Example: Load demands and limits

AI-generated Key Takeaways

• loadDemands specify the load a shipment requires, while loadLimits specify the maximum load a vehicle can handle.

• Both loadDemands and loadLimits are defined using types, which can represent weight, volume, or other custom categories.

• Shipments are assigned to vehicles based on their load demands and the vehicles' load limits, ensuring efficient capacity utilization.

• The OptimizeToursResponse provides details on vehicle loads at different points in the route, reflecting load transfers during pickups and deliveries.

• In addition to hard limits, soft load limits can be used to model preferences or costs associated with exceeding a preferred load threshold.

This example shows how to use loadDemands and loadLimits to manage vehicle capacity constraints in a Route Optimization API request.

For a complete conceptual overview, see the Load demands and limits key concepts document.

Example request

The following example demonstrates a scenario where a single vehicle with a load limit must deliver three shipments of different weights.

This example request contains the following load-related parameters:

• shipments[0] with a load demand amount of 50 weightKg.
• shipments[1] with a load demand amount of 10 weightKg.
• shipments[2] with a load demand amount of 80 weightKg.
• vehicles[0] with a load limit maxLoad of 100 weightKg.

See an example request with load demands and limits

{
  "populatePolylines": false,
  "populateTransitionPolylines": false,
  "model": {
    "globalStartTime": "2023-01-13T16:00:00Z",
    "globalEndTime": "2023-01-14T16:00:00Z",
    "shipments": [
      {
        "deliveries": [
          {
            "arrivalLocation": {
              "latitude": 37.789456,
              "longitude": -122.390192
            },
            "duration": "250s"
          }
        ],
        "pickups": [
          {
            "arrivalLocation": {
              "latitude": 37.794465,
              "longitude": -122.394839
            },
            "duration": "150s"
          }
        ],
        "penaltyCost": 100.0,
        "loadDemands": {
          "weightKg": {
            "amount": "50"
          }
        }
      },
      {
        "deliveries": [
          {
            "arrivalLocation": {
              "latitude": 37.789116,
              "longitude": -122.395080
            },
            "duration": "250s"
          }
        ],
        "pickups": [
          {
            "arrivalLocation": {
              "latitude": 37.794465,
              "longitude": -122.394839
            },
            "duration": "150s"
          }
        ],
        "penaltyCost": 15.0,
        "loadDemands": {
          "weightKg": {
            "amount": "10"
          }
        }
      },
      {
        "deliveries": [
          {
            "arrivalLocation": {
              "latitude": 37.795242,
              "longitude": -122.399347
            },
            "duration": "250s"
          }
        ],
        "pickups": [
          {
            "arrivalLocation": {
              "latitude": 37.794465,
              "longitude": -122.394839
            },
            "duration": "150s"
          }
        ],
        "penaltyCost": 50.0,
        "loadDemands": {
          "weightKg": {
            "amount": "80"
          }
        }
      }
    ],
    "vehicles": [
      {
        "endLocation": {
          "latitude": 37.794465,
          "longitude": -122.394839
        },
        "startLocation": {
          "latitude": 37.794465,
          "longitude": -122.394839
        },
        "costPerHour": 40.0,
        "costPerKilometer": 10.0,
        "loadLimits": {
          "weightKg": {
            "maxLoad": "100"
          }
        }
      }
    ]
  }
}
    

Example response

The response shows the optimized route for the vehicle. Because the total load of all shipments exceeds the vehicle's capacity, the optimizer creates a sequence of pickups and deliveries to ensure the loadLimits are not violated.

See a response to the request with load demands and limits

{
  "routes": [
    {
      "vehicleStartTime": "2023-01-13T16:00:00Z",
      "vehicleEndTime": "2023-01-13T16:43:27Z",
      "visits": [
        {
          "isPickup": true,
          "startTime": "2023-01-13T16:00:00Z",
          "detour": "0s",
          "loadDemands": {
            "weightKg": {
              "amount": "50"
            }
          }
        },
        {
          "shipmentIndex": 1,
          "isPickup": true,
          "startTime": "2023-01-13T16:02:30Z",
          "detour": "150s",
          "loadDemands": {
            "weightKg": {
              "amount": "10"
            }
          }
        },
        {
          "startTime": "2023-01-13T16:08:55Z",
          "detour": "150s",
          "loadDemands": {
            "weightKg": {
              "amount": "-50"
            }
          }
        },
        {
          "shipmentIndex": 1,
          "startTime": "2023-01-13T16:16:37Z",
          "detour": "343s",
          "loadDemands": {
            "weightKg": {
              "amount": "-10"
            }
          }
        },
        {
          "shipmentIndex": 2,
          "isPickup": true,
          "startTime": "2023-01-13T16:27:07Z",
          "detour": "1627s",
          "loadDemands": {
            "weightKg": {
              "amount": "80"
            }
          }
        },
        {
          "shipmentIndex": 2,
          "startTime": "2023-01-13T16:36:26Z",
          "detour": "0s",
          "loadDemands": {
            "weightKg": {
              "amount": "-80"
            }
          }
        }
      ],
      "transitions": [
        {
          "travelDuration": "0s",
          "waitDuration": "0s",
          "totalDuration": "0s",
          "startTime": "2023-01-13T16:00:00Z",
          "vehicleLoads": {
            "weightKg": {}
          }
        },
        {
          "travelDuration": "0s",
          "waitDuration": "0s",
          "totalDuration": "0s",
          "startTime": "2023-01-13T16:02:30Z",
          "vehicleLoads": {
            "weightKg": {
              "amount": "50"
            }
          }
        },
        {
          "travelDuration": "235s",
          "travelDistanceMeters": 795,
          "waitDuration": "0s",
          "totalDuration": "235s",
          "startTime": "2023-01-13T16:05:00Z",
          "vehicleLoads": {
            "weightKg": {
              "amount": "60"
            }
          }
        },
        {
          "travelDuration": "212s",
          "travelDistanceMeters": 791,
          "waitDuration": "0s",
          "totalDuration": "212s",
          "startTime": "2023-01-13T16:13:05Z",
          "vehicleLoads": {
            "weightKg": {
              "amount": "10"
            }
          }
        },
        {
          "travelDuration": "380s",
          "travelDistanceMeters": 1190,
          "waitDuration": "0s",
          "totalDuration": "380s",
          "startTime": "2023-01-13T16:20:47Z",
          "vehicleLoads": {
            "weightKg": {}
          }
        },
        {
          "travelDuration": "409s",
          "travelDistanceMeters": 1371,
          "waitDuration": "0s",
          "totalDuration": "409s",
          "startTime": "2023-01-13T16:29:37Z",
          "vehicleLoads": {
            "weightKg": {
              "amount": "80"
            }
          }
        },
        {
          "travelDuration": "171s",
          "travelDistanceMeters": 665,
          "waitDuration": "0s",
          "totalDuration": "171s",
          "startTime": "2023-01-13T16:40:36Z",
          "vehicleLoads": {
            "weightKg": {}
          }
        }
      ],
      "metrics": {
        "performedShipmentCount": 3,
        "travelDuration": "1407s",
        "waitDuration": "0s",
        "delayDuration": "0s",
        "breakDuration": "0s",
        "visitDuration": "1200s",
        "totalDuration": "2607s",
        "travelDistanceMeters": 4812,
        "maxLoads": {
          "weightKg": {
            "amount": "80"
          }
        }
      },
      "routeCosts": {
        "model.vehicles.cost_per_kilometer": 48.12,
        "model.vehicles.cost_per_hour": 28.966666666666665
      },
      "routeTotalCost": 77.086666666666659
    }
  ],
  "metrics": {
    "aggregatedRouteMetrics": {
      "performedShipmentCount": 3,
      "travelDuration": "1407s",
      "waitDuration": "0s",
      "delayDuration": "0s",
      "breakDuration": "0s",
      "visitDuration": "1200s",
      "totalDuration": "2607s",
      "travelDistanceMeters": 4812,
      "maxLoads": {
        "weightKg": {
          "amount": "80"
        }
      }
    },
    "usedVehicleCount": 1,
    "earliestVehicleStartTime": "2023-01-13T16:00:00Z",
    "latestVehicleEndTime": "2023-01-13T16:43:27Z",
    "totalCost": 77.086666666666659,
    "costs": {
      "model.vehicles.cost_per_hour": 28.966666666666665,
      "model.vehicles.cost_per_kilometer": 48.12
    }
  }
}
    

Because the combined loadDemands of the three shipments (50 + 10 + 80 = 140) exceeds the vehicle's loadLimits (100), the vehicle can't pick up all shipments at once. The optimizer only considers routes where shipment[0] and shipment[2] are not in the vehicle at the same time, since these shipments are the ones that exceed the vehicle's load limit with their combined weights.

The route has the following visits to not exceed the vehicle's load limit:

1. shipment[0] is picked up
2. shipment[1] is picked up
3. shipment[0] is delivered
4. shipment[1] is delivered
5. shipment[2] is picked up
6. shipment[2] is delivered

The vehicle's load changes throughout the route, which you can observe in the transitions array. For example, transitions[2] shows the vehicle carrying a load of 60 weightKg after picking up the first two shipments (50 + 10).

The maxLoads property in metrics shows that the maximum load carried at any point in the route was 80 weightKg, confirming that the solution successfully stayed within the vehicle's 100 weightKg limit.

Soft load limits

The following example shows how to use a soft load limit to optimize a route with multiple vehicles. The solution splits the shipments between the two vehicles to avoid the cost penalty for exceeding the vehicle's soft load limit.

Example request

This request now includes three delivery-only shipments and two vehicles with the same loadLimits and softMaxLoad.

Note: softMaxLoad can only be used on routes where vehicle's load changes in one direction only. This means the route must contain either all pickups where the load increases, or all deliveries where the load decreases. This example uses only deliveries to meet this requirement.

The key parameters for this example are:

• The three shipments have a combined loadDemands of 140 weightKg (50
  • 60 + 30).
• There are two vehicles available with a softMaxLoad of "100" weightKg and a costPerUnitAboveSoftMax of 5.0.

See an example request with a soft load limit

{
  "populatePolylines": false,
  "populateTransitionPolylines": false,
  "model": {
    "globalStartTime": "2023-01-13T16:00:00Z",
    "globalEndTime": "2023-01-14T16:00:00Z",
    "shipments": [
      {
        "deliveries": [
          {
            "arrivalLocation": {
              "latitude": 37.789456,
              "longitude": -122.390192
            },
            "duration": "250s"
          }
        ],
        
        "loadDemands": {
          "weightKg": {
            "amount": "50"
          }
        }
        
      },
      {
        "deliveries": [
          {
            "arrivalLocation": {
              "latitude": 37.789116,
              "longitude": -122.395080
            },
            "duration": "250s"
          }
        ],
        
        "loadDemands": {
          "weightKg": {
            "amount": "60"
          }
        }
        
      },
      {
        "deliveries": [
          {
            "arrivalLocation": {
              "latitude": 37.795242,
              "longitude": -122.399347
            },
            "duration": "250s"
          }
        ],
        
        "loadDemands": {
          "weightKg": {
            "amount": "30"
          }
        }
        
      }
    ],
    "vehicles": [
      {
        "endLocation": {
          "latitude": 37.794465,
          "longitude": -122.394839
        },
        "startLocation": {
          "latitude": 37.794465,
          "longitude": -122.394839
        },
        "costPerHour": 40.0,
        "costPerKilometer": 10.0,
        
        "loadLimits": {
          "weightKg": {
            "maxLoad": "150",
            "softMaxLoad": "100",
            "costPerUnitAboveSoftMax": 5.0
          }
        }
        
      },
      {
        "endLocation": {
          "latitude": 37.794465,
          "longitude": -122.394839
        },
        "startLocation": {
          "latitude": 37.794465,
          "longitude": -122.394839
        },
        "costPerHour": 40.0,
        "costPerKilometer": 10.0,
        
        "loadLimits": {
          "weightKg": {
            "maxLoad": "150",
            "softMaxLoad": "100",
            "costPerUnitAboveSoftMax": 5.0
          }
        }
        
      }
    ]
  }
}
    

Example response

The response now contains two routes, one for each vehicle. The optimizer determines that using both vehicles is more cost-effective than using one vehicle and incurring the soft limit penalty.

See a response to the request with a soft load limit

{
  "routes": [
    {
      "vehicleStartTime": "2023-01-13T16:00:00Z",
      "vehicleEndTime": "2023-01-13T16:13:31Z",
      "visits": [
        {
          "startTime": "2023-01-13T16:03:53Z",
          "detour": "0s",
          "loadDemands": {
            "weightKg": {
              "amount": "-50"
            }
          }
        }
      ],
      "transitions": [
        {
          "travelDuration": "233s",
          "travelDistanceMeters": 794,
          "waitDuration": "0s",
          "totalDuration": "233s",
          "startTime": "2023-01-13T16:00:00Z",
          "vehicleLoads": {
            "weightKg": {
              "amount": "50"
            }
          }
        },
        {
          "travelDuration": "328s",
          "travelDistanceMeters": 1188,
          "waitDuration": "0s",
          "totalDuration": "328s",
          "startTime": "2023-01-13T16:08:03Z",
          "vehicleLoads": {
            "weightKg": {}
          }
        }
      ],
      "metrics": {
        "performedShipmentCount": 1,
        "travelDuration": "561s",
        "visitDuration": "250s",
        "totalDuration": "811s",
        "travelDistanceMeters": 1982,
        "maxLoads": {
          "weightKg": {
            "amount": "50"
          }
        }
      },
      "routeCosts": {
        "model.vehicles.cost_per_kilometer": 19.82,
        "model.vehicles.cost_per_hour": 9.01
      },
      "routeTotalCost": 28.83
    },
    {
      "vehicleIndex": 1,
      "vehicleStartTime": "2023-01-13T16:00:00Z",
      "vehicleEndTime": "2023-01-13T16:21:43Z",
      "visits": [
        {
          "shipmentIndex": 1,
          "startTime": "2023-01-13T16:05:54Z",
          "detour": "0s",
          "loadDemands": {
            "weightKg": {
              "amount": "-60"
            }
          }
        },
        {
          "shipmentIndex": 2,
          "startTime": "2023-01-13T16:13:52Z",
          "detour": "473s",
          "loadDemands": {
            "weightKg": {
              "amount": "-30"
            }
          }
        }
      ],
      "transitions": [
        {
          "travelDuration": "354s",
          "travelDistanceMeters": 1196,
          "waitDuration": "0s",
          "totalDuration": "354s",
          "startTime": "2023-01-13T16:00:00Z",
          "vehicleLoads": {
            "weightKg": {
              "amount": "90"
            }
          }
        },
        {
          "travelDuration": "228s",
          "travelDistanceMeters": 808,
          "waitDuration": "0s",
          "totalDuration": "228s",
          "startTime": "2023-01-13T16:10:04Z",
          "vehicleLoads": {
            "weightKg": {
              "amount": "30"
            }
          }
        },
        {
          "travelDuration": "221s",
          "travelDistanceMeters": 655,
          "waitDuration": "0s",
          "totalDuration": "221s",
          "startTime": "2023-01-13T16:18:02Z",
          "vehicleLoads": {
            "weightKg": {}
          }
        }
      ],
      "metrics": {
        "performedShipmentCount": 2,
        "travelDuration": "803s",
        "visitDuration": "500s",
        "totalDuration": "1303s",
        "travelDistanceMeters": 2659,
        "maxLoads": {
          "weightKg": {
            "amount": "90"
          }
        }
      },
      "routeCosts": {
        "model.vehicles.cost_per_kilometer": 26.59,
        "model.vehicles.cost_per_hour": 14.48
      },
      "routeTotalCost": 41.07
    }
  ],
  "metrics": {
    "aggregatedRouteMetrics": {
      "performedShipmentCount": 3,
      "travelDuration": "1364s",
      "visitDuration": "750s",
      "totalDuration": "2114s",
      "travelDistanceMeters": 4641,
      "maxLoads": {
        "weightKg": {
          "amount": "90"
        }
      }
    },
    "usedVehicleCount": 2,
    "earliestVehicleStartTime": "2023-01-13T16:00:00Z",
    "latestVehicleEndTime": "2023-01-13T16:21:43Z",
    "totalCost": 69.90,
    "costs": {
      "model.vehicles.cost_per_kilometer": 46.41,
      "model.vehicles.cost_per_hour": 23.49
    }
  }
}
    

The following fields show how the optimizer split the shipments across the two vehicles to keep the loads under its 100 weightKg soft limit.

• The first route (vehicleIndex: 0) handles the 50 weightKg shipment. Its maxLoads is "50", which is below the soft limit.
• The second route (vehicleIndex: 1) handles the 60 and 30 weightKg shipments. Its maxLoads is "90", which is also below the soft limit.
• Because neither vehicle violates its soft limit, the routeCosts for both routes show no costPerUnitAboveSoftMax penalty.