Last-mile delivery¶
An appliance delivery company based in Tilburg delivers washing machines, dryers, and other household appliances across North Brabant. When delivering a new appliance, the driver often picks up the customer's old one as well.
This example shows how to model a real-world delivery scenario that combines several FastVRP features:
- Load with deliveries and pickups: new appliances are delivered and old ones are picked up in the same visit.
- Time windows: customers select a morning, afternoon, or all-day delivery window.
- Vehicle restrictions: some deliveries require a two-person crew for carrying appliances upstairs.
- Cost optimisation: a two-person crew cost twice as much per hour, so the solver minimises their use.
Scenario¶
The company operates from a single depot in Tilburg and serves 20 customers across eight cities.
Load is measured in number of appliances. Most deliveries are a single appliance, and about half of the customers also have an old appliance to pick up. Three deliveries require a two-person crew to carry appliances upstairs in buildings without lifts. Each vehicle has a capacity of 10 appliances, so the solver must plan routes that never exceed this limit at any point along the way.
Time windows depend on the customer's preference:
| Window | Hours |
|---|---|
| All day | 08:00 - 17:00 |
| Morning | 08:00 - 12:00 |
| Afternoon | 13:00 - 17:00 |
Service duration of a standard delivery is 15 minutes. If the customer also has an old appliance to return, the service takes 30 minutes.
Vehicle types reflect crew size:
| Type | Crew | Fixed cost | Per hour | Per km | Capacity |
|---|---|---|---|---|---|
one-person-crew |
1 person | 175 | 25 | 0.25 | 10 |
two-person-crew |
2 persons | 175 | 50 | 0.25 | 10 |
The three crew-restricted tasks can only be served by two-person-crew using the allowed_vehicle_types restriction.
All other tasks can be served by either vehicle type, so the solver prefers the cheaper one-person crew vehicles when possible.
Both vehicle types work a 9-hour shift from 08:00 to 17:00.
An unlimited number of vehicles is available.
The complete routing request looks as follows:
request.json
{
"locations": [
{"id": "loc-depot-Tilburg", "latitude": 51.6023, "longitude": 5.0045},
{"id": "loc-Breda-1", "latitude": 51.5875, "longitude": 4.7895},
{"id": "loc-Breda-2", "latitude": 51.5987, "longitude": 4.7578},
{"id": "loc-Breda-3", "latitude": 51.6037, "longitude": 4.8000},
{"id": "loc-Breda-4", "latitude": 51.6126, "longitude": 4.7864},
{"id": "loc-Oosterhout-1", "latitude": 51.6338, "longitude": 4.8652},
{"id": "loc-Oosterhout-2", "latitude": 51.5852, "longitude": 4.9223},
{"id": "loc-Etten-Leur", "latitude": 51.5851, "longitude": 4.6560},
{"id": "loc-Zevenbergen", "latitude": 51.6411, "longitude": 4.5994},
{"id": "loc-Roosendaal", "latitude": 51.5452, "longitude": 4.4850},
{"id": "loc-Tilburg-1", "latitude": 51.5825, "longitude": 5.0929},
{"id": "loc-Tilburg-2", "latitude": 51.5455, "longitude": 5.0765},
{"id": "loc-Tilburg-3", "latitude": 51.5517, "longitude": 5.0543},
{"id": "loc-Tilburg-4", "latitude": 51.5745, "longitude": 5.0585},
{"id": "loc-Eindhoven-1", "latitude": 51.4716, "longitude": 5.4468},
{"id": "loc-Eindhoven-2", "latitude": 51.4464, "longitude": 5.4084},
{"id": "loc-Eindhoven-3", "latitude": 51.4321, "longitude": 5.3869},
{"id": "loc-Eindhoven-4", "latitude": 51.4751, "longitude": 5.4654},
{"id": "loc-Eindhoven-5", "latitude": 51.4449, "longitude": 5.5121},
{"id": "loc-Eindhoven-6", "latitude": 51.4746, "longitude": 5.4987},
{"id": "loc-Oisterwijk", "latitude": 51.5737, "longitude": 5.1901}
],
"tasks": [
{
"id": "task-Breda-1",
"location": "loc-Breda-1",
"delivery": [1],
"service_duration": "PT900S",
"time_windows": [
{"start": "2025-01-01T13:00:00", "end": "2025-01-01T17:00:00"}
]
},
{
"id": "task-Breda-2",
"location": "loc-Breda-2",
"delivery": [1],
"pickup": [1],
"service_duration": "PT1800S",
"time_windows": [
{"start": "2025-01-01T08:00:00", "end": "2025-01-01T17:00:00"}
],
"allowed_vehicle_types": ["two-person-crew"]
},
{
"id": "task-Breda-3",
"location": "loc-Breda-3",
"delivery": [1],
"pickup": [1],
"service_duration": "PT1800S",
"time_windows": [
{"start": "2025-01-01T08:00:00", "end": "2025-01-01T12:00:00"}
]
},
{
"id": "task-Breda-4",
"location": "loc-Breda-4",
"delivery": [1],
"service_duration": "PT900S",
"time_windows": [
{"start": "2025-01-01T13:00:00", "end": "2025-01-01T17:00:00"}
]
},
{
"id": "task-Oosterhout-1",
"location": "loc-Oosterhout-1",
"delivery": [1],
"pickup": [1],
"service_duration": "PT1800S",
"time_windows": [
{"start": "2025-01-01T08:00:00", "end": "2025-01-01T12:00:00"}
]
},
{
"id": "task-Oosterhout-2",
"location": "loc-Oosterhout-2",
"delivery": [1],
"service_duration": "PT900S",
"time_windows": [
{"start": "2025-01-01T08:00:00", "end": "2025-01-01T17:00:00"}
]
},
{
"id": "task-Etten-Leur",
"location": "loc-Etten-Leur",
"delivery": [1],
"pickup": [1],
"service_duration": "PT1800S",
"time_windows": [
{"start": "2025-01-01T08:00:00", "end": "2025-01-01T12:00:00"}
]
},
{
"id": "task-Zevenbergen",
"location": "loc-Zevenbergen",
"delivery": [1],
"service_duration": "PT900S",
"time_windows": [
{"start": "2025-01-01T08:00:00", "end": "2025-01-01T17:00:00"}
]
},
{
"id": "task-Roosendaal",
"location": "loc-Roosendaal",
"delivery": [1],
"pickup": [1],
"service_duration": "PT1800S",
"time_windows": [
{"start": "2025-01-01T08:00:00", "end": "2025-01-01T17:00:00"}
]
},
{
"id": "task-Tilburg-1",
"location": "loc-Tilburg-1",
"delivery": [1],
"service_duration": "PT900S",
"time_windows": [
{"start": "2025-01-01T13:00:00", "end": "2025-01-01T17:00:00"}
]
},
{
"id": "task-Tilburg-2",
"location": "loc-Tilburg-2",
"delivery": [1],
"pickup": [1],
"service_duration": "PT1800S",
"time_windows": [
{"start": "2025-01-01T13:00:00", "end": "2025-01-01T17:00:00"}
]
},
{
"id": "task-Tilburg-3",
"location": "loc-Tilburg-3",
"delivery": [1],
"service_duration": "PT900S",
"time_windows": [
{"start": "2025-01-01T13:00:00", "end": "2025-01-01T17:00:00"}
]
},
{
"id": "task-Tilburg-4",
"location": "loc-Tilburg-4",
"delivery": [1],
"pickup": [1],
"service_duration": "PT1800S",
"time_windows": [
{"start": "2025-01-01T08:00:00", "end": "2025-01-01T17:00:00"}
]
},
{
"id": "task-Eindhoven-1",
"location": "loc-Eindhoven-1",
"delivery": [1],
"pickup": [1],
"service_duration": "PT1800S",
"time_windows": [
{"start": "2025-01-01T08:00:00", "end": "2025-01-01T17:00:00"}
],
"allowed_vehicle_types": ["two-person-crew"]
},
{
"id": "task-Eindhoven-2",
"location": "loc-Eindhoven-2",
"delivery": [1],
"pickup": [1],
"service_duration": "PT1800S",
"time_windows": [
{"start": "2025-01-01T08:00:00", "end": "2025-01-01T17:00:00"}
],
"allowed_vehicle_types": ["two-person-crew"]
},
{
"id": "task-Eindhoven-3",
"location": "loc-Eindhoven-3",
"delivery": [1],
"service_duration": "PT900S",
"time_windows": [
{"start": "2025-01-01T08:00:00", "end": "2025-01-01T17:00:00"}
]
},
{
"id": "task-Eindhoven-4",
"location": "loc-Eindhoven-4",
"delivery": [1],
"pickup": [1],
"service_duration": "PT1800S",
"time_windows": [
{"start": "2025-01-01T08:00:00", "end": "2025-01-01T12:00:00"}
]
},
{
"id": "task-Eindhoven-5",
"location": "loc-Eindhoven-5",
"delivery": [1],
"service_duration": "PT900S",
"time_windows": [
{"start": "2025-01-01T08:00:00", "end": "2025-01-01T17:00:00"}
]
},
{
"id": "task-Eindhoven-6",
"location": "loc-Eindhoven-6",
"delivery": [1],
"pickup": [1],
"service_duration": "PT1800S",
"time_windows": [
{"start": "2025-01-01T08:00:00", "end": "2025-01-01T17:00:00"}
]
},
{
"id": "task-Oisterwijk",
"location": "loc-Oisterwijk",
"delivery": [1],
"service_duration": "PT900S",
"time_windows": [
{"start": "2025-01-01T13:00:00", "end": "2025-01-01T17:00:00"}
]
}
],
"depots": [
{
"id": "depot-Tilburg",
"location": "loc-depot-Tilburg",
"time_window": {
"start": "2025-01-01T07:30:00",
"end": "2025-01-01T17:30:00"
}
}
],
"vehicle_types": [
{
"id": "one-person-crew",
"start_depot": "depot-Tilburg",
"end_depot": "depot-Tilburg",
"num_available": 10,
"capacity": [10],
"shift": {
"earliest_start": "2025-01-01T08:00:00",
"latest_end": "2025-01-01T17:00:00",
"duration": "PT32400S"
},
"costs": {
"fixed": "175.00",
"per_hour": "25.00",
"per_km": "0.25"
}
},
{
"id": "two-person-crew",
"start_depot": "depot-Tilburg",
"end_depot": "depot-Tilburg",
"num_available": 10,
"capacity": [10],
"shift": {
"earliest_start": "2025-01-01T08:00:00",
"latest_end": "2025-01-01T17:00:00",
"duration": "PT32400S"
},
"costs": {
"fixed": "175.00",
"per_hour": "50.00",
"per_km": "0.25"
}
}
],
"options": {
"stop": {
"type": "max_runtime",
"seconds": 5
}
}
}
Solution¶
solution.json
{
"summary": {
"total_cost": "923.57",
"distance_cost": "72.66",
"duration_cost": "500.91",
"fixed_vehicle_cost": "350.00",
"distance": 290662,
"duration": "PT48160S",
"travel_duration": "PT20260S",
"service_duration": "PT27900S",
"wait_duration": "P0D",
"num_planned": 20,
"num_unplanned": 0,
"num_routes": 2,
"load_duration": "P0D",
"overtime": "P0D"
},
"routes": [
{
"summary": {
"total_cost": "376.41",
"distance_cost": "33.42",
"duration_cost": "167.99",
"fixed_vehicle_cost": "175.00",
"distance": 133688,
"duration": "PT24190S",
"travel_duration": "PT9790S",
"service_duration": "PT14400S",
"wait_duration": "P0D",
"start_time": "2025-01-01T08:58:51",
"end_time": "2025-01-01T15:42:01",
"num_tasks": 10,
"num_activities": 12,
"slack_duration": "PT4335S",
"load_duration": "P0D",
"overtime": "P0D"
},
"vehicle_type_id": "one-person-crew",
"profile": "car",
"activities": [
{
"id": "depot-Tilburg",
"location": {
"id": "loc-depot-Tilburg",
"latitude": 51.6023,
"longitude": 5.0045
},
"type": "depot",
"start_time": "2025-01-01T08:58:51",
"end_time": "2025-01-01T08:58:51",
"duration": "P0D",
"wait_duration": "P0D",
"travel_duration": "P0D",
"distance": 0
},
{
"id": "task-Oosterhout-1",
"location": {
"id": "loc-Oosterhout-1",
"latitude": 51.6338,
"longitude": 4.8652
},
"type": "task",
"start_time": "2025-01-01T09:17:10",
"end_time": "2025-01-01T09:47:10",
"duration": "PT1800S",
"wait_duration": "P0D",
"travel_duration": "PT1099S",
"distance": 13893
},
{
"id": "task-Breda-3",
"location": {
"id": "loc-Breda-3",
"latitude": 51.6037,
"longitude": 4.8
},
"type": "task",
"start_time": "2025-01-01T10:00:13",
"end_time": "2025-01-01T10:30:13",
"duration": "PT1800S",
"wait_duration": "P0D",
"travel_duration": "PT783S",
"distance": 10343
},
{
"id": "task-Etten-Leur",
"location": {
"id": "loc-Etten-Leur",
"latitude": 51.5851,
"longitude": 4.656
},
"type": "task",
"start_time": "2025-01-01T10:47:45",
"end_time": "2025-01-01T11:17:45",
"duration": "PT1800S",
"wait_duration": "P0D",
"travel_duration": "PT1052S",
"distance": 11545
},
{
"id": "task-Roosendaal",
"location": {
"id": "loc-Roosendaal",
"latitude": 51.5452,
"longitude": 4.485
},
"type": "task",
"start_time": "2025-01-01T11:33:45",
"end_time": "2025-01-01T12:03:45",
"duration": "PT1800S",
"wait_duration": "P0D",
"travel_duration": "PT960S",
"distance": 16089
},
{
"id": "task-Zevenbergen",
"location": {
"id": "loc-Zevenbergen",
"latitude": 51.6411,
"longitude": 4.5994
},
"type": "task",
"start_time": "2025-01-01T12:22:11",
"end_time": "2025-01-01T12:37:11",
"duration": "PT900S",
"wait_duration": "P0D",
"travel_duration": "PT1106S",
"distance": 18694
},
{
"id": "task-Breda-4",
"location": {
"id": "loc-Breda-4",
"latitude": 51.6126,
"longitude": 4.7864
},
"type": "task",
"start_time": "2025-01-01T13:00:00",
"end_time": "2025-01-01T13:15:00",
"duration": "PT900S",
"wait_duration": "P0D",
"travel_duration": "PT1369S",
"distance": 19836
},
{
"id": "task-Breda-1",
"location": {
"id": "loc-Breda-1",
"latitude": 51.5875,
"longitude": 4.7895
},
"type": "task",
"start_time": "2025-01-01T13:23:44",
"end_time": "2025-01-01T13:38:44",
"duration": "PT900S",
"wait_duration": "P0D",
"travel_duration": "PT524S",
"distance": 4143
},
{
"id": "task-Tilburg-2",
"location": {
"id": "loc-Tilburg-2",
"latitude": 51.5455,
"longitude": 5.0765
},
"type": "task",
"start_time": "2025-01-01T14:05:26",
"end_time": "2025-01-01T14:35:26",
"duration": "PT1800S",
"wait_duration": "P0D",
"travel_duration": "PT1602S",
"distance": 26844
},
{
"id": "task-Tilburg-3",
"location": {
"id": "loc-Tilburg-3",
"latitude": 51.5517,
"longitude": 5.0543
},
"type": "task",
"start_time": "2025-01-01T14:40:16",
"end_time": "2025-01-01T14:55:16",
"duration": "PT900S",
"wait_duration": "P0D",
"travel_duration": "PT290S",
"distance": 2941
},
{
"id": "task-Tilburg-4",
"location": {
"id": "loc-Tilburg-4",
"latitude": 51.5745,
"longitude": 5.0585
},
"type": "task",
"start_time": "2025-01-01T15:01:54",
"end_time": "2025-01-01T15:31:54",
"duration": "PT1800S",
"wait_duration": "P0D",
"travel_duration": "PT398S",
"distance": 3179
},
{
"id": "depot-Tilburg",
"location": {
"id": "loc-depot-Tilburg",
"latitude": 51.6023,
"longitude": 5.0045
},
"type": "depot",
"start_time": "2025-01-01T15:42:01",
"end_time": "2025-01-01T15:42:01",
"duration": "P0D",
"wait_duration": "P0D",
"travel_duration": "PT607S",
"distance": 6181
}
],
"polyline": 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},
{
"summary": {
"total_cost": "547.16",
"distance_cost": "39.24",
"duration_cost": "332.92",
"fixed_vehicle_cost": "175.00",
"distance": 156974,
"duration": "PT23970S",
"travel_duration": "PT10470S",
"service_duration": "PT13500S",
"wait_duration": "P0D",
"start_time": "2025-01-01T08:00:00",
"end_time": "2025-01-01T14:39:30",
"num_tasks": 10,
"num_activities": 12,
"slack_duration": "PT4907S",
"load_duration": "P0D",
"overtime": "P0D"
},
"vehicle_type_id": "two-person-crew",
"profile": "car",
"activities": [
{
"id": "depot-Tilburg",
"location": {
"id": "loc-depot-Tilburg",
"latitude": 51.6023,
"longitude": 5.0045
},
"type": "depot",
"start_time": "2025-01-01T08:00:00",
"end_time": "2025-01-01T08:00:00",
"duration": "P0D",
"wait_duration": "P0D",
"travel_duration": "P0D",
"distance": 0
},
{
"id": "task-Oosterhout-2",
"location": {
"id": "loc-Oosterhout-2",
"latitude": 51.5852,
"longitude": 4.9223
},
"type": "task",
"start_time": "2025-01-01T08:12:11",
"end_time": "2025-01-01T08:27:11",
"duration": "PT900S",
"wait_duration": "P0D",
"travel_duration": "PT731S",
"distance": 10966
},
{
"id": "task-Breda-2",
"location": {
"id": "loc-Breda-2",
"latitude": 51.5987,
"longitude": 4.7578
},
"type": "task",
"start_time": "2025-01-01T08:44:10",
"end_time": "2025-01-01T09:14:10",
"duration": "PT1800S",
"wait_duration": "P0D",
"travel_duration": "PT1019S",
"distance": 13650
},
{
"id": "task-Eindhoven-1",
"location": {
"id": "loc-Eindhoven-1",
"latitude": 51.4716,
"longitude": 5.4468
},
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}
],
"unplanned": [],
"job_id": "77639186-16d0-48ea-a918-ed788c1b6b79",
"technical": {
"runtime": 5,
"iterations": 100000
}
}
The solution consists of two routes with a total cost of 923.57 and all 20 tasks planned:
- First route (one-person crew, 10 tasks, cost 376.41) starts in Oosterhout and Breda for the morning deliveries, then heads west to Etten-Leur, Roosendaal, and Zevenbergen. Afterwards, the route goes back east through Breda to finish with afternoon deliveries in Tilburg.
- Second route (two-person crew, 10 tasks, cost 547.16) handles the three restricted tasks plus the remaining customers. It starts with Oosterhout and Breda, then drives to Eindhoven for six deliveries before finishing with afternoon activities in Oisterwijk and Tilburg.
Conclusion¶
This example combines several FastVRP features to model a realistic appliance delivery operation. The key modelling decisions and the tutorials that explain them in further detail:
-
Vehicle restrictions for tasks. The
allowed_vehicle_typesfield on the three restricted tasks ensures only two-person crew vehicles serve them. Without this restriction, the solver would assign all tasks to the cheaper one-person crew vehicles. See the Vehicle restrictions tutorial. -
Cost-driven fleet assignment. Because two-person crew vehicles cost twice as much per hour, the solver assigns them only to the tasks that require them and fills the remaining routes with cheaper one-person crew vehicles. The result is a mixed fleet that balances capability with cost. See the Cost optimisation tutorial.
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Time windows shape the route order. Morning customers are visited first, afternoon customers later, and all-day customers fill the gaps. This avoids unnecessary waiting time and ensures no customer is visited outside their preferred window. See the Time windows tutorial.