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An interval scheduling problem can be described by an intersection graph, where each vertex is an interval, and there is an edge between two vertices if and only if their intervals overlap. In this representation, the interval scheduling problem is equivalent to finding the maximum independent set in this intersection graph. Finding a maximum ...
The activity selection problem is also known as the Interval scheduling maximization problem (ISMP), which is a special type of the more general Interval Scheduling problem. A classic application of this problem is in scheduling a room for multiple competing events, each having its own time requirements (start and end time), and many more arise ...
Schedule each job in this sequence into a machine in which the current load (= total processing-time of scheduled jobs) is smallest. Step 2 of the algorithm is essentially the list-scheduling (LS) algorithm. The difference is that LS loops over the jobs in an arbitrary order, while LPT pre-orders them by descending processing time.
To schedule a job , an algorithm has to choose a machine count and assign j to a starting time and to machines during the time interval [, +,). A usual assumption for this kind of problem is that the total workload of a job, which is defined as d ⋅ p j , d {\displaystyle d\cdot p_{j,d}} , is non-increasing for an increasing number of machines.
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 ...
interval order: Each job has an interval [s x,e x) and job is a predecessor of if and only if the end of the interval of is strictly less than the start of the interval for .= In the presence of a precedence relation one might in addition assume time lags. The time lag between two jobs is the amount of time that must be waited after the first ...
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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 ...
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