EV Automotive Algorithm: Optimal Mixed Integer Programming (MIP)




#Scheduling electric vehicles (EVs) in a #Mobility-#on-#Demand (#MoD) scheme involves determining the optimal assignment of EVs to customer requests while minimizing the overall cost or maximizing the revenue. The problem can be formulated as a mixed-integer programming (#MIP) problem as follows:


Decision Variables:

*x_ij: binary variable that takes value 1 if customer i is assigned to EV j, 0 otherwise

*y_j: binary variable that takes value 1 if EV j is in use, 0 otherwise


Objective Function:

*Minimize the total cost or maximize the total revenue:

Min/Max Σ(i,j) c_ij * x_ij - Σ(j) r_j * y_j


where c_ij is the cost (or revenue) of assigning customer i to EV j, and r_j is the cost (or revenue) of keeping EV j in use.



Constraints:

*Each customer is assigned to exactly one EV:

Σ(j) x_ij = 1, for all i


*Each EV can serve at most one customer at a time:

Σ(i) x_ij ≤ y_j, for all j


*Capacity constraints:

Σ(i) a_i * x_ij ≤ b_j * y_j, for all j


where a_i is the demand of customer i and b_j is the capacity of #EV j

Non-negativity constraints:

x_ij ≥ 0, for all i,j

y_j ≥ 0, for all j



The above MIP formulation can be solved using a range of #optimization software tools, such as #Gurobi, #CPLEX, or #SCIP. The solution to the MIP problem provides an optimal schedule of #EVs in the #MoD scheme, which can be used to minimize the #cost or maximize the revenue of the system while meeting the #demand of #customers.


#electricvehicles #software #programming

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