Approximation algorithms for the parallel flow shop problem
European Journal of Operational Research , Volume 216 - Issue 3 p. 544- 552
We consider the NP-hard problem of scheduling n jobs in m two-stage parallel flow shops so as to minimize the makespan. This problem decomposes into two subproblems: assigning the jobs to parallel flow shops; and scheduling the jobs assigned to the same flow shop by use of Johnson's rule. For m = 2, we present a 32-approximation algorithm, and for m = 3, we present a 127-approximation algorithm. Both these algorithms run in O(n log n) time. These are the first approximation algorithms with fixed worst-case performance guarantees for the parallel flow shop problem.
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Zhang, X, & van de Velde, S.L. (2012). Approximation algorithms for the parallel flow shop problem. European Journal of Operational Research, 216(3), 544–552. doi:10.1016/j.ejor.2011.08.007