Error in prob.Objective

Dear All,

I tried to solve optimization problem with objective to minimize the result (cost), the code is below :

% Source Data
InvCost = [700 600 650 800 400]';
Cap = [750 750 750 750 750]';
DelCost = [3 0 5 6 8 5 5; 4 4 5 5 7 0 3; 5 7 3 5 7 4 0; 5 6 0 6 7 3 2; 6 6 6 0 2 5 6];
Demand = [500 400 150 350 300 400 200];

% Create Objective
prob = optimproblem('ObjectiveSense','minimize');
X1 = optimvar('X1',5,1,'Type','integer','LowerBound',0,'UpperBound',1);
X2 = optimvar('X2',5,7,'Type','integer','LowerBound',0,'UpperBound',[]);
cost = (InvCost'*X1)+(DelCost'*X2);
prob.Objective = cost;

% Create Constraints - Demand
ConsDemand = sum(X2)==Demand;
prob.Constraints.ConsDemand = ConsDemand;

% Create Constraints - Capacity
ConsCap = sum(X2)-(Cap'*X1);
prob.Constraints.ConsCap = ConsCap;

% Create Solution
[sol,fval] = solve(prob);

When tried to run the code, I got error message on "prob.Objective = cost " that

"Objective must be a scalar OptimizationExpression or a struct containing a scalar OptimizationExpression."

Attached pic below :

Anyone here can help me, how to solve this issue ? Is the code I have written correct or not?

Thank you for your kindly help.

Answer 1

[prabhat kumar sharma]

Hi Angga,

I understand that you are facing this error in your objective function.

I tried to analyze your objective function, that is defined as:

cost = (InvCost'*X1) + (DelCost'*X2);

Here, InvCost is a column vector (5x1), and X1 is a matrix (5x1) of optimization variables. Their product, InvCost'*X1, is a scalar, which is correct.

However, DelCost is a matrix (5x7), and X2 is also a matrix (5x7) of optimization variables. Their product, DelCost'*X2, will result in a matrix (5x7), not a scalar, which is the source of the error.

To correct the error, you need to ensure that the entire expression for cost results in a scalar. For the delivery cost part, you want to sum all elements of the product of DelCost and X2 to get a total delivery cost. This can be achieved by element-wise multiplication followed by summing all elements.

Here's how you can correct it:

% Corrected Objective Function
cost = sum(InvCost'*X1) + sum(sum(DelCost.*X2));

I hope it helps to resolve your error!