title: OR-Tools CVRP_reload with Pickup-Delivery
body: <p>I use or-tools to solve problems such as picking up products from EC warehouses.</p>
  <p>What I want to do is very similar to the cvrp_reload sample.
  <a href="https://github.com/google/or-tools/blob/stable/ortools/constraint_solver/samples/cvrp_reload.py" rel="nofollow noreferrer">https://github.com/google/or-tools/blob/stable/ortools/constraint_solver/samples/cvrp_reload.py</a>
  The difference from the sample is that instead of bringing the load back to the depot, the picked up load is placed at a specific delivery point.</p>
  <p>I changed the source of cvrp_reload while looking at the Pickup &amp; Delivery sample in the guide. (Assuming that Node.1 to 5 are the delivery points)</p>
  <ol>
  <li>Add Pickup &amp; Delivery point list to data</li>
  </ol>
  <pre><code>    data['pickups_deliveries'] = [
          [6, 1], [7, 1],
          [8, 1], [9, 1],
          [10, 2], [11, 2],
          [12, 2], [13, 3],
          [14, 3], [15, 3],
          [16, 4], [17, 4],
          [18, 4], [19, 5],
          [20, 5], [21, 5]        
      ]
  </code></pre>
  <ol start="2">
  <li>Simplification of demands and time_windows in data</li>
  </ol>
  <pre><code>    data['demands'] = \
            [0, # depot
             -_capacity, # unload depot_first
             -_capacity, # unload depot_second
             -_capacity, # unload depot_third
             -_capacity, # unload depot_fourth
             -_capacity, # unload depot_fifth
             4, 4, # 1, 2   changed from original
             4, 4, # 3, 4   changed from original
             4, 4, # 5, 6   changed from original
             4, 4, # 7, 8   changed from original
             4, 4, # 9,10   changed from original
             4, 4, # 11,12   changed from original
             4, 4, # 13, 14   changed from original
             4, 4] # 15, 16   changed from original
      data['time_windows'] = \
            [(0, 0), # depot
             (0, 1500), # unload depot_first. changed from original
             (0, 1500), # unload depot_second. changed from original
             (0, 1500), # unload depot_third. changed from original
             (0, 1500), # unload depot_fourth. changed from original
             (0, 1500), # unload depot_fifth. changed from original
             (0, 750), (0, 750), # 1, 2   changed from original
             (0, 750), (0, 750), # 3, 4   changed from original
             (0, 750), (0, 750), # 5, 6   changed from original
             (0, 750), (0, 750), # 7, 8   changed from original
             (0, 750), (0, 750), # 9, 10   changed from original
             (750, 1500), (750, 1500), # 11, 12   changed from original
             (750, 1500), (750, 1500), # 13, 14   changed from original
             (750, 1500), (750, 1500)] # 15, 16   changed from original
  </code></pre>
  <ol start="3">
  <li>Define transportation requests in add_distance_dimension function</li>
  </ol>
  <pre><code>    for request in data['pickups_deliveries']:
          pickup_index = manager.NodeToIndex(request[0])
          delivery_index = manager.NodeToIndex(request[1])
          routing.AddPickupAndDelivery(pickup_index, delivery_index)
          routing.solver().Add(
              routing.VehicleVar(pickup_index) == routing.VehicleVar(
                  delivery_index))
          routing.solver().Add(
              distance_dimension.CumulVar(pickup_index) &lt;=
              distance_dimension.CumulVar(delivery_index))
  </code></pre>
  <p>Running this code will drop all nodes. However, limiting the list of P&amp;Ds to just a few gives a solution.</p>
  <pre><code>data['pickups_deliveries'] = [
      [6, 1], [7, 1],
      [8, 1], [9, 1],
      [10, 2], [11, 2],
      # [12, 2], [13, 3],
      # [14, 3], [15, 3],
      # [16, 4], [17, 4],
      # [18, 4], [19, 5],
      # [20, 5], [21, 5]        
  ]
  </code></pre>
  <p>Please give me a hint where my method is wrong.</p>
  <p>This is the entire code. Thanks for reading my question.</p>
  <pre><code>from functools import partial
  
  from ortools.constraint_solver import pywrapcp
  from ortools.constraint_solver import routing_enums_pb2
  
  
  ###########################
  # Problem Data Definition #
  ###########################
  def create_data_model():
      &quot;&quot;&quot;Stores the data for the problem&quot;&quot;&quot;
      data = {}
      _capacity = 15
      # Locations in block unit
      _locations = [
          (4, 4),  # depot
          (4, 4),  # unload depot_first
          (4, 4),  # unload depot_second
          (4, 4),  # unload depot_third
          (4, 4),  # unload depot_fourth
          (4, 4),  # 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 -&gt; 228m x 80m
      # here we use: 114m x 80m city block
      data['locations'] = [(l[0] * 114, l[1] * 80) for l in _locations]
      data['num_locations'] = len(data['locations'])
      data['demands'] = \
            [0, # depot
             -_capacity, # unload depot_first
             -_capacity, # unload depot_second
             -_capacity, # unload depot_third
             -_capacity, # unload depot_fourth
             -_capacity, # unload depot_fifth
             4, 4, # 1, 2   changed from original
             4, 4, # 3, 4   changed from original
             4, 4, # 5, 6   changed from original
             4, 4, # 7, 8   changed from original
             4, 4, # 9,10   changed from original
             4, 4, # 11,12   changed from original
             4, 4, # 13, 14   changed from original
             4, 4] # 15, 16   changed from original
      data['time_per_demand_unit'] = 5  # 5 minutes/unit
      data['time_windows'] = \
            [(0, 0), # depot
             (0, 1500), # unload depot_first. changed from original
             (0, 1500), # unload depot_second. changed from original
             (0, 1500), # unload depot_third. changed from original
             (0, 1500), # unload depot_fourth. changed from original
             (0, 1500), # unload depot_fifth. changed from original
             (0, 750), (0, 750), # 1, 2   changed from original
             (0, 750), (0, 750), # 3, 4   changed from original
             (0, 750), (0, 750), # 5, 6   changed from original
             (0, 750), (0, 750), # 7, 8   changed from original
             (0, 750), (0, 750), # 9, 10   changed from original
             (750, 1500), (750, 1500), # 11, 12   changed from original
             (750, 1500), (750, 1500), # 13, 14   changed from original
             (750, 1500), (750, 1500)] # 15, 16   changed from original
      #added p&amp;d list.##############################
      data['pickups_deliveries'] = [
          [6, 1], [7, 1],
          [8, 1], [9, 1],
          [10, 2], [11, 2],
          [12, 2], [13, 3],
          [14, 3], [15, 3],
          [16, 4], [17, 4],
          [18, 4], [19, 5],
          [20, 5], [21, 5]        
      ]
      ##############################################
      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):
      &quot;&quot;&quot;Computes the Manhattan distance between two points&quot;&quot;&quot;
      return (abs(position_1[0] - position_2[0]) +
              abs(position_1[1] - position_2[1]))
  
  
  def create_distance_evaluator(data):
      &quot;&quot;&quot;Creates callback to return distance between points.&quot;&quot;&quot;
      _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):
          &quot;&quot;&quot;Returns the manhattan distance between the two nodes&quot;&quot;&quot;
          return _distances[manager.IndexToNode(from_node)][manager.IndexToNode(
              to_node)]
  
      return distance_evaluator
  
  
  def add_distance_dimension(routing, manager, data, distance_evaluator_index):
      &quot;&quot;&quot;Add Global Span constraint&quot;&quot;&quot;
      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)
  
      # Define Transportation Requests. #######################################
      for request in data['pickups_deliveries']:
          pickup_index = manager.NodeToIndex(request[0])
          delivery_index = manager.NodeToIndex(request[1])
          routing.AddPickupAndDelivery(pickup_index, delivery_index)
          routing.solver().Add(
              routing.VehicleVar(pickup_index) == routing.VehicleVar(
                  delivery_index))
          routing.solver().Add(
              distance_dimension.CumulVar(pickup_index) &lt;=
              distance_dimension.CumulVar(delivery_index))
      ##########################################################################
  
  def create_demand_evaluator(data):
      &quot;&quot;&quot;Creates callback to get demands at each location.&quot;&quot;&quot;
      _demands = data['demands']
  
      def demand_evaluator(manager, from_node):
          &quot;&quot;&quot;Returns the demand of the current node&quot;&quot;&quot;
          return _demands[manager.IndexToNode(from_node)]
  
      return demand_evaluator
  
  
  def add_capacity_constraints(routing, manager, data, demand_evaluator_index):
      &quot;&quot;&quot;Adds capacity constraint&quot;&quot;&quot;
      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 in [1, 2, 3, 4, 5]:
          node_index = manager.NodeToIndex(node)
          routing.AddDisjunction([node_index], 0)
  
      # Allow to drop regular node with a cost.
      for node in range(6, len(data['demands'])):
          node_index = manager.NodeToIndex(node)
          capacity_dimension.SlackVar(node_index).SetValue(0)
          routing.AddDisjunction([node_index], 100_000)
  
  
  def create_time_evaluator(data):
      &quot;&quot;&quot;Creates callback to get total times between locations.&quot;&quot;&quot;
  
      def service_time(data, node):
          &quot;&quot;&quot;Gets the service time for the specified location.&quot;&quot;&quot;
          return abs(data['demands'][node]) * data['time_per_demand_unit']
  
      def travel_time(data, from_node, to_node):
          &quot;&quot;&quot;Gets the travel times between two locations.&quot;&quot;&quot;
          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):
          &quot;&quot;&quot;Returns the total time between the two nodes&quot;&quot;&quot;
          return _total_time[manager.IndexToNode(from_node)][manager.IndexToNode(
              to_node)]
  
      return time_evaluator
  
  
  def add_time_window_constraints(routing, manager, data, time_evaluator):
      &quot;&quot;&quot;Add Time windows constraint&quot;&quot;&quot;
      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
      &quot;&quot;&quot;Prints assignment on console&quot;&quot;&quot;
      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 order in range(6, routing.nodes()):
          index = manager.NodeToIndex(order)
          if assignment.Value(routing.NextVar(index)) == index:
              dropped.append(order)
      print(f'dropped orders: {dropped}')
      for reload in range(1, 6):
          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}) -&gt;'.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))
  
  
  ########
  # Main #
  ########
  def main():
      &quot;&quot;&quot;Entry point of the program&quot;&quot;&quot;
      # Instantiate the data problem.
      data = create_data_model()
  
      # Create the routing index manager
      manager = pywrapcp.RoutingIndexManager(data['num_locations'],
                                             data['num_vehicles'], data['depot'])
  
      # 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 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(&quot;No solution found !&quot;)
  
  
  if __name__ == '__main__':
      main()
  </code></pre>