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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.