The problem of Scheduling n Independent Jobs on m Unrelated Parallel Machines, when the number of machines m is xed, is considered. The standard problem of minimizing the makespan of the schedule (SUM) and the bicriteria problem of scheduling with bounded makespan and cost (SUMC) are addressed, and randomized fully linear time approximation schemes are shown for both of them. While matching the...

This paper introduces a stochastic scheduling problem. In this problem a directed acyclic graphs (DAG) represents the precedence relations among m tasks that n workers are scheduled to execute. The question is to find a schedule Σ such that if tasks are assigned to workers according toΣ , the expected time needed to execute all the tasks is minimized. The timeneeded to execute task t byworkerw ...

We show that the problems of minimizing total completion time and of minimizing the number of late jobs on unrelated parallel machines, when preemption is allowed, are both NP-hard in the strong sense. The former result settles a long-standing open question. A special case of the unrelated machine model is the identical machine model with the restriction that a job can only be processed on a sp...

A methodology for minimizing the weighted tardiness of jobs in unrelated parallel machining scheduling with sequence-dependent setups is presented in this paper. To comply with industrial situations, the dynamic release of jobs and dynamic availability of machines are assumed. Recognizing the inherent difficulty in solving industrial-size problems efficiently, six different search algorithms ba...

We consider the problem of scheduling n independent jobs on m unrelated parallel machines without preemption. Job i takes processing time pi j on machine j , and the total time used by a machine is the sum of the processing times for the jobs assigned to it. The objective is to minimize makespan. The best known approximation algorithms for this problem compute an optimum fractional solution and...

http://dx.doi.org/10.1016/j.cie.2014.05.012 0360-8352/ 2014 Elsevier Ltd. All rights reserved. q This manuscript was processed by Area Editor Hans Kellerer. ⇑ Corresponding author. Address: Department of Industrial Management, National Taiwan University of Science and Technology, 43 Keelung Road, Section 4, Taipei 106, Taiwan. Tel.: +886 2 2737 6337. E-mail address: [email protected] (C....

In this research we address a sequence-dependent group scheduling problem on a set of unrelated-parallel machines where the run time of each job differs on different machines. To benefit both producer and customers we attempt to minimize a linear combination of total weighted completion time and total weighted tardiness. Since the problem is shown to be NP-hard, meta-heuristic algorithms based ...

In this paper we study the unrelated parallel machines problem where n independent jobs must be assigned to one out of m parallel machines and the processing time of each job differs from machine to machine. We deal with the objective of the minimisation of the maximum completion time of the jobs, usually referred to as makespan or Cmax. This is a type of assignment problem that has been freque...

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 ...

The paper addresses the problem of scheduling in the two-stage flowshop with parallel unrelated machines and renewable resource constraints. The objective is minimization of makespan. The problem is NP-hard. Fast heuristic algorithms using list scheduling and greedy strategies are proposed. For evaluation of the performance of the algorithms computational experiments are performed on randomly g...