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The name originally came from the scheduling of jobs in a job shop, but the theme has wide applications beyond that type of instance. This problem is one of the best known combinatorial optimization problems, and was the first problem for which competitive analysis was presented, by Graham in 1966. [ 1 ]
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 ...
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 ...
Flow Shop Ordonnancement. Flow-shop scheduling is an optimization problem in computer science and operations research.It is a variant of optimal job scheduling.In a general job-scheduling problem, we are given n jobs J 1, J 2, ..., J n of varying processing times, which need to be scheduled on m machines with varying processing power, while trying to minimize the makespan – the total length ...
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 ...
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