In Japan, Dr. Ikegami of Seikei University was the first to raise the issue of the difficulty of creating a shift work schedule for nurses. (If you look at her book, you will see that it was initiated by the fact that she was hospitalized.)

References Nurse Scheduling

The problem is that obtaining an optimal solution for a nurse shift work schedule with complex constraints is very difficult.
According to my experience, nurse scheduling problems are not limited to nurses.
Midwives, nursing home caregivers, radiology technicians, physicians, etc., if the constraints are intertwined horizontally and vertically, all fall under the same category of nurse scheduling problems, i.e. These shift problems are challenging to solve rigorously.

The mathematical difficulty is classified as NP-difficult.
The nurse scheduling problem is a branch of combinatorial optimization.
It is the kind of problem that, as the problem size increases, the combinatorial explosion occurs, making it difficult to solve in a realistic time frame.
For example, the following video illustrates the difficulty of combinatorial optimization problems.

The real problem is not that finding the optimal solution to your shift work schedule will take billions of years.
We are only talking about the case of the scale of the problem.

Benchmark test - a performance indicator for software.

The professor published the problem as a 2003 benchmark test.
Researchers competed with each other to find the optimal solution, and in 2009, the optimal solution was determined.
It is an internationally renowned benchmark test.

Combinatorial optimization is the problem of finding an integer answer

The nurse scheduling problem is, academically, a branch of combinatorial optimization.
The solution to combinatorial optimization is always an integer.
For example, the solution of 4.5 staff members is not an integer and, therefore, cannot be an answer in combinatorial optimization.