We propose a model for non-preemptive scheduling under uncertainty. In this model, we combine the main characteristics of online and stochastic scheduling in a simple and natural way. Job processing times are assumed to be stochastic, but in contrast to the traditional stochastic scheduling models, we assume that jobs arrive online over time, and there is no knowledge about the jobs that will a...

Parallel environment (alpha in Graham’s notation): • P parallel identical • Q uniform machines: each machine has a given speed speed i, and all jobs have a size sizej, the processing time is given by sizej/speed i • R unrelated machines: the processing time of job j on machine i is given by pi,j, without any other constraints Sometimes the number of processors is fixed: for example, P2, F2, or Pm.

We model and solve the problem of sequencing a set of jobs with specified processing times and tool requirements on a set of identical parallel machines. Decisions concern the assignment of jobs to machines, their sequencing, and the allocation of tools on each machine. The objective function minimizes the makespan. We propose an adaptive large neighborhood search metaheuristic in which the des...

We consider the problem of scheduling on uniform processors which may not start processing at the same time with the purpose of minimizing the maximum completion time. We give a variant of the Multifit algorithm which generates schedules which end within 1.382 times the optimal maximum completion time for the general problem, and within √ 6/2 times the optimal maximum completion time for proble...

Classes of scheduling problems can be specified in terms of the three-field classification α|β|γ where • α specifies the machine environment, – P parallel identical – Q uniform machines: each machine has a given speed speed i, and all jobs have a size sizej, the processing time is given by sizej/speed i – R unrelated machines: the processing time of job j on machine i is given by pi,j, without ...