How can I multiply 4D array? Optimization assignment problem

Hi guys, I am currently working on an optimization problem:-

I have to assign my workers (i) to perform different tasks (j) under different sections (k) of different projects(L).

So I created a simple model : Maximize P = X(ijkl)*Y(ijkl) and Y(ijkl) is binary variable

here is my code

   .
  l = {'P1','P2',};
  k = {'S1','S2','S3','S4'};
  j = {'T1','T2','T3','T4','T5','T6','T7', 'T8'};
  i = {'W1','W2','W3','W4','W5','W6','W7','W8'};
  Y = optimvar('Y',i,j,k,l,'LowerBound',0,'UpperBound',1,'Type','integer');
  X = rand(8,8,4,2)
  Optimprob = optimproblem('ObjectiveSense','maximize','Objective',sum(sum(Y.*X)));
  [soln,fval,exitflag,output] = solve(Optimprob);

and turns out error is occur:-

Error using optimproblem (line 52) Objective must be a scalar OptimizationExpression or a struct containing a scalar OptimizationExpression.

The assignment method are based on the performance data X(ijlk), e.g. workers (i) have 20 marks in task (j) under section (k) in project (L).

Am I need to reshape the 4D-array to solve the problem? Can anyone give me some advise?

Thank you. Jim

Answer 1

[Torsten]

Use "reshape" to turn your 4d-matrices into an 1d-vector, multiply the vectors componentenwise and sum.

[Ngai Nang Wong]

It works!!Thank you!! One more question, how do I know the value of binary variable Y(ijkl) after the solution was found? I want to know which workers (i) got the Tasks (j)

[Torsten]

Did you impose sum constraints on the Y ? Otherwise, all of them will be 1, I guess.

[Ngai Nang Wong]

I made 2 constraints but not sure if it is work since I cannot see the value of Y(ijkl).

This is my constraints
Optimprob.Constraints.constr1 = sum(Y,2) == 1;
Optimprob.Constraints.constr2 = sum(Y,1) <= 1; 
end