This is not a good way to solve the timesheet issue.
This is a complex mathematical question and people will not provide good answers no matter how smart they are. Every artificial intelligence technique starts from a training, a database in which one has the best answers to a set of problems, from there the system learns to infer a new response close to the ideal for a similar new problem. Well I do not want to confuse you anymore, I'll tell you what your problem is.
This is an optimization problem, not artificial intelligence.
Defining with my words, every time we have a scarce resource that must be allocated, or a function that must be optimized for a goal obeying various constraints, we have an optimization problem.
Timetable is a classic problem of optimization, we have to allocate schedules for the work of people, say 24h, but we have several restrictions, for example, we have employees working 8 hours, 6 hours, we must have an interval of 1 hour between 8 o'clock, once a week, and several other legislative restrictions.
The algorithms then attempt to arrive at an optimized function that meets all constraints imposed, minimizing or maximizing the use of resources.
Another example would be cutting wood, maximizing reuse of the floor area and minimizing the cost. The constraints are the required cut shapes and their respective amount.
In fact, the time problem is exploited by some companies that provide consulting or software to facilitate modeling and resolution.
A former professor of mine gives classes in optimization, and has a company that specializes in making work scales using these techniques that I commented, the company is link
It even has software in which I did a temporary job, where people set up the work schedule and their restrictions, and the system resolves the best possible scale according to all the legislation, avoiding fines and minimizing the number of employees, in fact saving on corporate payroll.
I've had this business class and I find it harder than artificial intelligence, everything that has to decorate something I find more difficult :-), I did not find a good material to pass on but there is this one www.maxwell.vrac.puc -rio.br/20533/20533_4.PDF that talks about the subject, good basically there is an algorithm called min-max to solve these problems, it does not have a high computational efficiency of the classic form, there are more optimized and complex variations and methods, but it's a good start. This teacher I spoke to was student of this alien individual here:
Petr Iakovlevitch Ekel - link
This Petr teaches Mathematics Methods in the Master of Electrical Engineering of PUC and is simply the world's largest authority on the subject, the guy works for governments, optimizing the installation of electrical power meshes in countries, just to get an idea. ..