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Scheduling a maintenance activity on parallel identical machines. (English) Zbl 1158.90350
Summary: We study a problem of scheduling a maintenance activity on parallel identical machines, under the assumption that all the machines must be maintained simultaneously. One example for this setting is a situation where the entire system must be stopped for maintenance because of a required electricity shut-down. The objective is minimum flow-time. The problem is shown to be NP-hard, and moreover impossible to approximate unless $$P = NP$$. We introduce a pseudo-polynomial dynamic programming algorithm, and show how to convert it into a bicriteria FPTAS for this problem. We also present an efficient heuristic and a lower bound. Our numerical tests indicate that the heuristic provides in most cases very close-to-optimal schedules.

##### MSC:
 90B35 Deterministic scheduling theory in operations research 90C39 Dynamic programming
##### Keywords:
scheduling; parallel machines; flow-time; maintenance activity
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