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'''Flow-shop scheduling''' is an [[optimization problem]] in [[computer science]] and [[Operations Research|operations research]]. It is a variant of [[optimal job scheduling]]. In a general job-scheduling problem, 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'' machines with varying processing power, while trying to minimize the [[makespan]] – the total length of the schedule (that is, when all the jobs have finished processing). In the specific variant known as ''flow-shop scheduling'', each job contains exactly ''m'' operations. The ''i''-th operation of the job must be executed on the ''i''-th machine. No machine can perform more than one operation simultaneously. For each operation of each job, execution time is specified.
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