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VRP with Multi-Jobs
A multi-job as opposed to a simple job is a job that consists of multiple pickups and deliveries. The specific of such jobs is that they only can be considered as executed when all the tasks inside the job are done, otherwise, none of them will be executed. Also, the sum of demands for pickups and deliveries must be equal. A very common scenario for a multi-job problem could be executing multiple pickups at different locations followed by delivery to a single location.
We can imagine the multi-job VRP in real life as for example a daily routine of a school bus that has to pick up several children at different addresses and deliver them to school. As we can guess, taking the kids back to their homes from the school by the same school bus is a multi-job VRP as well.
Another example of multi-job VRP use in real life is the work of garbage collection companies when a vehicle has to execute several pickups and one delivery within the job (collect garbage from several locations in the city and deliver it to the dump location).
So let’s consider we have a multi-job with several pickups and one delivery in it. Let’s say we need to deliver 3 children to the local school from their specific address via the school bus. Regarding the vehicle, we need it to start and end the shift at one depo, that is at the same location. We specify the routine vehicle constraints like cost, distance, shift time, location, capacity and amount. Note that In the case of a school bus, for example, you may assume your capacity units as people/children.
{
"fleet": {
"types": [
{
"id": "b0130d2f754d",
"profile": "car_1",
"costs": {
"fixed": 5.0,
"distance": 0.007,
"time": 0.002
},
"shifts": [
{
"start": {
"time": "2021-08-27T08:03:00Z",
"location": {
"lat": 52.530971,
"lng": 13.384915
}
},
"end": {
"time": "2021-08-27T16:03:00Z",
"location": {
"lat": 52.48693181589403,
"lng": 13.308748991045801
}
}
}
],
"capacity": [
20
],
"amount": 1
}
],
"profiles": [
{
"type": "car",
"name": "car_1"
}
]
},
Regarding the jobs, in this very case, you can set them depending on your needs. One way is to add all of your pickups as separate jobs and then add a delivery job. The other way is to use a multi-job. In this way, you may add a multi-job with all the pickups and one delivery at the end. Let's build a problem where we would have one multi-job with 3 pickups and 1 delivery to deliver all those pickups in one location.
Problem
{
"fleet": {
"types": [
{
"id": "b0130d2f754d",
"profile": "car_1",
"costs": {
"fixed": 5.0,
"distance": 0.007,
"time": 0.002
},
"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
}
}
}
],
"capacity": [
30
],
"amount": 1
}
],
"profiles": [
{
"type": "car",
"name": "car_1"
}
]
},
"plan": {
"jobs": [
{
"id": "job_1",
"tasks": {
"pickups": [
{
"places": [
{
"location": {
"lat": 52.47706593757918,
"lng": 13.390815701172201
},
"duration": 660,
"tag": "Address_1"
}
],
"demand": [
1
]
},
{
"places": [
{
"location": {
"lat": 52.473571009931106,
"lng": 13.389035169086807
},
"duration": 1140,
"tag": "Address_2"
}
],
"demand": [
1
]
},
{
"places": [
{
"location": {
"lat": 52.53090538774364,
"lng": 13.384692097156309
},
"duration": 840,
"tag": "Address_3"
}
],
"demand": [
1
]
}
],
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.58919138279804,
"lng": 13.462161100698735
},
"duration": 1020,
"tag": "Address_4"
}
],
"demand": [
3
]
}
]
}
}
]
}
}
Solution
The solution for this problem will look as follows:
{
"statistic": {
"cost": 273.77500000000003,
"distance": 36041,
"duration": 8244,
"times": {
"driving": 4584,
"serving": 3660,
"waiting": 0,
"break": 0
}
},
"tours": [
{
"vehicleId": "b0130d2f754d_1",
"typeId": "b0130d2f754d",
"stops": [
{
"location": {
"lat": 52.530971,
"lng": 13.384915
},
"time": {
"arrival": "2021-08-27T08:03:00Z",
"departure": "2021-08-27T08:03:00Z"
},
"load": [
0
],
"activities": [
{
"jobId": "departure",
"type": "departure"
}
]
},
{
"location": {
"lat": 52.53090538774364,
"lng": 13.384692097156307
},
"time": {
"arrival": "2021-08-27T08:03:02Z",
"departure": "2021-08-27T08:17:02Z"
},
"load": [
1
],
"activities": [
{
"jobId": "job_1",
"type": "pickup",
"jobTag": "Address_3"
}
]
},
{
"location": {
"lat": 52.473571009931106,
"lng": 13.389035169086808
},
"time": {
"arrival": "2021-08-27T08:34:57Z",
"departure": "2021-08-27T08:53:57Z"
},
"load": [
2
],
"activities": [
{
"jobId": "job_1",
"type": "pickup",
"jobTag": "Address_2"
}
]
},
{
"location": {
"lat": 52.47706593757918,
"lng": 13.3908157011722
},
"time": {
"arrival": "2021-08-27T08:54:51Z",
"departure": "2021-08-27T09:05:51Z"
},
"load": [
3
],
"activities": [
{
"jobId": "job_1",
"type": "pickup",
"jobTag": "Address_1"
}
]
},
{
"location": {
"lat": 52.58919138279804,
"lng": 13.462161100698737
},
"time": {
"arrival": "2021-08-27T09:40:21Z",
"departure": "2021-08-27T09:57:21Z"
},
"load": [
0
],
"activities": [
{
"jobId": "job_1",
"type": "delivery",
"jobTag": "Address_4"
}
]
},
{
"location": {
"lat": 52.530971,
"lng": 13.384915
},
"time": {
"arrival": "2021-08-27T10:20:24Z",
"departure": "2021-08-27T10:20:24Z"
},
"load": [
0
],
"activities": [
{
"jobId": "arrival",
"type": "arrival"
}
]
}
],
"statistic": {
"cost": 273.77500000000003,
"distance": 36041,
"duration": 8244,
"times": {
"driving": 4584,
"serving": 3660,
"waiting": 0,
"break": 0
}
}
}
]
}
From this solution we can see that the vehicle starts its way from a depot, after that it executes 3 pickup and 1 delivery multi-job, and arrives back to the depot.
