Please help me on my periodic capacitated vehicle routing problem.
Find the same question here on google-groups.
What I am trying to model:
1 depot
multiple customers (let's assume 4)
multiple days (let's assume 3)
Multiple vehicle types with price per km and specific capacity
Every customer has: delivery frequency and demand per delivery
Every customer has to be assigned to a delivery pattern. Multiple delivery patterns are possible for each frequency. The pattern indicates if a delivery is possible on that day or not. For a frequency of 1 and 3 working days:
[[1,0,0],[0,1,0],[0,0,1]], a frequency of 2[[1,1,0],[1,0,1],[1,1,0]], a frequency of 3:[1,1,1]these are the possible patterns.
The demand of each customer per delivery is the same, for every day a delivery is performed
So we have a set of customers that have to be delivered by one depo. Multiple Vehicle Types are available for the job. The day of service is flexible because only the frequency is fixed to a customer, but there are multiple possibilities to fulfill the demand.
What I did so far:
I copied every node by the number of working days.
I restrict the start and end to the depo nodes of each day.
I multiply the vehicles by the number of days.
Furthermore, I handle the days as different kinds of cargo. I do assign a capacity of zero to the vehicle when it should not be used on that day.
[[10, 15, 15, 0, 0, 0, 0, 0, 0], [0, 0, 0, 10, 15, 15, 0, 0, 0], [0, 0, 0, 0, 0, 0, 10, 15, 15]]The first 3 vehicles are for day one, the second three are day two and the last 3 are day 3.
For the demand matrix I use the same trick. In a case of 4 customers + 1 depot the demand matrix could look like this
[[0, 3, 0, 5, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 3, 4, 5, 2, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2]]
The second entry in the first list (3) and the 7th entry in the second list (3) are for the same customer just on two different days. The nodes were copied.
This works good so far. But it's not what I want to do.
I do assign a demand for every customer and day by hand, but I want to assign the demand by a chosen delivery pattern for each customer.
The model could assign pattern [1,0,1] to one customer with a frequency of 2 and a pattern of [0,0,1] to another customer. This would result in the possibility to plan a tour on day 3 with both demands combined.
I need help to define a dimension that manages the assignment of patterns to customers which results in "flexible" demand matrix.
Thank you for your help.
Full Code:
"""Periodic Capacited Vehicles Routing Problem (PCVRP)."""
from ortools.constraint_solver import routing_enums_pb2
from ortools.constraint_solver import pywrapcp
import numpy as np
def dublicate_nodes(base_distance_matrix, num_days):
matrix = []
for i in range(num_days):
day_element = []
for node in range(len(base_distance_matrix)):
node_element = []
for day in range(num_days):
node_element.append(base_distance_matrix[node])
day_element.append(np.concatenate(node_element).tolist())
matrix.extend(day_element)
#print(matrix)
return matrix
def depo_nodes(num_days, num_verhicles, num_nodes):
depo_array = []
for day in range(num_days):
for veh in range(int(num_verhicles/num_days)):
depo_array.append(day*num_nodes)
#print(depo_array)
return depo_array
def veh_types_costs(cost_array, num_per_type, num_days):
cost_array_km = []
for day in range(num_days):
for i in range(len(cost_array)):
for num in range(num_per_type[i]):
cost_array_km.append(cost_array[i])
#print(cost_array_km)
return(cost_array_km)
def veh_capacity_matrix(num_vehicle_per_type, vehicle_capacity_type, num_days):
matrix= []
for index in range(num_days):
matrix_element = []
for day in range(num_days):
for i, num in enumerate(num_vehicle_per_type):
for times in range(num):
if day == index:
matrix_element.append(vehicle_capacity_type[i]);
else:
matrix_element.append(0)
matrix.append(matrix_element)
#print(matrix)
return matrix
def create_data_model():
data = {}
data["num_days"] = 3 #Anzahl Tage
### Definition der Fahrezugtypen
data["num_vehicle_per_type"] = [1, 2] #Anzahl Fahrzeuge pro Typ
data["vehicle_costs_type_per_km"] = [1, 0.01] #Kosten pro km pro Fahrzeugtyp
data["vehicle_costs_type_per_stop"] = [1, 1000] #Kosten pro Stop pro Fahrzeugtyp
data['price_per_km'] = veh_types_costs(data["vehicle_costs_type_per_km"], data["num_vehicle_per_type"], data["num_days"]) #Matrix für price_per_km je Fahrzeug ertsellen
data["price_per_stop"] = veh_types_costs(data["vehicle_costs_type_per_stop"], data["num_vehicle_per_type"], data["num_days"])
data["vehicle_capacity_type"] = [10, 15] # Kapaität pro Fahrzeugtyp
data['vehicle_capacities_matrix'] = veh_capacity_matrix(data["num_vehicle_per_type"], data["vehicle_capacity_type"], data["num_days"]) #Kapazitäten pro Fahrzeugs pro Tag
print('vehicle_capacities_matrix')
print(data['vehicle_capacities_matrix'])
data["num_vehicles_per_day"] = sum(data["num_vehicle_per_type"]) #Gesamtanzahl der Fahrzeuge pro Tag
data['num_vehicles'] = data["num_days"] * data["num_vehicles_per_day"]# Gesamtanzahl der Fahrzeuge in gesamten Zeitraum
###Distanzmatrix bestimmen
data["base_distance_matrix"] = [
[
0, 548, 776, 696, 582
],
[
548, 0, 684, 308, 194
],
[
776, 684, 0, 992, 878
],
[
696, 308, 992, 0, 114
],
[
582, 194, 878, 114, 0
]
] #Distanzmatrix mit allen Kunden einzeln
data['distance_matrix'] = dublicate_nodes(data["base_distance_matrix"], data["num_days"]) # Distanzmatrix mit mehrfachen Nodes pro Kunden, je Tag ein Node
###Start und Ende festlegen
data["num_nodes"] = len(data["base_distance_matrix"]) # Anzahl Kunden
data['starts'] = depo_nodes(data["num_days"], data['num_vehicles'], data["num_nodes"]) #Deponodes (Start) für die einzelnen Fahrzeuge (Tage)
data['ends'] = depo_nodes(data["num_days"], data['num_vehicles'], data["num_nodes"]) #Deponodes (Ende) für die einzelnen Fahrzeuge (Tage)
###Demand pro Kunde
data['demands_matrix'] = [[0, 3, 0, 5, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],[0, 0, 0, 0, 0, 0, 3, 4, 5, 2, 0, 0, 0, 0, 0],[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2]] #Demandmatrix mit je einer list pro Tag
return data
def print_solution(data, manager, routing, solution):
"""Prints solution on console."""
total_distance = 0
total_load = 0
for vehicle_id in range(data['num_vehicles']):
if vehicle_id % data["num_vehicles_per_day"] == 0:
print(("------Tag {}------").format(int(vehicle_id/data["num_vehicles_per_day"])))
if routing.IsVehicleUsed(assignment= solution, vehicle=vehicle_id) == False:
continue
index = routing.Start(vehicle_id)
if vehicle_id >= data["num_vehicles_per_day"]:
plan_output = 'Route for vehicle {}:\n'.format(abs(vehicle_id-data["num_vehicles_per_day"]*int(vehicle_id/data["num_vehicles_per_day"])))
else:
plan_output = 'Route for vehicle {}:\n'.format(vehicle_id)
route_costs = 0
route_load = 0
while not routing.IsEnd(index):
node_index = manager.IndexToNode(index)
capacity_ID = int(vehicle_id/data["num_vehicles_per_day"])
route_load += data['demands_matrix'][capacity_ID][node_index]
plan_output += ' {0} Load({1}) -> '.format(node_index, route_load)
previous_index = index
index = solution.Value(routing.NextVar(index))
route_costs += routing.GetArcCostForVehicle(
previous_index, index, vehicle_id)
plan_output += ' {0} Load({1})\n'.format(manager.IndexToNode(index),
route_load)
plan_output += 'Costs of the route: {}€\n'.format(route_costs)
plan_output += 'Load of the route: {}\n'.format(route_load)
print(plan_output)
total_distance += route_costs
total_load += route_load
print('Total costs of all routes: {}€'.format(total_distance))
print('Total load of all routes: {}'.format(total_load))
def main():
"""Periodic CVRP problem."""
# Instantiate the data problem.
data = create_data_model()
# Create the routing index manager.
manager = pywrapcp.RoutingIndexManager(len(data['distance_matrix']), data['num_vehicles'], data['starts'],
data['ends'])
# Create Routing Model.
routing = pywrapcp.RoutingModel(manager)
### Kostenfunktion je Fahrzeug festlegen ###
def create_cost_callback(dist_matrix, km_costs, stop_costs):
# Create a callback to calculate distances between cities.
def distance_callback(from_index, to_index):
from_node = manager.IndexToNode(from_index)
to_node = manager.IndexToNode(to_index)
return int(dist_matrix[from_node][to_node]) * (km_costs) + (stop_costs)
return distance_callback
for i in range(data['num_vehicles']):
cost_callback = create_cost_callback(data['distance_matrix'], data["price_per_km"][i],
data["price_per_stop"][i]) # Callbackfunktion erstellen
cost_callback_index = routing.RegisterTransitCallback(cost_callback) # registrieren
routing.SetArcCostEvaluatorOfVehicle(cost_callback_index, i) # Vehicle zuordnen
#Define Capacities for Vehicles for every Day
def create_demand_callback(demand_matrix, demand_index):
# Create a callback to calculate capacity usage.
def demand_callback(from_index):
#Returns the demand of the node.
# Convert from routing variable Index to demands NodeIndex.
from_node = manager.IndexToNode(from_index)
return demand_matrix[demand_index][from_node]
return demand_callback
for i in range(data["num_days"]): #Jedes Fahrzeug hat pro Tag eine andere Kapazität
demand_callback = create_demand_callback(data['demands_matrix'], i)
demand_callback_index = routing.RegisterUnaryTransitCallback(demand_callback)
dimension_name = 'Capacity_day_{}'.format(i)
routing.AddDimensionWithVehicleCapacity(
demand_callback_index,
0, # null capacity slack
data['vehicle_capacities_matrix'][i], # vehicle maximum capacities
True, # start cumul to zero
dimension_name)
# Setting first solution heuristic.
search_parameters = pywrapcp.DefaultRoutingSearchParameters()
search_parameters.first_solution_strategy = (
routing_enums_pb2.FirstSolutionStrategy.AUTOMATIC)
search_parameters.local_search_metaheuristic = (
routing_enums_pb2.LocalSearchMetaheuristic.AUTOMATIC)
search_parameters.time_limit.FromSeconds(1)
# Solve the problem.
solution = routing.SolveWithParameters(search_parameters)
# Print solution on console.
if solution:
print_solution(data, manager, routing, solution)
return solution
if __name__ == '__main__':
solution_array = []
solution = main()