write the optimization code with Gurobi

Hello
I have a mathematical model to minimize time violations. could you help me to Gurobi model.

\(P_ij^(k,w)\) = Binary variable=1, if truck k and w drive as a platoon on edge \(e_ij\)
\(ST^k\) = shortest path time of each truck

The objective function for time violation for all trucks \(Min z = ∑_k(x_ij^k*t_ij +WT^k ) –ST^k\)

constraints:

Calculate travelling time of truck at edge ij \( t_ij=d_ij /v\)
max (arrival time truck at platoon point i from origin point ) \( MT^k=max(P_ij^{k,w}*t_{o^k i}^k)\)
the arrival time of all trucks at platoon point i = last truck arrived at platoon( \( MT^k)\)
\( WT^k = MT^k\) – platoon arrival time of each truck point i
\(WT^k=0 \)If travelling time of each truck == \( ST^k\)
number of trucks in platoon <= 5
total travelling time of truck <= deadline of each truck

saving_factor = 0.1
number_of_nodes = 6
node_list = []
for i in range(1,number_of_nodes+1):
node_list.append(i)

group = {0: (1, 5), 1: (2, 6)} 
#group = {0:(1, 2), 1:(3, 4)}

graph = nx.DiGraph()
edges = [(1, 3, {'weight': 1}),(3, 1, {'weight': 1}),
(2, 3, {'weight': 2}),(3, 2, {'weight': 2}),
(4, 3, {'weight': 2}),(3, 4, {'weight': 2}), 
(4, 5, {'weight': 2}),(5, 4, {'weight': 2}), 
(4, 6, {'weight': 2}),(6, 4, {'weight': 2}), 
(1, 5, {'weight': 4.9}),(5, 1, {'weight': 4.9}), 
(2, 6, {'weight': 5.9}),(6, 2, {'weight': 5.9})]
speed = 1
graph.add_edges_from(edges)
road_network = graph

#shortest path time each truck = earliest_arrival_time_each_truck

earliest_arrival_time_each_truck={}
for h, locations in group.items():
    earliest_arrival_time_each_truck[h] = nx.dijkstra_path_length(road_network, source=locations[0], target=locations[1])/speed

model = Model("Routing")

## Variables

x = {}
y = {}
for edge in road_network.edges():
  x[edge] = {}
  y[edge] = model.addVar(vtype=GRB.BINARY, name="{}".format("y"+str(edge)))

  for h, _ in group.items():
     x[edge][h] = model.addVar(vtype=GRB.BINARY, name="{}".format("x" +str(edge)+str(h)))

for v in road_network.nodes():
  for h, locations in group.items():
     if locations[0] == v:
        b = 1
    elif locations[1] == v:
        b = -1
    else:
        b = 0
    model.addConstr(quicksum(x[edge][h] for edge in road_network.out_edges(v)) -
          quicksum(x[edge][h] for edge in road_network.in_edges(v)) == b, name='flow_' + str(v) + "_" + str(h))


for edge in road_network.edges():
    for h, locations in group.items():
           model.addConstr(x[edge][h] <= y[edge])

objective_function_main= gp.LinExpr()

total_travel_time_per_truck = {}
for h, _ in group.items():
    total_travel_time_per_truck[h] = gp.LinExpr()
    for e in road_network.edges():
        total_travel_time_per_truck[h] += x[e][h] * (road_network.get_edge_data(*e)["weight"] / speed)
objective_function_main+= (total_travel_time_per_truck[h] + waitingtime[h] - earliest_arrival_time_each_truck[h])

here in this gurobi code I already implement constraints for vehicle platoon problem.
I need to add the above mention constraint to my code.
could you help me, please?

Thank you

Official comment

Simranjit Kaur

Gurobi Staff

November 16, 2025 23:45

This post is more than three years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum, or try Gurobot, our chatbot interface offering instant, expert-level support.

Mario Ruthmair

January 25, 2022 16:14

write the optimization code with Gurobi

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