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Makespan Scheduling

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Abstract

In this chapter, we study the simple scheduling problem introduced in Section 2.1. Given n jobs with positive processing times p 1,…,p n , schedule them on two identical machines in a way such that the makespan, i.e., the overall completion time, is minimized. Let x∈{0,1}n be a decision vector. Job j is scheduled on machine 1 iff x j =0 holds and on machine 2 iff x j =1 holds. Hence, the goal is to minimize

$$f_{p_1,\dots,p_n}(x):=\max \left\{\sum_{i=1}^np_jx_j,\sum_{i=1}^np_j(1-x_j)\right\},$$

where the index p 1,…,p n is often omitted for the sake of readability. Note that the representation is redundant in the sense that a search point x and its bitwise binary complement \(\bar{x}\) lead to the same fvalue.

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Correspondence to Carsten Witt .

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© 2010 Springer-Verlag Berlin Heidelberg

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Neumann, F., Witt, C. (2010). Makespan Scheduling. In: Bioinspired Computation in Combinatorial Optimization. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16544-3_7

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  • DOI: https://doi.org/10.1007/978-3-642-16544-3_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16543-6

  • Online ISBN: 978-3-642-16544-3

  • eBook Packages: Computer ScienceComputer Science (R0)