Related papers: EPTAS for load balancing problem on parallel machi…
We consider the non-preemptive scheduling problem on identical machines where there is a parameter B and each machine in every unit length time interval can process up to B different jobs. The goal function we consider is the makespan…
We consider a general load balancing problem on parallel machines. Our machine environment in particular generalizes the standard models of identical machines, and the model of uniformly related machines, as well as machines with a constant…
We consider basic problems of non-preemptive scheduling on uniformly related machines. For a given schedule, defined by a partition of the jobs into m subsets corresponding to the m machines, C_i denotes the completion time of machine i.…
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 study scheduling problems on a machine with varying speed. Assuming a known speed function we ask for a cost-efficient scheduling solution. Our main result is a PTAS for minimizing the total weighted completion time in this setting. This…
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 this paper we consider single machine scheduling problems with additional non-renewable resource constraints. Examples for non-renewable resources include raw materials, energy, or money. Usually they have an initial stock and…
We study classic scheduling problems on uniformly related machines. Efficient polynomial time approximation schemes (EPTAS's) are fast and practical approximation schemes. New methods and techniques are essential in developing such improved…
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.…
Machine scheduling is a fundamental optimization problem in computer science. The task of scheduling a set of jobs on a given number of machines and minimizing the makespan is well studied and among other results, we know that EPTAS's for…
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…
We consider a natural generalization of classical scheduling problems in which using a time unit for processing a job causes some time-dependent cost which must be paid in addition to the standard scheduling cost. We study the scheduling…
Various new scheduling problems have been arising from practical production processes and spawning new research areas in the scheduling field. We study the parallel multi-stage open shops problem, which generalizes the classic open shop…
We study three two-stage optimization problems with a similar structure and different objectives. In the first stage of each problem, the goal is to assign input jobs of positive sizes to unsplittable bags. After this assignment is decided,…
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.…
In the restricted assignment problem, the input consists of a set of machines and a set of jobs each with a processing time and a subset of eligible machines. The goal is to find an assignment of the jobs to the machines minimizing the…
We consider non-preemptive scheduling problems on parallel identical machines where machines change their status from being available to being unavailable and vice versa along the time horizon. The particular form of unavailability we…
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…
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 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…