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
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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© 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
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