Scheduling jobs on unrelated parallel machines so as to minimize makespan is one of the basic problems in the area of machine scheduling. In the first part of the paper, we prove that the power of preemption, i.e., the worst-case ratio between the makespan of an optimal nonpreemptive and that of an optimal preemptive schedule, is at least 4. This matches the upper bound proposed in Lin and Vitt...

This research deals with the problem of scheduling N jobs on M unrelated parallel machines. Each job has a due date and requires a single operation. A setup that includes detaching one die and attaching another from the appropriate die type is incurred if the type of the job scheduled is different from the last job on that machine. Due to the mechanical structure of machines and the fitness of ...

Two important characteristics encountered in many real-world scheduling problems are heterogeneous processors and a certain degree of uncertainty about the sizes of jobs. In this paper we address both, and study for the first time a scheduling problem that combines the classical unrelated machine scheduling model with stochastic processing times of jobs. Here, the processing time of job j on ma...

This paper reviews results related to the parallel machine scheduling problem under availability constraints. The motivation of this paper comes from the fact that no survey focusing on this specific problem was published. The problems of single machine, identical, uniform, and unrelated parallel machines under different constraints and optimizing various objective functions were analyzed. For ...

m unrelated parallel machines scheduling problems with variable job processing times are considered, where the processing time of a job is a function of its position in a sequence, its starting time, and its resource allocation. The objective is to determine the optimal resource allocation and the optimal schedule to minimize a total cost function that dependents on the total completion (waitin...

We investigate the max flow time scheduling problem in the off-line and on-line setting. We prove positive and negative theoretical results. In the off-line setting, we address the unrelated parallel machines model and present the first known fully polynomial time approximation scheme, when the number of machines is fixed. In the on-line setting and when the machines are identical, we analyze t...

In this paper, we firstly describe a technique named Duplicating, which duplicates machines in batch scheduling environment. Then we discuss several applications of Duplicating in solving batch scheduling problems, for the batch scheduling problem on unrelated parallel machines to minimize makespan, we give an (4− 2 B )-approximation algorithm and an (2− 1 B + ǫ) algorithm when m is fixed. We a...