Help with CVRP Reload

[mertbakir]

ortools-discuss: https://groups.google.com/g/or-tools-discuss/c/-0uZTwB1S9M/m/ol3AQcUmAAAJ

I'm trying to use OR-Tools' Routing Solver to solve a Multi Trip Capacitated VRP. What I need is

• one depot, route starts and ends here.
• one unloading location (different from the depot)
• set time window and demand for each node

So the vehicles should pick up the goods from each node until the capacity is filled. Then go to "unloading location", unload all their weight and keep collecting the demand from nodes until a time limit is reached or all the goods are collected. Then return back to the depot.

CVRP Reload Example seems very close but in my case, at the end of the route vehicles should visit the unloading location before the depot. In other words a vehicle can not go to the depot (starting, ending location) with load.

Example:

0: Depot
1: Unloading Location
2, 3, 4, 5, 6, 7: Nodes to pick up demand


0 > 2 > 3 > 4 > 1 (unload) > 5 > 6 > 7 > 1 (unload) > 0
0 > 2 > 3 > 4 > 1 (unload) > 5 > 6 > 7 > 0 This is the result cvrp_reload returns.

I'm fairly new to or-tools, and trying to figure it out. Can you help me if you have any ideas?
PS. I'm using Python and or-tools v8.2

[lperron]

This is not an issue. Moving to discussions.

[Amarjeet0890]

I do not have any time windows or time constraints

[mertbakir]

@mertbakir @Mizux I am working on a similar problem. There are depots, demand points and delivery points. The vehicle starts from the depot goes to the demand point (demand at points >Vehicle capacity) and is delivered to the delivery point then the vehicle goes back to the demand point and delivers until it finishes all the demand. I have the pair of specific Pickup-delivery points and the O-d time matrix. I am unable to solve the revisits and also the o-D time matrix is 534 *534 points which creates a problem in loading. Could you please suggest to me how to implement this problem in Python?

I would decrease the size of the problem by clustering first. 534 is, in my experience, is a big number for OR-Tools to handle, or you can try to relax some of the constraints. Mizux may suggest a better way.

[Amarjeet0890]

@mertbakir @Mizux Thank you so much for your suggestion. I will try reducing the number of points. Still, I am unable to figure out the re-routing part from the delivery point again to the pickup point (back and forth) until the demand is over and then go back to the depot. This problem contains multi-depots,multi-pickups and multi-delivery points plus the demand at pickup also exceeds one vehicle capacity. there is no time constraint anywhere.

[mertbakir]

You need to create dummy nodes at the pickup locations if the demand is greater than the vehicle capacity. Because each node can be visited only once. If the demand is greater than the vehicle capacity and you don't allow the demand to be fulfilled partially then the node can not be visited. If a node can not be visited (because of the constraints), and you don't allow disjuctions (not visiting nodes) then you won't get a solution.

[mertbakir]

Consider joining the discord channel https://discord.gg/ENkQrdf

[mertbakir]

So, I thought I can come with a count_dimension to set a preceding constraint (unload before the last depot). Yet, I wasn't able to implement the idea.

So, the count_dimension function is commented out and I tried to add new dummy locations:

    _locations = [
    (4, 4),  # depot 0 
    (4, 4),  # depot 1
    (4, 4),  # depot 2
    (4, 4),  # depot 3
    (4, 4),  # depot 4
    (4, 4),  # depot 5
    (2, 3),  # unload depot_prime
    (2, 3),  # unload depot_second
    (2, 3),  # unload depot_fourth
    (2, 3),  # unload depot_fourth
    (2, 3),  # unload depot_fifth
....]

I tried to end the routes at 3, 4, 5 which are just dummy depots.

manager = pywrapcp.RoutingIndexManager(data['num_locations'],
                                           data['num_vehicles'], [0, 1, 2], [3, 4, 5])

This one returns an error: Process finished with exit code -1073741819 (0xC0000005)

---

It works fine when I set the vehicles start from 0, 1, 2 and end at 0, 1, 2. Returns a result at least. Demands of these nodes (depots and unload depots) are:

_demand = [0, 0, 0, 0, 0, 0,
           -_capacity, #6
           -_capacity, #7
           -_capacity, #8
           -_capacity, #9
           -_capacity, #10,
...]

---

Here is the whole code, it's basically cvrp_reload I'm trying to make modifications:

from functools import partial

from ortools.constraint_solver import pywrapcp
from ortools.constraint_solver import routing_enums_pb2

pickup_location_index = 11

###########################
# Problem Data Definition #
###########################
def create_data_model():
    """Stores the data for the problem"""
    data = {}
    _capacity = 15
    # Locations in block unit
    _locations = [
        (4, 4),  # depot
        (4, 4),  # depot
        (4, 4),  # depot
        (4, 4),  # depot
        (4, 4),  # depot
        (4, 4),  # depot
        (2, 3),  # unload depot_prime
        (2, 3),  # unload depot_second
        (2, 3),  # unload depot_fourth
        (2, 3),  # unload depot_fourth
        (2, 3),  # unload depot_fifth
        (2, 0),
        (8, 0),  # locations to visit
        (0, 1),
        (1, 1),
        (5, 2),
        (7, 2),
        (3, 3),
        (6, 3),
        (5, 5),
        (8, 5),
        (1, 6),
        (2, 6),
        (3, 7),
        (6, 7),
        (0, 8),
        (7, 8)
    ]
    # Compute locations in meters using the block dimension defined as follow
    # Manhattan average block: 750ft x 264ft -> 228m x 80m
    # here we use: 114m x 80m city block
    # src: https://nyti.ms/2GDoRIe 'NY Times: Know Your distance'
    data['locations'] = [(l[0] * 114, l[1] * 80) for l in _locations]
    data['num_locations'] = len(data['locations'])
    data['demands'] = \
          [0,
           0, 0, 0, 0, 0,
           -_capacity, #6
           -_capacity, #7
           -_capacity, #8
           -_capacity, #9
           -_capacity, #10
           3, 3, # 1, 2
           3, 4, # 3, 4
           3, 4, # 5, 6
           8, 8, # 7, 8
           3, 3, # 9,10
           3, 3, # 11,12
           4, 4, # 13, 14
           8, 8] # 15, 16
    data['time_per_demand_unit'] = 5  # 5 minutes/unit
    data['time_windows'] = \
          [(0, 0), # depot
           (0, 1000),
           (0, 1000),
           (0, 1000),
           (0, 1000),
           (0, 1000),
           (0, 1000),
           (0, 1000),
           (0, 1000),
           (0, 1000),
           (0, 1000),
           (75, 850), (75, 850), # 1, 2
           (60, 700), (45, 550), # 3, 4
           (0, 800), (50, 600), # 5, 6
           (0, 1000), (10, 200), # 7, 8
           (0, 1000), (75, 850), # 9, 10
           (85, 950), (5, 150), # 11, 12
           (15, 250), (10, 200), # 13, 14
           (45, 550), (30, 400)] # 15, 16
    data['num_vehicles'] = 3
    data['vehicle_capacity'] = _capacity
    data['vehicle_max_distance'] = 10_000
    data['vehicle_max_time'] = 1_500
    data[
        'vehicle_speed'] = 5 * 60 / 3.6  # Travel speed: 5km/h to convert in m/min
    data['depot'] = 0
    return data


#######################
# Problem Constraints #
#######################
def manhattan_distance(position_1, position_2):
    """Computes the Manhattan distance between two points"""
    return (abs(position_1[0] - position_2[0]) +
            abs(position_1[1] - position_2[1]))


def create_distance_evaluator(data):
    """Creates callback to return distance between points."""
    _distances = {}
    # precompute distance between location to have distance callback in O(1)
    for from_node in range(data['num_locations']):
        _distances[from_node] = {}
        for to_node in range(data['num_locations']):
            if from_node == to_node:
                _distances[from_node][to_node] = 0
            # Forbid start/end/reload node to be consecutive.
            elif from_node in range(6) and to_node in range(6):
                _distances[from_node][to_node] = data['vehicle_max_distance']
            else:
                _distances[from_node][to_node] = (manhattan_distance(
                    data['locations'][from_node], data['locations'][to_node]))

    def distance_evaluator(manager, from_node, to_node):
        """Returns the manhattan distance between the two nodes"""
        return _distances[manager.IndexToNode(from_node)][manager.IndexToNode(
            to_node)]

    return distance_evaluator


def add_count_dimension(routing, manager, data):
    count_dimension_name = 'Count'
    routing.AddConstantDimensionWithSlack(1, 10**8, 10**8, True, count_dimension_name)
    count_dimension = routing.GetDimensionOrDie(count_dimension_name)

    A_index = manager.NodeToIndex(0)
    B_index = manager.NodeToIndex(1)
    C_index = manager.NodeToIndex(2)

    A1_index = manager.NodeToIndex(6)
    A2_index = manager.NodeToIndex(7)
    A3_index = manager.NodeToIndex(8)

    routing.solver().Add(routing.VehicleVar(A_index) == routing.VehicleVar(B_index))
    routing.solver().Add(count_dimension.CumulVar(A_index) <= count_dimension.CumulVar(B_index))

    # routing.solver().Add(routing.VehicleVar(1) == routing.VehicleVar(11))
    # routing.solver().Add(routing.VehicleVar(17) == routing.VehicleVar(18))


def add_distance_dimension(routing, manager, data, distance_evaluator_index):
    """Add Global Span constraint"""
    distance = 'Distance'
    routing.AddDimension(
        distance_evaluator_index,
        0,  # null slack
        data['vehicle_max_distance'],  # maximum distance per vehicle
        True,  # start cumul to zero
        distance)
    distance_dimension = routing.GetDimensionOrDie(distance)
    # Try to minimize the max distance among vehicles.
    # /!\ It doesn't mean the standard deviation is minimized
    distance_dimension.SetGlobalSpanCostCoefficient(100)


def create_demand_evaluator(data):
    """Creates callback to get demands at each location."""
    _demands = data['demands']

    def demand_evaluator(manager, from_node):
        """Returns the demand of the current node"""
        return _demands[manager.IndexToNode(from_node)]

    return demand_evaluator


def add_capacity_constraints(routing, manager, data, demand_evaluator_index):
    """Adds capacity constraint"""
    vehicle_capacity = data['vehicle_capacity']
    capacity = 'Capacity'
    routing.AddDimension(
        demand_evaluator_index,
        vehicle_capacity,
        vehicle_capacity,
        True,  # start cumul to zero
        capacity)

    # Add Slack for reseting to zero unload depot nodes.
    # e.g. vehicle with load 10/15 arrives at node 1 (depot unload)
    # so we have CumulVar = 10(current load) + -15(unload) + 5(slack) = 0.
    capacity_dimension = routing.GetDimensionOrDie(capacity)
    # Allow to drop reloading nodes with zero cost.
    for node_index in range(pickup_location_index):
        index = manager.NodeToIndex(node_index)
        routing.AddDisjunction([node_index], 0)

    # Allow to drop regular node with a cost.
    for node_index in range(pickup_location_index, len(data['demands'])):
        index = manager.NodeToIndex(node_index)
        capacity_dimension.SlackVar(index).SetValue(0)
        routing.AddDisjunction([node_index], 100_000)


def create_time_evaluator(data):
    """Creates callback to get total times between locations."""

    def service_time(data, node):
        """Gets the service time for the specified location."""
        return abs(data['demands'][node]) * data['time_per_demand_unit']

    def travel_time(data, from_node, to_node):
        """Gets the travel times between two locations."""
        if from_node == to_node:
            travel_time = 0
        else:
            travel_time = manhattan_distance(
                    data['locations'][from_node], data['locations'][to_node]) / data['vehicle_speed']
        return travel_time

    _total_time = {}
    # precompute total time to have time callback in O(1)
    for from_node in range(data['num_locations']):
        _total_time[from_node] = {}
        for to_node in range(data['num_locations']):
            if from_node == to_node:
                _total_time[from_node][to_node] = 0
            else:
                _total_time[from_node][to_node] = int(
                    service_time(data, from_node) + travel_time(
                        data, from_node, to_node))

    def time_evaluator(manager, from_node, to_node):
        """Returns the total time between the two nodes"""
        return _total_time[manager.IndexToNode(from_node)][manager.IndexToNode(
            to_node)]

    return time_evaluator


def add_time_window_constraints(routing, manager, data, time_evaluator):
    """Add Time windows constraint"""
    time = 'Time'
    max_time = data['vehicle_max_time']
    routing.AddDimension(
        time_evaluator,
        max_time,  # allow waiting time
        max_time,  # maximum time per vehicle
        False,  # don't force start cumul to zero since we are giving TW to start nodes
        time)
    time_dimension = routing.GetDimensionOrDie(time)
    # Add time window constraints for each location except depot
    # and 'copy' the slack var in the solution object (aka Assignment) to print it
    for location_idx, time_window in enumerate(data['time_windows']):
        if location_idx == 0:
            continue
        index = manager.NodeToIndex(location_idx)
        time_dimension.CumulVar(index).SetRange(time_window[0], time_window[1])
        routing.AddToAssignment(time_dimension.SlackVar(index))
    # Add time window constraints for each vehicle start node
    # and 'copy' the slack var in the solution object (aka Assignment) to print it
    for vehicle_id in range(data['num_vehicles']):
        index = routing.Start(vehicle_id)
        time_dimension.CumulVar(index).SetRange(data['time_windows'][0][0],
                                                data['time_windows'][0][1])
        routing.AddToAssignment(time_dimension.SlackVar(index))
        # Warning: Slack var is not defined for vehicle's end node
        #routing.AddToAssignment(time_dimension.SlackVar(self.routing.End(vehicle_id)))


###########
# Printer #
###########
def print_solution(data, manager, routing, assignment):  # pylint:disable=too-many-locals
    """Prints assignment on console"""
    print(f'Objective: {assignment.ObjectiveValue()}')
    total_distance = 0
    total_load = 0
    total_time = 0
    capacity_dimension = routing.GetDimensionOrDie('Capacity')
    time_dimension = routing.GetDimensionOrDie('Time')
    dropped = []
    for node in range(pickup_location_index, routing.nodes()):
        index = manager.NodeToIndex(node)
        if assignment.Value(routing.NextVar(index)) == index:
            dropped.append(node)
    print(f'dropped orders: {dropped}')
    dropped = []
    for reload in range(1, pickup_location_index):
        index = manager.NodeToIndex(reload)
        if assignment.Value(routing.NextVar(index)) == index:
            dropped.append(reload)
    print(f'dropped reload stations: {dropped}')

    for vehicle_id in range(data['num_vehicles']):
        index = routing.Start(vehicle_id)
        plan_output = f'Route for vehicle {vehicle_id}:\n'
        distance = 0
        while not routing.IsEnd(index):
            load_var = capacity_dimension.CumulVar(index)
            time_var = time_dimension.CumulVar(index)
            plan_output += ' {0} Load({1}) Time({2},{3}) ->'.format(
                manager.IndexToNode(index),
                assignment.Value(load_var),
                assignment.Min(time_var), assignment.Max(time_var))
            previous_index = index
            index = assignment.Value(routing.NextVar(index))
            distance += routing.GetArcCostForVehicle(previous_index, index,
                                                     vehicle_id)
        load_var = capacity_dimension.CumulVar(index)
        time_var = time_dimension.CumulVar(index)
        plan_output += ' {0} Load({1}) Time({2},{3})\n'.format(
            manager.IndexToNode(index),
            assignment.Value(load_var),
            assignment.Min(time_var), assignment.Max(time_var))
        plan_output += f'Distance of the route: {distance}m\n'
        plan_output += f'Load of the route: {assignment.Value(load_var)}\n'
        plan_output += f'Time of the route: {assignment.Value(time_var)}min\n'
        print(plan_output)
        total_distance += distance
        total_load += assignment.Value(load_var)
        total_time += assignment.Value(time_var)
    print('Total Distance of all routes: {}m'.format(total_distance))
    print('Total Load of all routes: {}'.format(total_load))
    print('Total Time of all routes: {}min'.format(total_time))

    # for i in range(data['num_locations']):
    #     print(f'Node {i}:')
    #     print(routing.VehicleVar(i))
    #     print('------')



########
# Main #
########
def main():
    """Entry point of the program"""
    # Instantiate the data problem.
    data = create_data_model()

    # Create the routing index manager
    manager = pywrapcp.RoutingIndexManager(data['num_locations'],
                                           data['num_vehicles'], [0, 1, 2], [0, 1, 2])

    # Create Routing Model
    routing = pywrapcp.RoutingModel(manager)

    # Define weight of each edge
    distance_evaluator_index = routing.RegisterTransitCallback(
        partial(create_distance_evaluator(data), manager))
    routing.SetArcCostEvaluatorOfAllVehicles(distance_evaluator_index)

    # Add Distance constraint to minimize the longuest route
    add_distance_dimension(routing, manager, data, distance_evaluator_index)

    # Add Capacity constraint
    demand_evaluator_index = routing.RegisterUnaryTransitCallback(
        partial(create_demand_evaluator(data), manager))
    add_capacity_constraints(routing, manager, data, demand_evaluator_index)

    # add_count_dimension(routing, manager, data)

    # Add Time Window constraint
    time_evaluator_index = routing.RegisterTransitCallback(
        partial(create_time_evaluator(data), manager))
    add_time_window_constraints(routing, manager, data, time_evaluator_index)

    # Setting first solution heuristic (cheapest addition).
    search_parameters = pywrapcp.DefaultRoutingSearchParameters()
    search_parameters.first_solution_strategy = (
        routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC)  # pylint: disable=no-member
    search_parameters.local_search_metaheuristic = (
        routing_enums_pb2.LocalSearchMetaheuristic.GUIDED_LOCAL_SEARCH)
    search_parameters.time_limit.FromSeconds(3)

    # Solve the problem.
    solution = routing.SolveWithParameters(search_parameters)
    if solution:
        print_solution(data, manager, routing, solution)
    else:
        print("No solution found !")


if __name__ == '__main__':
    main()

This is the result:

Objective: 317544
dropped orders: []
dropped reload stations: [3, 4, 5]
Route for vehicle 0:
 0 Load(0) Time(0,0) -> 19 Load(0) Time(2,10) -> 18 Load(3) Time(20,28) -> 9 Load(11) Time(65,73) -> 22 Load(0) Time(142,150) -> 21 Load(3) Time(158,513) -> 13 Load(6) Time(179,534) -> 14 Load(9) Time(195,550) -> 10 Load(13) Time(218,774) -> 6 Load(0) Time(293,849) -> 7 Load(0) Time(368,924) -> 17 Load(0) Time(444,1000) -> 0 Load(8) Time(486,1500)
Distance of the route: 2488m
Load of the route: 8
Time of the route: 486min

Route for vehicle 1:
 1 Load(0) Time(0,0) -> 24 Load(0) Time(10,200) -> 26 Load(4) Time(32,400) -> 20 Load(12) Time(76,850) -> 1 Load(15) Time(97,1500)
Distance of the route: 1552m
Load of the route: 15
Time of the route: 97min

Route for vehicle 2:
 2 Load(0) Time(0,0) -> 15 Load(0) Time(3,43) -> 16 Load(3) Time(50,60) -> 12 Load(7) Time(75,83) -> 11 Load(10) Time(98,106) -> 8 Load(13) Time(115,123) -> 25 Load(0) Time(197,205) -> 23 Load(8) Time(242,250) -> 2 Load(12) Time(266,1500)
Distance of the route: 3104m
Load of the route: 12
Time of the route: 266min

Total Distance of all routes: 7144m
Total Load of all routes: 35
Total Time of all routes: 849min

[Mizux]

if you have 3 vehicles you must duplicate your "unloading" location since it can only be visited once.

Simply add a constraint load_dimension.CumulVar(vehicle_end_node) == 0 for all vehicle end node

[mertbakir]

if you have 3 vehicles you must duplicate your "unloading" location since it can only be visited once.

Simply add a constraint load_dimension.CumulVar(vehicle_end_node) == 0 for all vehicle end node

Yes, but it's already duplicated. First 6 nodes (0, 1, .., 5) are depots, and next 5 (6, .., 11) are the unloading ones. In reality there is only 1 depot and 1 unloading location. Can you elaborate what you mean? I didn't get it. :/

How can I get the vehicle_end_node in load_dimension.CumulVar(vehicle_end_node) == 0?

Lastly, should I use dummy duplicates of the depot

manager = pywrapcp.RoutingIndexManager(data['num_locations'],
                                           data['num_vehicles'], [0, 1, 2], [3, 4, 5])

or just

manager = pywrapcp.RoutingIndexManager(data['num_locations'],
                                           data['num_vehicles'], data['depot'])

or will load_dimension.CumulVar(vehicle_end_node) == 0 overwrite the RoutingIndexManager setting, so it's not important?

[Mizux]

Simply add

    # Vehicles must be empty upon arrival
    capacity_dimension = routing.GetDimensionOrDie("Capacity")
    for v in range(manager.GetNumberOfVehicles()):
        print(f"vehicle {v}")
        end = routing.End(v)
        #routing.solver().Add(capacity_dimension.CumulVar(end) == 0) # see comment below
        capacity_dimension.SetCumulVarSoftUpperBound(end, 0, 100_000)

possible output:

./2442_unload.py
...
I0417 23:53:02.181640 17437 search.cc:260] Solution #317 (372696, objective maximum = 4838552, time = 2969 ms, branches = 3223, failures = 940, depth = 33, MakeInactiveOperator, neighbors = 265820, filtered neighbors = 317, accepted neighbors = 317, memory used = 14.93 MB, limit = 99%)
I0417 23:53:20.290527 17437 search.cc:260] Solution #318 (469816, objective minimum = 372696, objective maximum = 4838552, time = 2987 ms, branches = 3239, failures = 945, depth = 33, MakeInactiveOperator, neighbors = 267395, filtered neighbors = 318, accepted neighbors = 318, memory used = 14.93 MB, limit = 99%)
I0417 23:53:21.045410 17437 search.cc:260] Solution #319 (469816, objective minimum = 372696, objective maximum = 4838552, time = 2988 ms, branches = 3247, failures = 947, depth = 33, MakeActiveOperator, neighbors = 267415, filtered neighbors = 319, accepted neighbors = 319, memory used = 14.93 MB, limit = 99%)
I0417 23:53:22.304931 17437 search.cc:260] Solution #320 (372696, objective maximum = 4838552, time = 2989 ms, branches = 3253, failures = 949, depth = 33, MakeActiveOperator, neighbors = 267464, filtered neighbors = 320, accepted neighbors = 320, memory used = 14.93 MB, limit = 99%)
I0417 23:53:30.987548 17437 search.cc:260] Finished search tree (time = 2998 ms, branches = 3259, failures = 982, neighbors = 268318, filtered neighbors = 320, accepted neigbors = 320, memory used = 14.93 MB)
I0417 23:53:31.046630 17437 search.cc:260] End search (time = 2998 ms, branches = 3259, failures = 982, memory used = 14.93 MB, speed = 1087 branches/s)
Objective: 372696
dropped orders: [25]
dropped reload stations: [3, 5]
Route for vehicle 0:
 0 Load(0) Time(0,0) -> 20 Load(0) Time(75,506) -> 12 Load(3) Time(94,525) -> 14 Load(6) Time(119,550) -> 13 Load(10) Time(140,700) -> 8 Load(13) Time(159,1000) -> 0 Load(0) Time(237,1500)
Distance of the route: 2624m
Load of the route: 0
Time of the route: 237min

Route for vehicle 1:
 1 Load(0) Time(0,0) -> 19 Load(0) Time(2,182) -> 24 Load(3) Time(20,200) -> 26 Load(7) Time(42,400) -> 4 Load(15) Time(89,770) -> 7 Load(15) Time(92,773) -> 11 Load(0) Time(169,850) -> 17 Load(3) Time(188,959) -> 10 Load(11) Time(229,1000) -> 1 Load(0) Time(307,1500)
Distance of the route: 2648m
Load of the route: 0
Time of the route: 307min

Route for vehicle 2:
 2 Load(0) Time(0,0) -> 23 Load(0) Time(15,63) -> 22 Load(4) Time(37,85) -> 21 Load(7) Time(85,101) -> 9 Load(10) Time(104,120) -> 18 Load(0) Time(184,200) -> 16 Load(8) Time(226,600) -> 15 Load(12) Time(248,800) -> 6 Load(15) Time(268,1000) -> 2 Load(0) Time(346,1500)
Distance of the route: 2624m
Load of the route: 0
Time of the route: 346min

Total Distance of all routes: 7896m
Total Load of all routes: 0
Total Time of all routes: 890min

note: I use the Soft constraint since otherwise the solver prefer to drop all nodes and never manage to escape from this solution search space point.

[mertbakir]

Thanks @Mizux.