About ten years ago, we had a project with a major car manufacturer in the U.K.. It was concerned with scheduling preventive maintenance (PM) on the production line. Some items had to be maintained every week, others at intervals of two, three, four or more weeks. Weekly maintenance was easy. But the other items were more difficult. If you needed one person-day to maintain items A (2 weeks), B (3 weeks) and C (4 weeks), then in successive weeks you would need:
However, we were given many more items than three (A, B and C), and the problem of unequal work-load was much more severe. Our project was concerned with finding ways of changing some of the intervals within a permitted range. So changing C from 4 weeks to 3 weeks after week 8, and then back to 4 weeks would smooth the work-load.
But, things were not so simple. Every so often, an item broke down, and needed repair. The opportunity might be taken to perform maintenance on other systems while the repair was in progress. After that, it was put back into service, and its schedule of PM started afresh. We developed a tool for rescheduling all the PM work when there had been such a repair. It smoothed out the work-load for the teams doing PM in the factory. It was a case study that was never published; because the interface used by the PM manager was a spreadsheet, the optimisation used a commercial genetic algorithm, whose details were a trade secret. So, little could have been written up to describe the process. And the car company did not want publicity for the interface.
There are circumstances where people need regular hospital appointments, just like the machines needing PM. Medical check-ups for some conditions need to be scheduled at fixed intervals. So, one might suppose that the same approach could be used to schedule their visits to the hospital or doctor. But it isn't as simple. People are not machines; they have lives besides their need for a check-up. So, they might be available on Thursday at 2 pm one week, but the following week they have an appointment for lunch and cannot have a check-up before 3pm. And another week they may be on holiday. Machines don't have lunch dates, nor go on holiday! Patients with similar needs, medically, may have different social conditions. Exeter's hospital draw people from a wide area. Some of them rely on public transport to come and go, so depend on the local schedule for their part of Devon. That means that there is an inbuilt priority for those whose transport needs are more limited. Within reason, the scheduled PM work for any one day does not prioritise jobs and so they could be carried out in any order.
So ... scheduling people in this situation has more complications than for arranging regular work on machines, even though there is an underlying need to smooth the workload in the hospital. So, in these circumstances, a manual approach sems to work reasonably well. But - maybe - there is a system which can do some of the work automatically, without degrading the dignity those being scheduled.
I have dental check-ups every nine months, and give blood every three. The two systems for scheduling the next appointment differ. At the dentist, the book for future appointments extends for at least a year, and so I can normally find a date and time which is convenient, because very few other people are competing for a visit so far in advance. So, most of my check-ups are on the same day of the week, starting at the same time in the morning. Obviously, there is some slack in the dentist's timetable to allow for emergency visits, so the book is never quite filled. Here a manual system works extremely well. In contrast, the blood donor sessions do not hold a book open very far in advance. There are fewer opportunities to give blood (the dentist is open five days each week, donor sessions are monthly). Because people are not machines (see above), if a donor can't come to the next session, they book for the earliest one they can after that. And many (perhaps most) donors prefer an early appointment, because, inevitably, delays in the queues build up and later arrivals spend more time waiting than the earlier ones. So, one often finds that the early slots at successive sessions have been taken when it comes to booking a three-month visit. Here is a manual scheduling system with very little slack, and consequently, frustration (which machines do not feel). Maybe it could be mechanised, but would it be worth it?
And that is the bottom line. As O.R. people, we can look at problems involving human beings, recognise that there are similarities with problems concerned with "Things", but need to account for and remember that people are not things!