Demand Constraint Project -

Optimize the cost of charging shared e-vehicles at a single station under demand constraints.

• A is the vehicles assignment matrix
• B is the station assignment matrix
• D is the vector of demand for e-vehicles at time step k and can only take two values: 0 or 1
• R is the vector of returned e-vehicles
• c is the vector representing charging stations
• b is a vector representing the station at which there is a vehicle. It is a state variable. If there is a vehicle at station i, then b_i= 1
• d is a vector representing if a vehicle is available or not
• α represents the marginal cost of charging a charging point, considered fixed so far
• β and γ are design variables and represent how much not meeting the demand in vehicles or stations is penalized. It was fixed to 1 for the simulations
• N is the number of vehicles at the considered station
• T is the number of time steps in our time horizon

Then, for each time step k ≥ 1, let's define:

1. The first term represents the cost of charging: the sum over all time steps.

2. The second term represents the penalization for the demand in e-vehicle that cannot be met. This term must be considered per time step: let's assume that demand at time step k is

and the actual assignment is

3. The third term represents the same type of penalization, but for not meeting demand in free stations.

Attachment:- Assignment File.rar