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'''Uniform machine scheduling''' (also called '''uniformly-related machine scheduling''' or '''related machine scheduling''') is an [[optimization problem]] in [[computer science]] and [[Operations Research|operations research]]. It is a variant of [[optimal job scheduling]]. We are given ''n'' jobs ''J''<sub>1</sub>, ''J''<sub>2</sub>, ..., ''J<sub>n</sub>'' of varying processing times, which need to be scheduled on ''m'' different machines. The goal is to minimize the [[makespan]] - the total time required to execute the schedule. The time that machine ''i'' needs in order to process job j is denoted by ''p<sub>i,j</sub>''. In the general case, the times ''p<sub>i,j</sub>'' are unrelated, and any matrix of positive processing times is possible. In the specific variant called ''uniform machine scheduling'', some machines are ''uniformly'' faster than others. This means that, for each machine ''i'', there is a speed factor ''s<sub>i</sub>'', and the run-time of job ''j'' on machine ''i'' is ''p<sub>i,j</sub>'' = ''p<sub>j</sub>'' / ''s<sub>i</sub>''.
In the standard [[Optimal job scheduling|three-field notation for optimal job scheduling problems]], the uniform-machine variant is denoted by '''Q''' in the first field. For example, the problem denoted by " '''Q||'''<math>C_\max</math>" is a uniform machine scheduling problem with no constraints, where the goal is to minimize the maximum completion time.
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