Related papers: Scheduling on uniform and unrelated machines with …
In this paper we consider the problem of scheduling on parallel machines with a presence of incompatibilities between jobs. The incompatibility relation can be modeled as a complete multipartite graph in which each edge denotes a pair of…
The problem of scheduling jobs on parallel machines (identical, uniform, or unrelated), under incompatibility relation modeled as a block graph, under the makespan optimality criterion, is considered in this paper. No two jobs that are in…
In the paper we consider the problem of scheduling $n$ identical jobs on 4 uniform machines with speeds $s_1 \geq s_2 \geq s_3 \geq s_4,$ respectively. Our aim is to find a schedule with a minimum possible length. We assume that jobs are…
This paper considers parallel machine scheduling with incompatibilities between jobs. The jobs form a graph and no two jobs connected by an edge are allowed to be assigned to the same machine. In particular, we study the case where the…
We consider a natural generalization of scheduling $n$ jobs on $m$ parallel machines so as to minimize the makespan. In our extension the set of jobs is partitioned into several classes and a machine requires a setup whenever it switches…
One of the most important open problems in machine scheduling is the problem of scheduling a set of jobs on unrelated machines to minimize the makespan. The best known approximation algorithm for this problem guarantees an approximation…
Parallel machine scheduling has been extensively studied in the past decades, with applications ranging from production planning to job processing in large computing clusters. In this work we study some of these fundamental optimization…
A very well-known machine model in scheduling allows the machines to be unrelated, modelling jobs that might have different characteristics on each machine. Due to its generality, many optimization problems of this form are very difficult…
In the paper we consider the problem of scheduling $n$ identical jobs on 3 uniform machines with speeds $s_1, s_2,$ and $s_3$ to minimize the schedule length. We assume that jobs are subjected to some kind of mutual exclusion constraints,…
In the classical problem of scheduling on unrelated parallel machines, a set of jobs has to be assigned to a set of machines. The jobs have a processing time depending on the machine and the goal is to minimize the makespan, that is the…
We consider the problem of minimizing the makespan on batch processing identical machines, subject to compatibility constraints, where two jobs are compatible if they can be processed simultaneously in a same batch. These constraints are…
Machine scheduling problems involving conflict jobs can be seen as a constrained version of the classical scheduling problem, in which some jobs are conflict in the sense that they cannot be proceeded simultaneously on different machines.…
We study approximation algorithms for the problem of minimizing the makespan on a set of machines with uncertainty on the processing times of jobs. In the model we consider, which goes back to~\cite{BertsimasS03}, once the schedule is…
We investigate the scheduling of $n$ jobs divided into $c$ classes on $m$ identical parallel machines. For every class there is a setup time which is required whenever a machine switches from the processing of one class to another class.…
This paper addresses the problem of scheduling jobs on identical machines with conflict constraints, where certain jobs cannot be scheduled simultaneously on different machines. We focus on the case where conflicts can be represented by a…
We consider a basic problem of preemptive scheduling of $n$ non-simultaneously released jobs on a group of $m$ unrelated parallel machines so as to minimize maximum job completion time, the makespan. In the scheduling literature, the…
The paper considers scheduling on parallel machines under the constraint that some pairs of jobs cannot be processed concurrently. Each job has an associated weight, and all jobs have the same deadline. The objective is to maximise the…
In malleable job scheduling, jobs can be executed simultaneously on multiple machines with the processing time depending on the number of allocated machines. In this setting, jobs are required to be executed non-preemptively and in unison,…
We consider the problem of scheduling $n$ precedence-constrained jobs on $m$ uniformly-related machines in the presence of an arbitrary, fixed communication delay $\rho$. We consider a model that allows job duplication, i.e. processing of…
This paper considers scheduling on identical machines. The scheduling objective considered in this paper generalizes most scheduling minimization problems. In the problem, there are $n$ jobs and each job $j$ is associated with a…