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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 mathematical modeling of job shop scheduling problems, disjunctive graphs are a way of modeling a system of tasks to be scheduled and timing constraints that must be respected by the schedule. They are mixed graphs , in which vertices (representing tasks to be performed) may be connected by both directed and undirected edges ...
It is named after Edward G. Coffman, Jr. and Ronald Graham, who published it in 1972 for an application in job shop scheduling. In this application, the elements to be ordered are jobs, the bound W is the number of jobs that can be scheduled at any one time, and the partial order describes prerequisite relations between the jobs. The goal is to ...
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 ...
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.
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