Abstract
We consider the makespan minimization in a flowshop environment where the job sequence does not have to be the same for all the machines. Contrarily to the classical permutation flowshop scheduling problem, this strongly NP-hard problem received very scant attention in the literature. In this paper, some improved single-machine-based adjustment procedures are proposed, and a new two-machine-based one is introduced. Based on these adjustments, new lower and upper bounding schemes are derived. Our experimental analysis shows that the proposed procedures provide promising results.
Highlights
In this paper, we focus on the following scheduling problem: a set of n jobs (1, . . . , n) has to be processed on a set of m machines M1, M2, . . . , Mm in that order
We describe how we can use the adjustment procedures in order to construct an upper bound for the nonpermutation flowshop scheduling problem
We present an empirical analysis of the performance of the proposed lower and upper bounds that are derived from our adjustment procedures
Summary
We focus on the following scheduling problem: a set of n jobs (1, . . . , n) has to be processed on a set of m machines M1, M2, . . . , Mm in that order. In studying flowshop scheduling problems, it is usually assumed that the sequence in which each machine processes the jobs is identical on all machines. Potts et al [3] exhibit a family of instances for which the value of the optimal permutation schedule is worse than that of the optimal nonpermutation schedule by a factor of more than (1/2)⌈√m + 1/2⌉ This is a nonnegligible gap since it can reach 50% for a 4-machine flowshop instance. We consider the nonpermutation case where the job sequence is not necessarily identical on all the machines. We conclude our paper by providing a synthesis of our research and indicating some directions for future research
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