A combination of flow shop scheduling and the shortest path problem
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This paper studies a combinatorial optimization problem which is obtained by combining the flow shop scheduling problem and the shortest path problem. The objective of the obtained problem is to select a subset of jobs that constitutes a feasible solution to the shortest path problem, and to execute the selected jobs on the flow shop machines to minimize the makespan. We argue that this problem is NP-hard even if the number of machines is two, and is NP-hard in the strong sense for the general case. We propose an intuitive approximation algorithm for the case where the number of machines is an input, and an improved approximation algorithm for fixed number of machines.
KeywordsApproximation algorithm Combination of optimization problems Flow shop scheduling Shortest path
This study has been supported by the Bilateral Scientific Cooperation Project BIL10/10 between Tsinghua University and KU Leuven, and Wang’s research work has been supported by NSFC No. 11371216.
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