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Hope you are well. Responding to your need for a scheduling program. I believe I can help you with your requirements. I have experience of this type of problem in the context of academic scheduling. It is a simple linear optimisation problem. Unfortunately something like Prolog only deals with satisfiability and not optimal fit. There are many free solvers available that will easily crunch the problem, it is just a question of formulating it mathematically and the rest like user interface is just icing on the cake. Please message me if you are interested in discussing.
Based on your requirements, I would Google around for timetable or time management software not scheduling software. There seems to be a schedule element, but it doesn't seem to be too large.
Something like PagerDuty might work. Before you laugh, it fills the logic requirements so you could just interact with the API into a front-end that "rebrands" their endpoints into something you can use.
I recently did a custom web based payroll scheduling solution for a big labour broker in the eastrand that
runs daily and schedules weekly/fortnightly/monthly payrolls for processing with deadlines.
This took the company off printed excel sheets and saved them a huge amount of time.
It's also in the cloud and I'm currently doing a mobile extension app for them to manage payroll delivery by their drivers.
so I have something recent to show on the very problem you have
I do quite a lot of work around scheduling I do mobile/web/cloud/desktop full stack development.
I also have experience in GIS and Mapping if you need to do geo-fencing for the vehicles
or just want to log routes taken by your students.