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Unrelated-machines scheduling is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. We need to schedule n jobs J1, J2, ..., Jn on m different machines, such that a certain objective function is optimized (usually, the makespan should be minimized). The time that machine i needs in order to process job j is denoted by pi,j. The term unrelated emphasizes that there is no relation between values of pi,j for different i and j. This is in contrast to two special cases of this problem: uniform-machines scheduling - in which pi,j = pi / sj (where sj is the speed of machine j), and identical-machines scheduling - in which pi,j = pi (the same run-time on all machines).

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  • Unrelated-machines scheduling (en)
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  • Unrelated-machines scheduling is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. We need to schedule n jobs J1, J2, ..., Jn on m different machines, such that a certain objective function is optimized (usually, the makespan should be minimized). The time that machine i needs in order to process job j is denoted by pi,j. The term unrelated emphasizes that there is no relation between values of pi,j for different i and j. This is in contrast to two special cases of this problem: uniform-machines scheduling - in which pi,j = pi / sj (where sj is the speed of machine j), and identical-machines scheduling - in which pi,j = pi (the same run-time on all machines). (en)
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  • Unrelated-machines scheduling is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. We need to schedule n jobs J1, J2, ..., Jn on m different machines, such that a certain objective function is optimized (usually, the makespan should be minimized). The time that machine i needs in order to process job j is denoted by pi,j. The term unrelated emphasizes that there is no relation between values of pi,j for different i and j. This is in contrast to two special cases of this problem: uniform-machines scheduling - in which pi,j = pi / sj (where sj is the speed of machine j), and identical-machines scheduling - in which pi,j = pi (the same run-time on all machines). In the standard three-field notation for optimal job scheduling problems, the unrelated-machines variant is denoted by R in the first field. For example, the problem denoted by " R||" is an unrelated-machines scheduling problem with no constraints, where the goal is to minimize the maximum completion time. In some variants of the problem, instead of minimizing the maximum completion time, it is desired to minimize the average completion time (averaged over all n jobs); it is denoted by R||. More generally, when some jobs are more important than others, it may be desired to minimize a weighted average of the completion time, where each job has a different weight. This is denoted by R||. In a third variant, the goal is to maximize the minimum completion time, " R||" . This variant corresponds to the problem of Egalitarian item allocation. (en)
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