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Assignment problems with changeover cost

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Abstract

We consider some variant models, having changeover cost, of the assignment problem. In these models, multiple assignments to an operator are allowed. In addition to assignment costs, a changeover cost is incurred if an operator does one job after another is completed. Two different types of changeover costs and related two models are considered. Mathematical programming formulations are given for the models. When changeover costs are dependent on the operator but independent of the jobs and are non-negative, a linear programming model is obtained. For the case when changeover costs are dependent on the jobs, a linear integer programming formulation is obtained. We also show that, this problem is strongly NP-hard. A heuristic solution method is suggested for it. Numerical findings on the performance of the method are given.

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References

  • Anotreicher, K. M., Brixius, N. W., Linderoth, J., & Goux, J. P. (2002). Solving large quadratic assignment problems on computational grids. Mathematical Programming, Series B, 91, 563–568.

    Article  Google Scholar 

  • Balinski, M. L. (1985). Signature methods for the assignment problem. Operations Research, 33(3), 527–536.

    Article  Google Scholar 

  • Bernard, R., & Slowinski, R. (2006). Multi-criteria assignment problem with incompatibility and capacity constraints. Annals of Operations Research, 141(1), 287–316.

    Google Scholar 

  • Bertsekas, D. P. (1988). The auction algorithm: a distributed relaxation method for the assignment problem. Annals of Operations Research, 14(1), 105–123.

    Article  Google Scholar 

  • Chu, P. C., & Beasley, J. E. (1997). A genetic algorithm for the generalized assignment problem. Computers & Operations Research, 24(1), 17–23.

    Article  Google Scholar 

  • Garey, M. R., & Johnson, D. S. (1979). Computers and intractability—a guide to the theory of NP-completeness. San Francisco: Freeman.

    Google Scholar 

  • Garfinkel, R. (1971). An improved algorithm for the bottleneck assignment problem. Operations Research, 19, 1747–1751.

    Article  Google Scholar 

  • Heller, I., & Tompkins, C. (1956). An extension of a theorem of Dantzig. Annals of Mathematics Studies, 38, 247–254.

    Google Scholar 

  • Kuhn, H. W. (1955). The Hungarian method for the assignment problem. Naval Research Logistics Quarterly, 2, 325–344.

    Article  Google Scholar 

  • Mills, P., Tsang, E., & Ford, J. (2003). Applying an extended guided local search to the quadratic assignment problem. Annals of Operations Research, 118(1–4), 121–135.

    Article  Google Scholar 

  • Nauss, R. M. (2003). Solving the generalized assignment problem: an optimizing and heuristic approach. INFORMS Journal on Computing, 15(3), 249–266.

    Article  Google Scholar 

  • Oliveira, C. A. S., & Pardalos, P. M. (2004). Randomized parallel algorithms for the multidimensional assignment problem. Applied Numerical Mathematics, 49(1), 117–133.

    Article  Google Scholar 

  • Pentico, D. W. (2007). Assignment problems: a golden anniversary survey. European Journal of Operational Research, 176(2), 774–793.

    Article  Google Scholar 

  • Pinedo, M. (2002). Scheduling (theory, algorithms and systems). New Jersey: Prentice Hall.

    Google Scholar 

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Authors and Affiliations

  1. Quantitative Methods & Operations Management Area, Indian Institute of Management Kozhikode, Kozhikode, 673570, Kerala, India

    Pritibhushan Sinha

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  1. Pritibhushan Sinha
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Correspondence to Pritibhushan Sinha.

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Sinha, P. Assignment problems with changeover cost. Ann Oper Res 172, 447–457 (2009). https://doi.org/10.1007/s10479-009-0620-6

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  • DOI: https://doi.org/10.1007/s10479-009-0620-6

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