MATLAB: How to multiply 4D array? Optimization assignment problem

4doptimization

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

Best Answer

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