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VRP with Breaks
Very often, there are situations when drivers have breaks in their shifts. The most trivial case is a lunch break for example. Those breaks should be considered when planning a tour with the time windows specified for the jobs. Note that in fact, a break can happen anywhere within the break time window. The duration and times properties are required for the breaks. In case a break is defined for a vehicle, the duration of the break is added to the shiftTime. In the example below we have three cars with fixed shifts and breaks and 6 jobs to execute with the specific time windows.
Problem
{
"fleet": {
"types": [
{
"id": "6290a20b08a7",
"profile": "car_1",
"costs": {
"fixed": 10.0,
"distance": 0.001,
"time": 0.006
},
"shifts": [
{
"start": {
"time": "2021-08-27T08:03:00Z",
"location": {
"lat": 52.530971,
"lng": 13.384915
}
},
"end": {
"time": "2021-08-27T16:03:00Z",
"location": {
"lat": 52.530971,
"lng": 13.384915
}
},
"breaks": [
{
"duration": 1800,
"times": [
[
"2021-08-27T12:03:00Z",
"2021-08-27T13:03:00Z"
]
]
}
]
}
],
"capacity": [
7
],
"limits": {
"maxDistance": 300000
},
"amount": 1
},
{
"id": "973bccabf941",
"profile": "car_1",
"costs": {
"fixed": 12.0,
"distance": 0.004,
"time": 0.005
},
"shifts": [
{
"start": {
"time": "2021-08-27T08:03:00Z",
"location": {
"lat": 52.530971,
"lng": 13.384915
}
},
"end": {
"time": "2021-08-27T16:03:00Z",
"location": {
"lat": 52.530971,
"lng": 13.384915
}
},
"breaks": [
{
"duration": 1800,
"times": [
[
"2021-08-27T11:03:00Z",
"2021-08-27T13:03:00Z"
]
]
}
]
}
],
"capacity": [
3
],
"limits": {
"maxDistance": 300000
},
"amount": 1
},
{
"id": "92d3cd5cca04",
"profile": "car_1",
"costs": {
"fixed": 10.0,
"distance": 0.004,
"time": 0.009
},
"shifts": [
{
"start": {
"time": "2021-08-27T08:03:00Z",
"location": {
"lat": 52.530971,
"lng": 13.384915
}
},
"end": {
"time": "2021-08-27T17:03:00Z",
"location": {
"lat": 52.530971,
"lng": 13.384915
}
},
"breaks": [
{
"duration": 1800,
"times": [
[
"2021-08-27T12:03:00Z",
"2021-08-27T13:03:00Z"
]
]
}
]
}
],
"capacity": [
2
],
"limits": {
"maxDistance": 300000
},
"amount": 1
}
],
"profiles": [
{
"type": "car",
"name": "car_1"
}
]
},
"plan": {
"jobs": [
{
"id": "job_1",
"tasks": {
"deliveries": [
{
"places": [
{
"times": [
[
"2021-08-27T09:03:00Z",
"2021-08-27T10:03:00Z"
]
],
"location": {
"lat": 52.59175589353722,
"lng": 13.350747750372257
},
"duration": 360
}
],
"demand": [
1
]
}
]
}
},
{
"id": "job_2",
"tasks": {
"deliveries": [
{
"places": [
{
"times": [
[
"2021-08-27T14:03:00Z",
"2021-08-27T16:03:00Z"
]
],
"location": {
"lat": 52.43363386232821,
"lng": 13.403232562191313
},
"duration": 540
}
],
"demand": [
1
]
}
]
}
},
{
"id": "job_3",
"tasks": {
"deliveries": [
{
"places": [
{
"times": [
[
"2021-08-27T10:03:00Z",
"2021-08-27T16:03:00Z"
]
],
"location": {
"lat": 52.473321658918245,
"lng": 13.28972099097991
},
"duration": 660
}
],
"demand": [
1
]
}
]
}
},
{
"id": "job_4",
"tasks": {
"deliveries": [
{
"places": [
{
"times": [
[
"2021-08-27T06:03:00Z",
"2021-08-27T17:03:00Z"
]
],
"location": {
"lat": 52.54165532725351,
"lng": 13.365047170290309
},
"duration": 1140
}
],
"demand": [
1
]
}
]
}
},
{
"id": "job_5",
"tasks": {
"deliveries": [
{
"places": [
{
"times": [
[
"2021-08-27T06:03:00Z",
"2021-08-27T17:03:00Z"
]
],
"location": {
"lat": 52.569368,
"lng": 13.314579
},
"duration": 1140
}
],
"demand": [
1
]
}
]
}
},
{
"id": "job_6",
"tasks": {
"deliveries": [
{
"places": [
{
"times": [
[
"2021-08-27T06:03:00Z",
"2021-08-27T17:03:00Z"
]
],
"location": {
"lat": 52.593857,
"lng": 13.338440
},
"duration": 1140
}
],
"demand": [
1
]
}
]
}
}
]
}
}
Solution
The solution for such a problem will look as follows:
{
"statistic": {
"cost": 180.973,
"distance": 63465,
"duration": 17918,
"times": {
"driving": 6897,
"serving": 4980,
"waiting": 4241,
"break": 1800
}
},
"tours": [
{
"vehicleId": "6290a20b08a7_1",
"typeId": "6290a20b08a7",
"stops": [
{
"location": {
"lat": 52.530971,
"lng": 13.384915
},
"time": {
"arrival": "2021-08-27T08:03:00Z",
"departure": "2021-08-27T09:43:41Z"
},
"load": [
6
],
"activities": [
{
"jobId": "departure",
"type": "departure"
}
]
},
{
"location": {
"lat": 52.59175589353722,
"lng": 13.350747750372255
},
"time": {
"arrival": "2021-08-27T10:03:00Z",
"departure": "2021-08-27T10:09:00Z"
},
"load": [
5
],
"activities": [
{
"jobId": "job_1",
"type": "delivery"
}
]
},
{
"location": {
"lat": 52.593857,
"lng": 13.33844
},
"time": {
"arrival": "2021-08-27T10:13:08Z",
"departure": "2021-08-27T10:32:08Z"
},
"load": [
4
],
"activities": [
{
"jobId": "job_6",
"type": "delivery"
}
]
},
{
"location": {
"lat": 52.569368,
"lng": 13.314579
},
"time": {
"arrival": "2021-08-27T10:40:26Z",
"departure": "2021-08-27T10:59:26Z"
},
"load": [
3
],
"activities": [
{
"jobId": "job_5",
"type": "delivery"
}
]
},
{
"location": {
"lat": 52.54165532725351,
"lng": 13.365047170290309
},
"time": {
"arrival": "2021-08-27T11:10:41Z",
"departure": "2021-08-27T12:33:00Z"
},
"load": [
2
],
"activities": [
{
"jobId": "job_4",
"type": "delivery",
"location": {
"lat": 52.54165532725351,
"lng": 13.365047170290309
},
"time": {
"start": "2021-08-27T11:10:41Z",
"end": "2021-08-27T11:29:41Z"
}
},
{
"jobId": "break",
"type": "break",
"location": {
"lat": 52.54165532725351,
"lng": 13.365047170290309
},
"time": {
"start": "2021-08-27T11:29:41Z",
"end": "2021-08-27T12:33:00Z"
}
}
]
},
{
"location": {
"lat": 52.473321658918245,
"lng": 13.28972099097991
},
"time": {
"arrival": "2021-08-27T12:54:53Z",
"departure": "2021-08-27T13:05:53Z"
},
"load": [
1
],
"activities": [
{
"jobId": "job_3",
"type": "delivery"
}
]
},
{
"location": {
"lat": 52.43363386232821,
"lng": 13.403232562191311
},
"time": {
"arrival": "2021-08-27T13:25:38Z",
"departure": "2021-08-27T14:12:00Z"
},
"load": [
0
],
"activities": [
{
"jobId": "job_2",
"type": "delivery"
}
]
},
{
"location": {
"lat": 52.530971,
"lng": 13.384915
},
"time": {
"arrival": "2021-08-27T14:42:19Z",
"departure": "2021-08-27T14:42:19Z"
},
"load": [
0
],
"activities": [
{
"jobId": "arrival",
"type": "arrival"
}
]
}
],
"statistic": {
"cost": 180.973,
"distance": 63465,
"duration": 17918,
"times": {
"driving": 6897,
"serving": 4980,
"waiting": 4241,
"break": 1800
}
}
}
]
}
Evaluate the Solution
From this solution we can see all the routine statistics for the tour like the total cost, distance, duration, and times including time for driving, serving, waiting, and time for the breaks. The shift breaks of the vehicles were considered and the tour was planned regarding those constraints.
Please note that currently breaks functionality is implemented as soft constraints, therefore in some cases, breaks can be skipped by the algorithm in favour of additional jobs (e.g. when inserting the break would lead to a significant increase in the amount of unassigned jobs).
