A note: Simple heuristics for scheduling a maintenance activity on unrelated machines

Following several recent papers discussing various problems of scheduling a maintenance activity, we focus here on scheduling a maintenance activity on unrelated parallel machines. The objective is to minimize flow-time. In the basic setting, we assume that all the machines must be maintained simultaneously. The problem is known to be NP-hard, and we introduce and test numerically an efficient heuristic and a lower bound, both based on a solution of a matching problem. We also study the relaxed version, where the machines are not restricted to be maintained at the same time. Similar heuristic and lower bound are proposed and tested.