We consider the well known problem of scheduling jobs with release dates to minimize their average weighted completion time. When multiple machines are available, the machine environment may range from identical machines (the processing time required by a job is invariant across the machines) at one end of the spectrum to unrelated machines (the processing time required by a job on each machine...

We consider the well known problem of scheduling jobs with release dates to minimize their average weighted completion time. When multiple machines are available, the machine environment may range from identical machines (the processing time required by a job is invariant across the machines) at one end of the spectrum to unrelated machines (the processing time required by a job on each machine...

Maintenance is important to manufacturing process with a view to sustaining production efficiency. In this study scheduling of unrelated parallel machines with effects of learning and aging and multi maintenance activities is considered. The objective is to find the optimal maintenance periods, optimal maintenance frequencies and optimal job sequences such that the makespan of all jobs are mini...

Here, we consider approximation algorithms for the Graph Balancing problem which is a special case of the job scheduling on unrelated parallel machines to minimize the makespan. We present an interpretation of the 2approximation LP-rounding algorithm given by Lenstra et al. to the special case of graph balancing. We then show how the approximation guarantee can be improved by the technique of a...

A kind of unrelated parallel machines scheduling problem is discussed. The memberships of fuzzy due dates denote the grades of satisfaction with respect to completion times with jobs. Objectives of scheduling are to maximize the minimum grade of satisfaction while makespan is minimized in the meantime. Two kind of genetic algorithms are employed to search optimal solution set of the problem. Bo...

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 ...

Many academic disciplines including information systems, computer science, and operations management face scheduling problems as important decision making tasks. Since many scheduling problems are NP-hard in the strong sense, there is a need for developing solution heuristics. For scheduling problems with setup times on unrelated parallel machines, there is limited research on solution methods ...

We show how to approximate in NC the problem of Scheduling Unrelated Parallel Machines, for a xed number of machines. We develop a (2 + ")-approximate parallel algorithm for the problem. Our approach shows how to relate the linear program obtained by relaxing the integer programming formulation of the problem with a linear program formulation that is positive and in the packing/covering form. T...

Abstract In this paper, we study an important real-life scheduling problem that can be formulated as unrelated parallel machine with sequence-dependent setup times, due dates, and eligibility constraints. The objective is to minimise total tardiness makespan. We adapt extend a mathematical model find optimal solutions for small instances. Additionally, propose several variants of simulated anne...

Consider a task scheduling problem of a given fine grained task graph on distributed-memory parallel machines. In this paper, we report that schedules with small makespan generated by existing task scheduling algorithms do not usually become fast parallel programs on distributed-memory parallel machines. That is caused by no consideration to message packaging. To obtain fast parallel programs u...