MILP - Multidimensional optimization

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

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).

But I have problem in creating the performance data in matlab. I have tried to create 4-D matrix but error occur. Can anyone give me some advise?

Thank you. Jim

---Updated---

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.

[Alan Weiss]

Please show us some code and the full error message.

Alan Weiss

MATLAB mathematical toolbox documentation

[Ngai Nang Wong]

I edited the question with my code, thank you so much!

Answer 1

[Aurele Turnes]

Your objective is

obj = sum(sum(Y.*X))

which is not scalar, but a 1-by-1-by-4-by-2 ND array.

Currently, the problem-based optimization only supports linear and mixed-integer linear problems: https://www.mathworks.com/help/optim/problem-based-lp-milp.html

All these solvers expect the objective to return a scalar value, so the objective is expected to be a 1-by-1 expression.

Answer 2

[BOWEN LI]

Hi, I am working on a similar question as yours, have you solved this question?