On sequencing with earliest starts and due dates with application to computing bounds for the (n/m/G/F_max) problem

Abstract

ABSTRAtXRecent efforts to improve lower bounds in implicit enumeration algorithms for the general (nlmlGIF,) crequencing problem have been directed to the solution of M auxiliary single machine problem that results from the relaxation of some of the interference constraints. We develop M algorithm that obtains optimal and near optimal solutions for this relaxed problem with relatively little computational effort. We report on computational results achieved when this method is used to obtain lower bounds for the general problem. Finally, we show the equivalence of this problem to a single machine sequencing problem with earliest start and due date constraints where the objective is to minimize the maximum lateness.

Fifty years of scheduling: a survey of milestones

“…Let S i denote the set of operations that require machine i, let r * = min u∈S i r u and q * = min u∈S i q u . The following lower bounds based on this subproblem have been proposed: (a) r * + u∈S i p u ; (Schrage (1970A), Charlton and Death (1970)) (b) T i + q * , where T i is the optimal makespan on machine i obtained by sequencing the jobs in non-decreasing order of r u ; (Brooks and White (1965)) (c) r * +U i , where U i is the optimal schedule completion time for the subproblem on machine i obtained by ignoring release dates and sequencing the jobs in non-increasing order of q u ; (Schrage (1970B)) (d) V i , where V i is the optimal schedule completion time for the subproblem on machine i obtained by an enumerative algorithm; (Bratley et al (1973), McMahon and Florian (1975)). …”

A new class of scheduling criteria and their optimization

“…When the jobs are available at the same time, the problem can be polynomially solved using Jackson's algorithm (Jackson 1955). If the release dates are unequal, the problem has been considered by Dessouky and Margenthaler (1972), Shwimer (1972), Bratley, Florian and Robillard (1973), Baker and Su (1974), McMahon and Florian (1975), Lageweg, Lenstra and Rinnooy Kan (1976), Potts (1980), Carlier (1982, Larson, Dessouky and Devor (1985), Grabowski, Nowicki and Zdrzalka (1986), Hall and Rhee (1986). The algorithm proposed by Carlier (1982) is able to handle problems with up to 10000 jobs.…”

Un domaine très ouvert : les problèmes d'ordonnancement

“…De nombreux auteurs ont proposé des méthodes arborescentes (Baker et aï., [3], Bratley et al, [4], Lageweg et al, [29]) utilisant l'algorithme de Schrage. Ces méthodes permettent de traiter des exemples de 1000 tâches entre 1 et 10 secondes sur IRIS 80 (Carlier,[10]).…”