Bicriterion Single Machine Scheduling with Resource Dependent Processing Times

Bicriterion Single Machine Scheduling with Resource Dependent Processing Times

A bicriterion problem of scheduling jobs on a single machine is studied. The processing time of each job is a linear decreasing function of the amount of a common discrete resource allocated to the job. A solution is specified by a sequence of the jobs and a resource allocation. The quality of a solution is measured by two criteria, F1 and F2. The first criterion is the maximal or total (weight...

Machine scheduling with resource dependent processing times

We consider several parallel machine scheduling settings with the objective to minimize the schedule makespan. The most general of these settings is unrelated parallel machine scheduling. We assume that, in addition to its machine dependence, the processing time of any job is dependent on the usage of a scarce renewable resource. A given amount of that resource, e.g. workers, can be distributed...

Unrelated Parallel Machine Scheduling with Resource Dependent Processing Times

We consider unrelated machine scheduling problems with the objective to minimize the schedule makespan. In addition to its machinedependence, the processing time of any job is also dependent on the usage of a scarce renewable resource. An amount of k units of that resource, e.g. workers, can be distributed over the jobs in process, and the more of that resource is allocated to a job, the smalle...

On scheduling a single machine with resource dependent release times

Single-machine scheduling with time window-dependent processing times

In the one-machine scheduling problems analysed in this paper, the processing time of a job depends on the time at which the job is started. More precisely, the horizon is divided into time windows and with each one a coe cient is associated that is used to determine the actual processing time of a job starting in it. Two models are introduced, and one of them has direct connections with models...