This paper presents a survey of single machine scheduling problem with uniform parallel machines. The single machine scheduling problem with uniform parallel machines consists of n jobs, each with single operation, which are to be scheduled on m parallel machines with different speeds. These parallel machines are also called proportional machines or related machines. There are several measures ...

Parallel job scheduling is the problem of how to run a work-load of multiple parallel jobs in a single parallel machine. Dynamic means that the possibility of arbitrary arrival times for new jobs is allowed. The scheduler is responsible for nding the best scheduling allocation, both temporal and spatial, as a function of the existing workload. In this study jobs are assumed to be data parallel ...

In this paper we consider a class of parallel machine scheduling problems and their associated set-partitioning formulations. We show that the tightness of the linear programming relaxation of these formulations is directly related to the performance of a class of heuristics called parameter list scheduling heuristics. This makes it possible to characterize the worst possible gap between optima...

Flexible flow shop (or a hybrid flow shop) scheduling problem is an extension of classical flow shop scheduling problem. In a simple flow shop configuration, a job having ‘g’ operations is performed on ‘g’ operation centres (stages) with each stage having only one machine. If any stage contains more than one machine for providing alternate processing facility, then the problem...

In this paper we address a multi-objective scheduling problem for unrelated parallel machines. In unrelated parallel systems, the processing cost/time of a given job on different machines may vary. The objective of scheduling is to simultaneously determine the job-machine assignment and job sequencing on each machine. In such a way the total cost of the schedule is minimized. The cost function ...

This thesis presents new and improved scheduling algorithms for a number of scheduling problems. The first part of the thesis deals with two online-list scheduling problems, both with the objective to minimize the makespan. In these problems, the jobs arrive one by one and the decision maker has to irrevocably schedule the arriving job before the next job becomes known. In the second part, a ne...

In this paper, we provide a new class of randomized approximation algorithms for scheduling problems by directly interpreting solutions to so-called time-indexed LPs as probabilities. The most general model we consider is scheduling unrelated parallel machines with release dates (or even network scheduling) so as to minimize the average weighted completion time. The crucial idea for these multi...