We are given M machines, J jobs, the order of processing jobs on each machine and processing time for each job on each machine in the order of processing and a time limit T.
We have to decide if it is possible to sequence the jobs on the machines according to the following constraints:
- Each job has to be processed on every machine once.
- Each job consists of an ordered sequence of tasks, each representing the processing of the job on one of the machines
- Each job has one task per machine, and cannot start a task while the previous task of the job is not completed
- Each task has a given processing time and each machine can only process one task at a time.
- We have to decide if it is possible to sequence the jobs such that they don't take more than T time units in total for completion.