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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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References

  • Aggarwal V (1983) The assignment problem under categorized jobs. Eur J Oper Res 14:193–195

    Article  MATH  Google Scholar 

  • Aggarwal V, Tikekar VG, Hsu LF (1986) Bottleneck assignment problems under categorization. Comput Oper Res 13(1):11–26

    Article  MathSciNet  MATH  Google Scholar 

  • Armstrong RD, Zhiying J (1992) Solving linear bottleneck assignment problems via strong spanning trees. Oper Res Lett 12:179–180

    Article  MathSciNet  MATH  Google Scholar 

  • Bansal S, Puri MC (1980) A min–max problem. ZOR 24:191–200

    MathSciNet  MATH  Google Scholar 

  • Bhatia HL (1977) Time minimizing assignment problem. SCIMA 6:75–83

    MATH  Google Scholar 

  • Brandt A, Intrator Y (1971) The assignment problem with three job categories. Casopis pro Pestovani Matematiky 96:8–11

    MathSciNet  MATH  Google Scholar 

  • Carpaneto G, Toth P (1981) Algorithm for the solution of the bottleneck assignment problem. Computing 27:179–187

    Article  MATH  Google Scholar 

  • Derigs U (1984) Alternate strategies for solving bottleneck assignment problems-analysis and computational results. Computing 33:95–106

    Article  MathSciNet  MATH  Google Scholar 

  • Derigs U, Zimmermann U (1978) An augmenting path method for solving linear bottleneck assignment problems. Computing 19:285–295

    Article  MathSciNet  MATH  Google Scholar 

  • Edmonds J, Fulkerson DR (1970) Bottleneck extrema. J Comb Theory 8:299–306

    Article  MathSciNet  MATH  Google Scholar 

  • Ford DR, Fulkerson DR (1962) Flows in networks. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Fulkerson R, Glicksberg I, Gross O (1953) A production line assignment problem. Technical Report RM-1102, Rand Corporation, Sta. Monica, CA

  • Garfinkel R (1971) An improved algorithm for the bottleneck assignment problem. Oper Res 19:1747–1751

    Article  MATH  Google Scholar 

  • Gross O (1959) The bottleneck assignment problem. Technical Report P-1630, The Rand Corporation, Sta. Monica, CA

  • Kaur P, Sharma A, Verma V, Dahiya K (2016) A priority based assignment problem. Appl Math Model 40(7):7784–7795

    Article  MathSciNet  Google Scholar 

  • Kuhn HW (1955) The Hungarian method for the assignment problem. Naval Res Logist Q 2:83–97

    Article  MathSciNet  MATH  Google Scholar 

  • Page ES (1963) A note on assignment problems. Comput J 6:241–243

    Article  MATH  Google Scholar 

  • Pferschy U (1997) Solution methods and computational investigations for the linear bottleneck assignment problem. Computing 59(3):237–258

    Article  MathSciNet  MATH  Google Scholar 

  • Porsching TA (1963) Matrix assignments and an associated min–max problem. Math Comput 17(81):81–84

    MathSciNet  MATH  Google Scholar 

  • Punnen AP, Aneja YP (1993) Categorized assignment scheduling: a tabu search approach. J Oper Res Soc 44(7):673–679

    Article  MATH  Google Scholar 

  • Ravindran A, Ramaswami V (1977) On the bottleneck assignment problem. J Optim Theory Appl 21(4):451–458

    Article  MathSciNet  MATH  Google Scholar 

  • Seshan CR (1981) Some generalisations of the time minimising assignment problem. J Oper Res Soc 32(6):489–494

    Article  MathSciNet  MATH  Google Scholar 

  • Sonia, Puri MC (2008) Two-stage time minimizing assignment problem. Omega 36:730–740

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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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