Abstract
In a two-machine flow shop, the problem seeks to select and schedule jobs such that the processing of the selected jobs does not contain any idle time. The objective is to maximize the number of selected jobs. The problem is studied in the context of a resource-constrained scheduling problem. An $$O(n^2)$$ dynamic programming algorithm is proposed. The problem becomes ordinary NP-hard when job weights are introduced. A heuristic is designed and its performance ratio is analysed to be 3.
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