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# Multi-machine Scheduling with Variance Minimization

@article{Cai1998MultimachineSW, title={Multi-machine Scheduling with Variance Minimization}, author={Xiaoqiang Cai and T. C. Edwin Cheng}, journal={Discrete Applied Mathematics}, year={1998}, volume={84}, pages={55-70} }

- Published 1998 in Discrete Applied Mathematics
DOI:10.1016/S0166-218X(98)00020-1

This paper addresses the problem of scheduling n jobs on m identical parallel machines so as to minimize the completion time variance. Properties of optimal solutions are derived first. Then, complexity results are obtained, which show that the problem is NP-complete in the strong sense when m is arbitrary, and NP-complete in the ordinary sense when m is fixed. Two algorithms are proposed. The first algorithm can generate an optimal solution in time O(n2”P”(P P,)“-‘/[m”(m l)!]*), w h ere P is… CONTINUE READING