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This holds even for the special case in which the processing time of all jobs is =, since this special case is equivalent to the bin packing problem: each time-step corresponds to a bin, m is the bin size, each job corresponds to an item of size q j, and minimizing the makespan corresponds to minimizing the number of bins.
The basic form of the problem of scheduling jobs with multiple (M) operations, over M machines, such that all of the first operations must be done on the first machine, all of the second operations on the second, etc., and a single job cannot be performed in parallel, is known as the flow-shop scheduling problem.
In the literature, problems of optimal job scheduling are often called machine scheduling, processor scheduling, multiprocessor scheduling, or just scheduling. There are many different problems of optimal job scheduling, different in the nature of jobs, the nature of machines, the restrictions on the schedule, and the objective function.
The open-shop scheduling problem can be solved in polynomial time for instances that have only two workstations or only two jobs. It may also be solved in polynomial time when all nonzero processing times are equal: in this case the problem becomes equivalent to edge coloring a bipartite graph that has the jobs and workstations as its vertices, and that has an edge for every job-workstation ...
Single-machine scheduling or single-resource scheduling or Dhinchak Pooja is an optimization problem in computer science and operations research.We are given n jobs J 1, J 2, ..., J n of varying processing times, which need to be scheduled on a single machine, in a way that optimizes a certain objective, such as the throughput.
All jobs are equally prioritised. Johnson's rule is as follows: List the jobs and their times at each work center. Select the job with the shortest activity time. If that activity time is for the first work center, then schedule the job first. If that activity time is for the second work center then schedule the job last. Break ties arbitrarily ...
Sequence-dependent setup time is a situation where the setup time required for a job depends on the job that came before it, rather than being constant for all jobs (independent job setup time). Serafini [ 10 ] assumes unbounded splittings and preemptions and gives polynomial-time algorithms that minimize the maximum tardiness and the maximum ...
The problem of dividing several jobs among several machines in a way that optimizes some global objective function is well known and has been widely studied in computer science. In this type of problems there is a central designer that determines the allocation of jobs into machines and all the participating entities are assumed to obey the ...