A polynomial algorithm for the \([n/m/0,\;t_{ij}=1,\text{ tree}/C_{\max}]\) open shop problem. (English) Zbl 0798.90081

Summary: We consider the open shop problem with unit processing times and tree constraints among the jobs. The objective is to minimize the schedule length \(C_{\max}\). The complexity of this problem was open. We present a polynomial algorithm which decomposes the problem into subproblems by means of occurrence of unavoidable idle times. We consider two types of subproblems which can be solved by constructing special latin rectangles.


90B35 Deterministic scheduling theory in operations research
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