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.

Approximation algorithms, Hybrid flow shop, Parallel flow shop, Scheduling, Worst-case analysis
dx.doi.org/10.1016/j.ejor.2011.08.007, hdl.handle.net/1765/25743
ERIM Top-Core Articles
European Journal of Operational Research
Accepted manuscript attached
Erasmus Research Institute of Management

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