Preemptive scheduling with position costs

This paper is devoted to basic scheduling problems in which the scheduling cost of a job is not a function of its completion time. Instead, the cost is derived from the integration of a cost function over the time intervals on which the job is processed. This criterion is specially meaningful when job preemption is allowed. Polynomial algorithms are presented to solve some special cases including a one-machine problem with a common due date and a two-machine problem with linear nondecreasing cost functions

The Complexity of Mean Flow Time Scheduling Problems with Release Times

We study the problem of preemptive scheduling n jobs with given release times on m identical parallel machines. The objective is to minimize the average flow time. We show that when all jobs have equal processing times then the problem can be solved in polynomial time using linear programming. Our algorithm can also be applied to the open-shop problem with release times and unit processing times. For the general case (when processing times are arbitrary), we show that the problem is unary NP-hard.Comment: Subsumes and replaces cs.DS/0412094 and "Complexity of mean flow time scheduling problems with release dates" by P.B, S.

Problèmes d'optimisation combinatoire paramétrés par des fonctions linéaires par morceaux

National audienc

Preemptive and non-preemptive scheduling with irregular cost functions

International audienc

Preemptive Scheduling with Two Minimax Criteria

International audienceTwo preemptive single-machine bicriteria scheduling problems with release dates and deadlines are considered in this paper. Each criterion is formulated as a maximum cost. In the first problem the cost of both criteria depends on the completion time of the tasks. This problem can be solved by enumerating all the Pareto optimal points with an approach proposed by Hoogeveen (1996) for the nonpreemptive problem without release dates. In the second problem, the costs of one criterion are dependent on the completion times of the tasks and the costs of the other criterion are dependent on the start times. This problem is more difficult but an efficient algorithm is proposed for a sub-problem with heads, tails, release dates and deadlines that appears in the job-shop scheduling problem