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 -