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A decomposition strategy for solving the three machine flow-shop scheduling problem
Abstract
The large number of schedules which must be evaluated to develop an optimal solution as opposed to the time required to evaluate a single schedule of the Three Machine Flow-Shop Scheduling Problem when minimizing Makespan, the n/3/F/Cmax problem, causes this problem to be considered unsolvable. The objective of this research is to demonstrate the existence of exploitable structural properties which can be used to construct optimal or near-optimal solutions to the n/3/F/Cmax problem. The interaction of two structural properties identified, the Job Class Decomposition and the Complementary Makespan Paths, has led to theoretical results which reduce the previously smallest solution space known to exist for the n/3/F/Cmax problem; the permutation sequences. These theoretical results indicate that certain subsets of the permutation sequences are always dominated in Makespan Value while other subsets will generally dominate all other permutation sequences in Makespan Value. Each of these subsets are shown to have definable structural properties which exist among the 6 Job Classes defined by the Job Class Decomposition, such as Symmetry 1 and Symmetry 2. Symmetry 1 and Symmetry 2 relate to some strong dependencies which appear to exist among the 6 Job Classes. These strong dependencies suggest that certain sequencing patterns, defined as the Preferred Sequences, generally lead to optimal or near optimal Makespan sequences when implemented in algorithmic form; while other sequencing patterns, defined as the Dominance Categories, lead to sequences that are always dominated in Makespan Value. Eleven Sequencing Rules based upon the properties of the Preferred Sequences and the 6 Job Classes are developed. Four simple constructive algorithms are based upon these sequencing rules. A fifth algorithm is designed to capture all the interrelationships of the properties identified in this thesis. Seven instances of two simple constructive algorithms, one instance each of the two other constructive algorithms, three instances of the fifth algorithm and Palmer's Method are implemented to solve 100 job sets defined in each of six experiments. The results of the six experiments indicate that the fifth algorithm and several instances of the first two simple constructive algorithms, in general, construct a superior Makespan sequence to the one constructed by Palmer's 'Slope index' Method.
Subject Area
Operations research|Industrial engineering|Mathematics
Recommended Citation
Lizak, Chester Peter, "A decomposition strategy for solving the three machine flow-shop scheduling problem" (1992). Doctoral Dissertations Available from Proquest. AAI9219462.
https://scholarworks.umass.edu/dissertations/AAI9219462