Publisher's Synopsis
Excerpt from Slack-Based Lower Bound and Heuristic for Permutation Flowshop Models: June, 1993
Given n available jobs and m machines, the flowshop scheduling problem involves sequencing the n jobs to optimize some criterion of interest. All jobs have the same processing sequence but different processing times, machines can process only one job at a time, and jobs cannot undergo simultaneous processing at multiple machines. In permutation flowshops. Every machine processes the jobs in the same order. Thus, after we release jobs into the system in a certain sequence, they follow the fcfs discipline at all intermediate queues. We assume that the schedule does not contain any unforced idleness, i.e., machines are not idle unless they are blocked by downstream machines, or the upstream queue is empty machines are or timing constraints prevent commencing operations on the next job. Depending on the application context, the scheduling problem might include certain constraints on material storage and movement, and the Optimization Objective might vary. To distinguish between the common ?owshop scheduling models discussed in the literature, we first describe a classification scheme that is analagous to Graham et al.'s (1979) framework to classify general machine scheduling problems based on the machine environment, job characterisucs. And optimality criterion. We illustrate the differences between the various flowshop models in terms of their integer programming formulations, and relate their respective upper and lower bounds based on these formulation differences. We also introduce a new Objective function.
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