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 paper discusses design and comparison of Simulated Annealing Algorithm and Greedy Randomized Adaptive Search Procedure (GRASP) to minimize the makespan in scheduling n single operation independent jobs on m unrelated parallel machines. This problem of minimizing the makespan in single machine scheduling problem with uniform parallel machines is NP hard. Hence, heuristic development for suc...

The unrelated parallel machine scheduling problem, in its most general form, is applicable to many manufacturing and service environments. This problem requires the scheduling of a group of independent jobs on unrelated parallel machines as well as the sequencing of the jobs on each individual machine. In this paper, we propose a genetic algorithm with adaptive crossover selection to schedule ...

Parallel machines concept is a well-known and widely used system in the manufacturing facilities. Scheduling of these parallel machines has been a key activity in the successful product outcome. Though jobs are executed on schedules, in certain cases the completion time increases resulting in tardiness. This survey work identifies and compiles the optimization strategies and solution approaches...

Scheduling n independent jobs on m Unrelated Parallel Machines (SUM) is the problem of assigning n jobs j = 1, .., n to m machines i = 1, .., m so that each job is processed without interruption on one of the machines, and at any time, every machine processes at most one job. The objective is to minimize the makespan of the schedule. SUM is an NP-hard problem even when the number of machines is...

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...