Using metric spaces in optimum scheduling

D. I. Golenko-Ginzburg, S. M. Lyubkin, V. S. Rezer, S. L. Sitnyavskii

Research output: Contribution to journalArticlepeer-review


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, . . . , πm), where each permutation πi (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.

Original languageEnglish
Pages (from-to)1515-1523
Number of pages9
JournalAutomation and Remote Control
Issue number9
StatePublished - 1 Jan 2002

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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