Related papers: Parallel Machine Scheduling with a Single Resource…
The paper considers single-machine scheduling problems with a non-renewable resource. In this setting, we are given a set jobs, each of which is characterized by a processing time, a weight, and the job also has some resource requirement.…
Motivated by modern parallel computing applications, we consider the problem of scheduling parallel-task jobs with heterogeneous resource requirements in a cluster of machines. Each job consists of a set of tasks that can be processed in…
We study a scheduling problem in which jobs may be split into parts, where the parts of a split job may be processed simultaneously on more than one machine. Each part of a job requires a setup time, however, on the machine where the job…
We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job…
We consider the problem of scheduling multiprocessor jobs to minimize the total completion time under the given energy budget. Each multiprocessor job requires more than one processor at the same moment of time. Processors may operate at…
Given n jobs with release dates, deadlines and processing times we consider the problem of scheduling them on m parallel machines so as to minimize the total energy consumed. Machines can enter a sleep state and they consume no energy in…
In this paper, we consider an NP-hard problem of scheduling a set of jobs of equal processing time on two machines, given a partial precedence order on the set of jobs, with an objective to minimize the makespan. An approximation algorithm…
We consider the following shared-resource scheduling problem: Given a set of jobs $J$, for each $j\in J$ we must schedule a job-specific processing volume of $v_j>0$. A total resource of $1$ is available at any time. Jobs have a resource…
Consider the many shared resource scheduling problem where jobs have to be scheduled on identical parallel machines with the goal of minimizing the makespan. However, each job needs exactly one additional shared resource in order to be…
In the problem called single resource constraint scheduling, we are given $m$ identical machines and a set of jobs, each needing one machine to be processed as well as a share of a limited renewable resource $R$. A schedule of these jobs is…
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…
This paper considers the problem of scheduling jobs on single and parallel machines where all the jobs possess different processing times but a common due date. There is a penalty involved with each job if it is processed earlier or later…
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…
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…
We study the Parallel Task Scheduling problem $Pm|size_j|C_{\max}$ with a constant number of machines. This problem is known to be strongly NP-complete for each $m \geq 5$, while it is solvable in pseudo-polynomial time for each $m \leq 3$.…
We study the classical problem of minimizing the total weighted completion time on a fixed set of $m$ identical machines working in parallel, the $Pm||\sum w_jC_j$ problem in the standard three field notation for scheduling problems. This…
The Map-Reduce computing framework rose to prominence with datasets of such size that dozens of machines on a single cluster were needed for individual jobs. As datasets approach the exabyte scale, a single job may need distributed…
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…
We consider the weighted completion time minimization problem for capacitated parallel machines, which is a fundamental problem in modern cloud computing environments. We study settings in which the processed jobs may have varying duration,…
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…