How can i sanction changes in linear optimization?

I am trying to optimize Electrical Vehicle charge using a limited number of chargers. (Right now only looking at one hour)

The following Code is working:

% Define max. charger currrent, car capacity and max. car current
charger = [11,22,50];
cars = [10,20,30,40];
maxCurrentCar = [11,22,11,22];

x = optimvar('x',length(cars),length(charger),'LowerBound',0);

chargerconstr = sum(x,1) <= charger;
carcapconstr = sum(x,2) <= cars';
cartimeconstr = sum(x,2) <= maxCurrentCar';

chargertimeconstr = sum(x,1) <= charger;

prob = optimproblem;
prob.Objective = -1*sum(sum(x));
prob.Constraints.laderconstr = chargerconstr;
prob.Constraints.autoladungconstr = carcapconstr;
prob.Constraints.autozeitconstr = cartimeconstr;
prob.Constraints.ladezeitconstr = chargertimeconstr;

opts = optimoptions('intlinprog','Display','off','PlotFcn',@optimplotmilp);
[sol,fval,exitflag,output] = solve(prob,'options',opts);

As a result i get the matrix

0	0	10
0	20	0
11	0	0
0	2	20

Looking at row 4 i now would like to sanction the use of multiple chargers (if not really necessary). My idea would be to tell the car it need like 10 minutes to switch between chargers.

How would i do this?

I already tried implementing binary variables into the model, but without success.

Answer 1

[prabhat kumar sharma]

Hello Niklas,

To limit cars to using one charger at a time, introduce binary variables to indicate charger usage. Here's a streamlined approach:

1. Binary Variables: Create y(i,j) to show if car i uses charger j.
2. Constraints:

• Link x(i,j) (charging amount) to y(i,j) using a large constant (bigM): x(i,j) <= bigM * y(i,j).
• Ensure each car uses at most one charger: sum(y, 2) <= 1.

3. Objective: Maximize charging without changes.

charger = [11, 22, 50];
cars = [10, 20, 30, 40];
maxCurrentCar = [11, 22, 11, 22];

x = optimvar('x', length(cars), length(charger), 'LowerBound', 0);
y = optimvar('y', length(cars), length(charger), 'Type', 'integer', 'LowerBound', 0, 'UpperBound', 1);

bigM = max(charger);
prob = optimproblem;
prob.Objective = -sum(sum(x));
prob.Constraints.chargerconstr = sum(x, 1) <= charger;
prob.Constraints.carcapconstr = sum(x, 2) <= cars';
prob.Constraints.cartimeconstr = sum(x, 2) <= maxCurrentCar';
prob.Constraints.useChargerConstr = x <= bigM * y;
prob.Constraints.oneChargerPerCarConstr = sum(y, 2) <= 1;

opts = optimoptions('intlinprog', 'Display', 'off', 'PlotFcn', @optimplotmilp);
[sol, fval, exitflag, output] = solve(prob, 'options', opts);

disp(sol.x);

I hope it helps!