Abstract
The solution of an optimum problem of scheduling with n workpieces and m machine tools represents an optimum schedule of putting pieces on machines. In turn, the schedule is defined by an optimum collection of m permutations out of n objects, i.e., the vector permutation π = (π1, ..., π m ), where each permutation π i (1 ≤ i ≤ m) points up the sequence of working of all pieces on the ith machine. In this case, to each admissible schedule there must correspond an integral point from the m-dimensional Euclidean space of permutations (or, which is practically the same, the permutation out of numbers {1, 2, ..., mn}. In an effort to seek an optimum schedule, use is made of the notion of a metric space in the set of admissible schedules and the justified methodology of the search for an optimum schedule. A few metric spaces are described and analyzed and their comparative effectiveness is investigated for the solution of a different-route problem of scheduling.
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Golenko-Ginzburg, D.I., Lyubkin, S.M., Rezer, V.S. et al. Using Metric Spaces in Optimum Scheduling. Automation and Remote Control 63, 1515–1523 (2002). https://doi.org/10.1023/A:1020098624562
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DOI: https://doi.org/10.1023/A:1020098624562