OptimizeToursRequest applies constraints across the following:
- Shipments, affecting how shipments are performed
- Vehicles, affecting how vehicle routes are computed
- Globally, affecting both vehicles and shipments.
This guide focuses on an essential shipment constraint: time windows.
Time windows are a type of constraint that you supply in the
OptimizeToursRequest message (REST, gRPC) in order to specify
time-based limits to shipment activities. This type of constraint influences
both when and how a shipment can be performed as well as the vehicle assignment
for the shipment. With these constraints, the optimizer gives preference to
those vehicles that can best satisfy the time constraints of the shipment.
Shipment constraints: time windows
You specify when a pickup or delivery can occur in the Shipment.VisitRequest
message as follows:
- Use the
timeWindowsproperty in the message (REST, gRPC) - Specify the start and ending time in the
TimeWindowmessage (REST, gRPC).
Example request with time window constraints
The example here illustrates three different shipments, each with their own
delivery window. For simplicity, this example sets time windows on deliveries
only, but time windows can also be applied to pickups. Multiple time windows can
be specified, though this example only uses one per delivery VisitRequest.
See an example request with time windows
{
"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",
"timeWindows": [
{
"startTime": "2023-01-13T18:00:00Z",
"endTime": "2023-01-13T19:00:00Z"
}
]
}
],
"pickups": [
{
"arrivalLocation": {
"latitude": 37.794465,
"longitude": -122.394839
},
"duration": "150s"
}
],
"penaltyCost": 100.0
},
{
"deliveries": [
{
"arrivalLocation": {
"latitude": 37.789116,
"longitude": -122.395080
},
"duration": "250s",
"timeWindows": [
{
"startTime": "2023-01-13T18:00:00Z",
"endTime": "2023-01-13T18:30:00Z"
}
]
}
],
"pickups": [
{
"arrivalLocation": {
"latitude": 37.794465,
"longitude": -122.394839
},
"duration": "150s"
}
],
"penaltyCost": 20.0
},
{
"deliveries": [
{
"arrivalLocation": {
"latitude": 37.795242,
"longitude": -122.399347
},
"duration": "250s",
"timeWindows": [
{
"startTime": "2023-01-13T17:30:00Z",
"endTime": "2023-01-13T18:00:00Z"
}
]
}
],
"pickups": [
{
"arrivalLocation": {
"latitude": 37.794465,
"longitude": -122.394839
},
"duration": "150s"
}
],
"penaltyCost": 50.0
}
],
"vehicles": [
{
"endLocation": {
"latitude": 37.794465,
"longitude": -122.394839
},
"startLocation": {
"latitude": 37.794465,
"longitude": -122.394839
},
"costPerHour": 40.0,
"costPerKilometer": 10.0
}
]
}
}
Example response with time window constraints
In the example response, the vehicle's start and end time are 17:35:50 and
18:17:24 respectively. These times reflect the optimizer minimizing the time
required to operate the vehicle specified in the request as costPerHour while
satisfying all time window constraints. Using 17:35:50 as a start time
eliminates the need for the vehicle to wait at a visit location until the
visit's time window starts. This appears in the response as zero waitDuration
values.
See a response to the example request with time windows
{
"routes": [
{
"vehicleStartTime": "2023-01-13T17:35:50Z",
"vehicleEndTime": "2023-01-13T18:17:24Z",
"visits": [
{
"isPickup": true,
"startTime": "2023-01-13T17:35:50Z",
"detour": "0s"
},
{
"shipmentIndex": 1,
"isPickup": true,
"startTime": "2023-01-13T17:38:20Z",
"detour": "150s"
},
{
"shipmentIndex": 2,
"isPickup": true,
"startTime": "2023-01-13T17:40:50Z",
"detour": "300s"
},
{
"shipmentIndex": 2,
"startTime": "2023-01-13T17:50:09Z",
"detour": "0s"
},
{
"shipmentIndex": 1,
"startTime": "2023-01-13T18:00:00Z",
"detour": "796s"
},
{
"startTime": "2023-01-13T18:07:35Z",
"detour": "1520s"
}
],
"transitions": [
{
"travelDuration": "0s",
"waitDuration": "0s",
"totalDuration": "0s",
"startTime": "2023-01-13T17:35:50Z"
},
{
"travelDuration": "0s",
"waitDuration": "0s",
"totalDuration": "0s",
"startTime": "2023-01-13T17:38:20Z"
},
{
"travelDuration": "0s",
"waitDuration": "0s",
"totalDuration": "0s",
"startTime": "2023-01-13T17:40:50Z"
},
{
"travelDuration": "409s",
"travelDistanceMeters": 1371,
"waitDuration": "0s",
"totalDuration": "409s",
"startTime": "2023-01-13T17:43:20Z"
},
{
"travelDuration": "341s",
"travelDistanceMeters": 1312,
"waitDuration": "0s",
"totalDuration": "341s",
"startTime": "2023-01-13T17:54:19Z"
},
{
"travelDuration": "205s",
"travelDistanceMeters": 636,
"waitDuration": "0s",
"totalDuration": "205s",
"startTime": "2023-01-13T18:04:10Z"
},
{
"travelDuration": "339s",
"travelDistanceMeters": 1276,
"waitDuration": "0s",
"totalDuration": "339s",
"startTime": "2023-01-13T18:11:45Z"
}
],
"metrics": {
"performedShipmentCount": 3,
"travelDuration": "1294s",
"waitDuration": "0s",
"delayDuration": "0s",
"breakDuration": "0s",
"visitDuration": "1200s",
"totalDuration": "2494s",
"travelDistanceMeters": 4595
},
"routeCosts": {
"model.vehicles.cost_per_hour": 27.711111111111112,
"model.vehicles.cost_per_kilometer": 45.95
},
"routeTotalCost": 73.661111111111111
}
],
"metrics": {
"aggregatedRouteMetrics": {
"performedShipmentCount": 3,
"travelDuration": "1294s",
"waitDuration": "0s",
"delayDuration": "0s",
"breakDuration": "0s",
"visitDuration": "1200s",
"totalDuration": "2494s",
"travelDistanceMeters": 4595
},
"usedVehicleCount": 1,
"earliestVehicleStartTime": "2023-01-13T17:35:50Z",
"latestVehicleEndTime": "2023-01-13T18:17:24Z",
"totalCost": 73.661111111111111,
"costs": {
"model.vehicles.cost_per_hour": 27.711111111111112,
"model.vehicles.cost_per_kilometer": 45.95
}
}
}
Time windows have ordered the vehicle's visits so that the shipments with the
earliest time windows are delivered first.
shipments[2]is delivered at 17:50shipments[1]is delivered at 18:00shipments[0]is delivered at 18:07
The example request specifies hard time window constraints, requiring
deliveries to be completed within those windows. If completing a shipment's
VisitRequests within any of its time windows is not feasible or
cost-effective, the optimizer skips the shipment. If the shipment has a
penaltyCost, the optimizer adds it to the costs reported in response
metrics. Otherwise, the skippedMandatoryShipmentCount property of the
OptimizeToursResponse message (REST, gRPC) increases.
If you change the time windows by shifting shipment[1]'s window several hours
later (to 21:00 from 18:00), the results will be different as illustrated in the
following examples.
See an example request with time windows that cannot be satisfied
{
"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",
"timeWindows": [
{
"startTime": "2023-01-13T18:00:00Z",
"endTime": "2023-01-13T19:00:00Z"
}
]
}
],
"pickups": [
{
"arrivalLocation": {
"latitude": 37.794465,
"longitude": -122.394839
},
"duration": "150s"
}
],
"penaltyCost": 100.0
},
{
"deliveries": [
{
"arrivalLocation": {
"latitude": 37.789116,
"longitude": -122.395080
},
"duration": "250s",
"timeWindows": [
{
"startTime": "2023-01-13T21:00:00Z",
"endTime": "2023-01-13T21:30:00Z"
}
]
}
],
"pickups": [
{
"arrivalLocation": {
"latitude": 37.794465,
"longitude": -122.394839
},
"duration": "150s"
}
],
"penaltyCost": 20.0
},
{
"deliveries": [
{
"arrivalLocation": {
"latitude": 37.795242,
"longitude": -122.399347
},
"duration": "250s",
"timeWindows": [
{
"startTime": "2023-01-13T17:30:00Z",
"endTime": "2023-01-13T18:00:00Z"
}
]
}
],
"pickups": [
{
"arrivalLocation": {
"latitude": 37.794465,
"longitude": -122.394839
},
"duration": "150s"
}
],
"penaltyCost": 50.0
}
],
"vehicles": [
{
"endLocation": {
"latitude": 37.794465,
"longitude": -122.394839
},
"startLocation": {
"latitude": 37.794465,
"longitude": -122.394839
},
"costPerHour": 40.0,
"costPerKilometer": 10.0
}
]
}
}
See a response to the second example request with time windows, where a shipment is skipped
{
"routes": [
{
"vehicleStartTime": "2023-01-13T17:37:49Z",
"vehicleEndTime": "2023-01-13T18:09:49Z",
"visits": [
{
"isPickup": true,
"startTime": "2023-01-13T17:37:49Z",
"detour": "0s"
},
{
"shipmentIndex": 2,
"isPickup": true,
"startTime": "2023-01-13T17:40:19Z",
"detour": "150s"
},
{
"shipmentIndex": 2,
"startTime": "2023-01-13T17:49:38Z",
"detour": "0s"
},
{
"startTime": "2023-01-13T18:00:00Z",
"detour": "946s"
}
],
"transitions": [
{
"travelDuration": "0s",
"waitDuration": "0s",
"totalDuration": "0s",
"startTime": "2023-01-13T17:37:49Z"
},
{
"travelDuration": "0s",
"waitDuration": "0s",
"totalDuration": "0s",
"startTime": "2023-01-13T17:40:19Z"
},
{
"travelDuration": "409s",
"travelDistanceMeters": 1371,
"waitDuration": "0s",
"totalDuration": "409s",
"startTime": "2023-01-13T17:42:49Z"
},
{
"travelDuration": "372s",
"travelDistanceMeters": 1348,
"waitDuration": "0s",
"totalDuration": "372s",
"startTime": "2023-01-13T17:53:48Z"
},
{
"travelDuration": "339s",
"travelDistanceMeters": 1276,
"waitDuration": "0s",
"totalDuration": "339s",
"startTime": "2023-01-13T18:04:10Z"
}
],
"metrics": {
"performedShipmentCount": 2,
"travelDuration": "1120s",
"waitDuration": "0s",
"delayDuration": "0s",
"breakDuration": "0s",
"visitDuration": "800s",
"totalDuration": "1920s",
"travelDistanceMeters": 3995
},
"routeCosts": {
"model.vehicles.cost_per_kilometer": 39.95,
"model.vehicles.cost_per_hour": 21.333333333333332
},
"routeTotalCost": 61.283333333333331
}
],
"skippedShipments": [
{
"index": 1
}
],
"metrics": {
"aggregatedRouteMetrics": {
"performedShipmentCount": 2,
"travelDuration": "1120s",
"waitDuration": "0s",
"delayDuration": "0s",
"breakDuration": "0s",
"visitDuration": "800s",
"totalDuration": "1920s",
"travelDistanceMeters": 3995
},
"usedVehicleCount": 1,
"earliestVehicleStartTime": "2023-01-13T17:37:49Z",
"latestVehicleEndTime": "2023-01-13T18:09:49Z",
"totalCost": 81.283333333333331,
"costs": {
"model.shipments.penalty_cost": 20,
"model.vehicles.cost_per_hour": 21.333333333333332,
"model.vehicles.cost_per_kilometer": 39.95
}
}
}
In this example, the later time window has caused shipment[1] to be skipped,
because the extra vehicle operating time required to complete the shipment's
delivery within its specified time window exceeded the shipment's penalty cost.
The penalty cost for shipment[1] appears in metrics.costs, and its index
appears in skippedShipments.
Soft time window constraints
As mentioned briefly in Cost Model Parameters, time windows can be applied as soft constraints. Soft constraints differ from hard constraints as follows:
- Hard constraints: Cannot be violated, and the optimizer does not offer a solution that violates the constraint, even if that means skipping a shipment.
- Soft constraints: May be violated, which means that the optimizer may provide a solution that violates a soft constraint. However, the optimizer also applies a cost to any violation. You supply this cost as an additional property in the time window, typically as a cost per hour for each hour before or after the time window in which the activity occurs.
Time windows are softened by using softStartTime or softEndTime instead of
startTime or endTime respectively, and by setting
costPerHourBeforeSoftStartTime or costPerHourAfterSoftEndTime.
Use soft time window constraints when pickups or deliveries should occur within a specified time window, but pickup or delivery within that window is not absolutely required. You can use hard and soft time window constraints together to express business objectives. For example:
- Hard time window: Indicates a customer's hours of business, such as from 9AM to 5PM.
- Soft time window: Indicates the timeframe for delivery or pickup that matches the notification sent to the customer, such as 9AM to 1PM.
In this example, the shipment that was previously skipped because its time window started too late has its start time constraint softened. The other shipments have had their time windows' end times softened as well.
See an example request with hard and soft time windows
{
"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",
"timeWindows": [
{
"startTime": "2023-01-13T18:00:00Z",
"softEndTime": "2023-01-13T19:00:00Z",
"costPerHourAfterSoftEndTime": 2.0
}
]
}
],
"pickups": [
{
"arrivalLocation": {
"latitude": 37.794465,
"longitude": -122.394839
},
"duration": "150s"
}
],
"penaltyCost": 100.0
},
{
"deliveries": [
{
"arrivalLocation": {
"latitude": 37.789116,
"longitude": -122.395080
},
"duration": "250s",
"timeWindows": [
{
"softStartTime": "2023-01-13T21:00:00Z",
"endTime": "2023-01-13T21:30:00Z",
"costPerHourBeforeSoftStartTime": 2.0
}
]
}
],
"pickups": [
{
"arrivalLocation": {
"latitude": 37.794465,
"longitude": -122.394839
},
"duration": "150s"
}
],
"penaltyCost": 20.0
},
{
"deliveries": [
{
"arrivalLocation": {
"latitude": 37.795242,
"longitude": -122.399347
},
"duration": "250s",
"timeWindows": [
{
"startTime": "2023-01-13T17:30:00Z",
"softEndTime": "2023-01-13T18:00:00Z",
"costPerHourAfterSoftEndTime": 2.0
}
]
}
],
"pickups": [
{
"arrivalLocation": {
"latitude": 37.794465,
"longitude": -122.394839
},
"duration": "150s"
}
],
"penaltyCost": 50.0
}
],
"vehicles": [
{
"endLocation": {
"latitude": 37.794465,
"longitude": -122.394839
},
"startLocation": {
"latitude": 37.794465,
"longitude": -122.394839
},
"costPerHour": 40.0,
"costPerKilometer": 10.0
}
]
}
}
See a response to the example request with hard and soft time windows
{
"routes": [
{
"vehicleStartTime": "2023-01-13T17:48:35Z",
"vehicleEndTime": "2023-01-13T18:24:28Z",
"visits": [
{
"isPickup": true,
"startTime": "2023-01-13T17:48:35Z",
"detour": "0s"
},
{
"shipmentIndex": 1,
"isPickup": true,
"startTime": "2023-01-13T17:51:05Z",
"detour": "150s"
},
{
"shipmentIndex": 2,
"isPickup": true,
"startTime": "2023-01-13T17:53:35Z",
"detour": "300s"
},
{
"startTime": "2023-01-13T18:00:00Z",
"detour": "300s"
},
{
"shipmentIndex": 1,
"startTime": "2023-01-13T18:07:42Z",
"detour": "493s"
},
{
"shipmentIndex": 2,
"startTime": "2023-01-13T18:17:27Z",
"detour": "873s"
}
],
"transitions": [
{
"travelDuration": "0s",
"waitDuration": "0s",
"totalDuration": "0s",
"startTime": "2023-01-13T17:48:35Z"
},
{
"travelDuration": "0s",
"waitDuration": "0s",
"totalDuration": "0s",
"startTime": "2023-01-13T17:51:05Z"
},
{
"travelDuration": "0s",
"waitDuration": "0s",
"totalDuration": "0s",
"startTime": "2023-01-13T17:53:35Z"
},
{
"travelDuration": "235s",
"travelDistanceMeters": 795,
"waitDuration": "0s",
"totalDuration": "235s",
"startTime": "2023-01-13T17:56:05Z"
},
{
"travelDuration": "212s",
"travelDistanceMeters": 791,
"waitDuration": "0s",
"totalDuration": "212s",
"startTime": "2023-01-13T18:04:10Z"
},
{
"travelDuration": "335s",
"travelDistanceMeters": 1204,
"waitDuration": "0s",
"totalDuration": "335s",
"startTime": "2023-01-13T18:11:52Z"
},
{
"travelDuration": "171s",
"travelDistanceMeters": 665,
"waitDuration": "0s",
"totalDuration": "171s",
"startTime": "2023-01-13T18:21:37Z"
}
],
"metrics": {
"performedShipmentCount": 3,
"travelDuration": "953s",
"waitDuration": "0s",
"delayDuration": "0s",
"breakDuration": "0s",
"visitDuration": "1200s",
"totalDuration": "2153s",
"travelDistanceMeters": 3455
},
"routeCosts": {
"model.shipments.deliveries.time_windows.cost_per_hour_after_soft_end_time": 0.58166666666666667,
"model.shipments.deliveries.time_windows.cost_per_hour_before_soft_start_time": 5.7433333333333332,
"model.vehicles.cost_per_hour": 23.922222222222221,
"model.vehicles.cost_per_kilometer": 34.55
},
"routeTotalCost": 64.797222222222217
}
],
"metrics": {
"aggregatedRouteMetrics": {
"performedShipmentCount": 3,
"travelDuration": "953s",
"waitDuration": "0s",
"delayDuration": "0s",
"breakDuration": "0s",
"visitDuration": "1200s",
"totalDuration": "2153s",
"travelDistanceMeters": 3455
},
"usedVehicleCount": 1,
"earliestVehicleStartTime": "2023-01-13T17:48:35Z",
"latestVehicleEndTime": "2023-01-13T18:24:28Z",
"totalCost": 64.797222222222217,
"costs": {
"model.vehicles.cost_per_kilometer": 34.55,
"model.shipments.deliveries.time_windows.cost_per_hour_before_soft_start_time": 5.7433333333333332,
"model.shipments.deliveries.time_windows.cost_per_hour_after_soft_end_time": 0.58166666666666667,
"model.vehicles.cost_per_hour": 23.922222222222221
}
}
}
Where the example with only hard time window constraints completely skipped
shipment[1], softening its delivery time window causes it to be delivered
before its time window start time. Similarly, softening the end times of the
other shipments allowed shipment[2] to be delivered after its time window
ends.
At the same time, both costs and total shipments have changed:
totalCost: decreased from 81.283 to 64.797- total completed shipments: increased from 2 to 3
The optimizer has found a less expensive solution because the time window constraints were relaxed compared to the previous example.
Finally, the metrics.costs property also includes a new key to indicate the
actual cost incurred based on the product of the constraint and the length of
time that the delivery window was missed. That is:
costPerHourBeforeSoftStartTimeof 2.0 and- the time between the actual delivery and the start of the time window: 2.83583 hours
Result:
model.shipments.deliveries.time_windows.cost_per_hour_before_soft_start_time:
5.6716666666666669.
These metrics allow you to do cost analysis to see the tradeoff between hard
constraints and soft constraints, which you can use to tune your constraints to
better suit your particular business rules. In this case, the total cost is
less than shipment[1].penalty_cost of 20.0. The optimizer has identified
that it is more cost-effective to deliver the shipment early than it is to
skip the shipment.