TY - JOUR

T1 - Using metric spaces in optimum scheduling

AU - Golenko-Ginzburg, D. I.

AU - Lyubkin, S. M.

AU - Rezer, V. S.

AU - Sitnyavskii, S. L.

N1 - Funding Information:
1 This work was supported by the Paul Ivanier fund “Robot Engineering and Production Control” at the Ben-Gurion University in Negev (Israel).

PY - 2002/1/1

Y1 - 2002/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84904242920&partnerID=8YFLogxK

U2 - 10.1023/A:1020098624562

DO - 10.1023/A:1020098624562

M3 - Article

AN - SCOPUS:84904242920

SN - 0005-1179

VL - 63

SP - 1515

EP - 1523

JO - Automation and Remote Control

JF - Automation and Remote Control

IS - 9

ER -