Scheduling periodic preventive maintenance with a single server in a finite horizon

A deterministic scheduling problem of a single maintenance crew or facility responsible for the periodic preventive maintenance of n machines of a production system is considered. Each machine has a cost (e.g., an environmental emission) that deteriorates over time according to a convex and increasing function. The objective is to find a maintenance sequence policy that optimises the overall efficiency (e.g., minimises the total emission) of the system in a finite horizon, under a continuous time relaxation, i.e., the time is considered continuous and not discrete. The proposed greedy algorithm is proven to yield optimal solutions for the relaxed problem.