A recently published paper by E. Mokotoff presents an exact algorithm for the classical P ||Cmax scheduling problem, evaluating its average performance through computational experiments on a series of randomly generated test problems. It is shown that, on the same types of instances, an exact algorithm proposed 10 years ago by the authors of the present note outperforms the new algorithm by som...

In industries machine maintenance is used in order to avoid untimely machine fails as well as to improve production effectiveness. This research regards a permutation flow shop scheduling problem with aging and learning effects considering maintenance process. In this study, it is assumed that each machine may be subject to at most one maintenance activity during the planning horizon. The objec...

We consider online scheduling of splittable tasks on parallel machines. In our model, each task can be split into a limited number of parts, that can then be scheduled independently. We consider both the case where the machines are identical and the case where some subset of the machines have a (fixed) higher speed than the others. We design a class of algorithms which allows us to give tight b...

We consider online scheduling of splittable tasks on parallel machines. In our model, each task can be split into a limited number of parts, that can then be scheduled independently. We consider both the case where the machines are identical and the case where some subset of the machines have a (fixed) higher speed than the others. We design a class of algorithms which allows us to give tight b...

Makespan minimization onm identical machines is a fundamental scheduling problem. The goal is to assign a sequence of jobs, each specified by a processing time, to parallel machines so as to minimize the maximum completion time of any job. Deterministic online algorithms achieve a competitive ratio of about 1.92. Due to this relatively high competitiveness and the lack of progress in the area o...

Machine scheduling problems are a long-time key domain of algorithms and complexity research. A novel approach to machine scheduling problems are fixed-parameter algorithms. To stimulate this thriving research direction, we propose 15 open questions in this area whose resolution we expect to lead to the discovery of new approaches and techniques both in scheduling and parameterized complexity t...

Abstract We consider the problem of scheduling jobs with equal lengths and arbitrary sizes on uniform parallel batch machines different capacities. Each machine can only process whose are not larger than its capacity. Several be processed as a simultaneously machine, long their total size does exceed machine’s The objective is to minimize makespan. Under divisibility constraint, we obtain two e...