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