We study the parallel machine scheduling problem with release dates and we consider several “min-sum” objective functions including total weighted tardiness, total tardiness, total weighted completion time and total completion time. We describe several lower bounds for these problems, most of them being original ones. We provide experimental results to compare these lower bounds according to th...

We consider parallel machine scheduling problems with identical machines and preemption allowed. It is shown that every such problem with chain precedence constraints and release dates and an integer-concave objective function satisfies the following integrality property : for any problem instance with integral data there exists an optimal schedule where all interruptions occur at integral date...

This paper is concerned with scheduling when the data are not fully known before the execution. In that case computing a complete schedule off-line with estimated data may lead to poor performances. Some flexibility must be added to the scheduling process. We propose to start from a partial schedule and to postpone the complete scheduling until execution, thus introducing what we call a stabili...

The minimization of maximum completion time for scheduling n jobs on m identical parallel machines is an NP-hard problem for which many excellent heuristic algorithms have been developed. In this paper, the problem is investigated under the assumption that only limited information about the jobs is available. Specifically, processing times are not known for the jobs; rather, the ordering of the...

We consider the problem of scheduling unrelated parallel machines so as to minimize the total weighted completion time of jobs. Whereas the best previously known approximation algorithms for this problem are based on LP relaxations, we give a 2 –approximation algorithm that relies on a convex quadratic programming relaxation. For the special case of two machines we present a further improvement...

This paper considers the problem of online job scheduling on M identical machines with hard deadlines. The processing time and delay time of a job are known only on its arrival. Jobs are discarded if they do not meet delay time requirement. The objective of the present work is to minimize the number of tardy jobs. A lower bound of competitive ratio when the processing time and delay time are bo...

This paper focuses on the problem of scheduling a set of independent jobs with setup times and job splitting, on a set of identical parallel machines such that total tardiness is minimized. In this study, it is assumed that a job can be split into sub-jobs and these sub-jobs can be processed independently on parallel machines. Because the problem is NP-hard, a memetic algorithm (MA) is proposed...