Creating an optimization constraint - how to only schedule one employee per time slot

I'm trying to add a constraint to my linear programming problem but am not sure how to form it. Instead of showing all of my code, I will give you an example of a solution that is expected as an output with this constraint implemented.

The program is a nurse scheduling problem. It works correctly now given the constraints I have implemented, but it is scheduling all employees during the same shift (because that maximizes the reward -- which is the objective function). An example of what x could be is this:

x = [
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0]

What I don't know is what I should add to the A/b matrices to ensure this kind of a result (to expalin further, each 5 rows are the 5 options of where an employee can work. As you can see from this output, the employees are working in time slots 5, 4, 1 and 2 respectively i.e. not in the same time slot).

[Dave Campbell]

Maybe another way to form this question is, how do I find A/b such that the sum of every corresponding row is <= 1? i.e. the 1st row value + 6th row value + 11th row value + 16th row value <= 1 and so on

Answer 1

[Matt J]

The problem-based optimization workflow is especially handy for matrix-valued optimization variables. It lets you write constraints using literal row/column summation commands, and doesn't require you to find equivalent A,b matrices at all. For this problem, the skeleton of it would be,

x=optimvar('x',[5,4],'type','integer','LowerBound',0,'UpperBound',1);

prob=optimproblem;
prob.Constraints.rowsum =  ( sum(x,2)<=1  );
prob.Objective=...

solution=solve(problem)

Answer 2

[Christian Schumacher]

I need more code to help here, but i general: you must formulate a maximum nurses per shift. it should be something like this

i = 1:length(shift)
nursing_problem.Constraints.max_nurses = shift(i) == max_nurses;