Abstract
We consider a model of an assignment problem, in which an operator can do one job, multiple jobs, or no job at all. There is a job changeover cost, for any extra assignment in excess of one. The changeover costs depend only on the operator, but can be negative. We give a nonlinear integer programming formulation of the problem. We show that, the problem is NP-hard.
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References
Cela, E.: Assignment problems. In: Pardalos, P., Resende, M. (eds.) Handbook of Applied Optimization, pp. 661–678. Oxford University Press, Oxford (2002)
Pentico, D.W.: Assignment problems: a golden anniversary survey. Eur. J. Oper. Res. 176(2), 774–793 (2007)
Sinha, P.: Assignment problems with changeover cost. Ann. Oper. Res. 172(1), 447–457 (2009)
Keachie, E.C., Fontana, R.J.: Effects of learning on optimal lot size. Manag. Sci. 13, 102–1108 (1966)
Mosheiov, G.: Parallel machine scheduling with a learning effect. J. Oper. Res. Soc. 52(10), 1165–1169 (2001)
Pellegrino, R., Costantion, N.: An empirical investigation of the learning effect in concrete operations. Eng. Constr. Archit. Manag. 25(3), 342–357 (2018)
Karp, M.R.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum, New York (1972)
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Sinha, P. Some results on an assignment problem variant. OPSEARCH 58, 144–147 (2021). https://doi.org/10.1007/s12597-020-00472-7
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DOI: https://doi.org/10.1007/s12597-020-00472-7