Maintenance and Optimal Stopping

Imagine we have a machine in a factory that makes products which are sold to the general public. Ideally we want to make as many products as possible so we can sell them all to make a nice healthy profit. This means that we really want to be running the machine all through the day with no unnecessary stoppages.

Realistically however we know that machines do in fact breakdown and companies employ teams of people whose job it is to maintain the machines so that they can keep them running or repair them if they do break. Generally these maintenance teams will have a planned schedule of times when they will stop the machine in order to do their necessary checks and servicing.

maintanence

This approach works well except for the fact that there are often conflicting views between the maintenance department and the production department. The production department wants to make sure that products are always being made (as few stops as possible), whereas the maintenance viewpoint is that the aim should be to stop the machine breaking down (needing a lot of stops). This poses the question of how to find the optimum balance between having a reliable machine and a productive machine?

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