Relations
Relations are used to specify the association between different tasks that should be performed in a certain order. NextBillion.ai’s Route Optimization V2 offers three types of relations that the users can enforce:
-
in_same_route: All the steps mentioned in this type of relation will be part of the same route. -
in_sequence: All the steps mentioned in this relation will follow the specified sequence but other steps might be inserted by the optimizer, if feasible. -
in_direct_sequence: All the steps mentioned in this relation will follow the specified sequence without any other steps being inserted between them by the solver.
However, a few points might be worthy to note here. Relations are a hard configuration, and the solution will not give precedence to tasks time_windows, soft constraint parameters etc. Also, when using relations the vehicle properties like capacity and skills should be matched to what the tasks on those relations need.
Relations is a good feature to take care of certain special cases of task fulfillment within overall optimization problems.
Get Started
Readers would need a valid NextBillion API key to try this example out. If you don’t have one, please contact us to get your API key now!
Setup
Once you have a valid API Key, you can start setting up the components to be used in this example. Let’s take a look at them below.
Jobs & Shipments
We start by defining 10 jobs and 3 shipments. Let’s define the properties of these tasks:
-
A unique identifier for each task
-
Location indexes for each task
-
Specify the schedule of tasks. This is done by adding time windows within which a task must be completed. We have added a 15 min time window for all tasks.
The actual time taken to complete the tasks once the driver/vehicle is at the task’s location i.e. the service time for each task.
Let’s take a look at the jobs JSON after the above properties are configured:
1{
2 "jobs": [
3 {
4 "id": 1,
5 "location_index": 0,
6 "service": 120,
7 "pickup": [0],
8 "time_windows": [[1693386000, 1693386900]]
9 },
10 {
11 "id": 2,
12 "location_index": 1,
13 "service": 180,
14 "pickup": [0],
15 "time_windows": [[1693387800, 1693388700]]
16 },
17 {
18 "id": 3,
19 "location_index": 2,
20 "service": 120,
21 "pickup": [0],
22 "time_windows": [[1693389600, 1693390500]]
23 },
24 {
25 "id": 4,
26 "location_index": 3,
27 "service": 120,
28 "pickup": [0],
29 "time_windows": [[1693391400, 1693392300]]
30 },
31 {
32 "id": 5,
33 "location_index": 4,
34 "service": 60,
35 "pickup": [0],
36 "time_windows": [[1693393200, 1693394100]]
37 },
38 {
39 "id": 6,
40 "location_index": 5,
41 "service": 120,
42 "pickup": [0],
43 "time_windows": [[1693396800, 1693397700]]
44 },
45 {
46 "id": 7,
47 "location_index": 6,
48 "service": 120,
49 "pickup": [0],
50 "time_windows": [[1693398600, 1693399500]]
51 },
52 {
53 "id": 8,
54 "location_index": 7,
55 "service": 150,
56 "pickup": [0],
57 "time_windows": [[1693401300, 1693402200]]
58 },
59 {
60 "id": 9,
61 "location_index": 8,
62 "service": 80,
63 "pickup": [0],
64 "time_windows": [[1693404000, 1693404900]]
65 },
66 {
67 "id": 10,
68 "location_index": 9,
69 "service": 120,
70 "pickup": [0],
71 "time_windows": [[1693405800, 1693406700]]
72 }
73 ],
74 "shipments": [
75 {
76 "pickup": {
77 "description": "Shipment Pickup 1",
78 "id": 1,
79 "location_index": 10,
80 "service": 120,
81 "time_windows": [[1693395000, 1693395900]]
82 },
83 "delivery": {
84 "description": "Shipment Delivery 1",
85 "id": 1,
86 "location_index": 11,
87 "service": 120,
88 "time_windows": [[1693397700, 1693398600]]
89 },
90 "amount": [2]
91 },
92 {
93 "pickup": {
94 "description": "Shipment Pickup 2",
95 "id": 2,
96 "location_index": 12,
97 "service": 120,
98 "time_windows": [[1693399500, 1693400400]]
99 },
100 "delivery": {
101 "description": "Shipment Delivery 2",
102 "id": 2,
103 "location_index": 13,
104 "service": 120,
105 "time_windows": [[1693402200, 1693403100]]
106 },
107 "amount": [2]
108 },
109 {
110 "pickup": {
111 "description": "Shipment Pickup 3",
112 "id": 3,
113 "location_index": 14,
114 "service": 120,
115 "time_windows": [[1693400400, 1693401300]]
116 },
117 "delivery": {
118 "description": "Shipment Delivery 3",
119 "id": 3,
120 "location_index": 15,
121 "service": 120,
122 "time_windows": [[1693407600, 1693408500]]
123 },
124 "amount": [2]
125 }
126 ]
127}Vehicles
Next, we add 4 vehicles that will be responsible for fulfilling the tasks within the defined constraints. To describe the vehicles and their properties we add:
-
A unique ID for each vehicle
-
Vehicle shift time or the time window
-
Capacity to denote the amount of load that the vehicle can take
-
Start_index to denote the point from where the vehicle would start.
-
Costs for all vehicles. We have specified
fixedcost for all vehicles andper_hourcost for two of the vehicles. -
max_travel_costto put a cap on the overall cost that a vehicle can incur. We are going with 5000 seconds as the maximum cost per vehicle. Please observe that the cost is in seconds as we are not explicitly mentioning anytravel_costsettings. As a result, the solver goes with the default setting ofdurationfor cost. -
max_tasksto limit the number of tasks that each vehicle can take. We set this constraint to 5 tasks for each vehicle. It needs to be highlighted here that a job represents 1 task whereas a shipment represents 2 tasks (1 each for the pickup and the delivery step).
Once the vehicle and their properties are defined, the resulting vehicles JSON is:
1{
2 "vehicles": [
3 {
4 "id": 1,
5 "start_index": 16,
6 "capacity": [20],
7 "costs": {
8 "fixed": 1000
9 },
10 "time_window": [1693382400, 1693418400]
11 },
12 {
13 "id": 2,
14 "start_index": 17,
15 "capacity": [20],
16 "costs": {
17 "fixed": 1000
18 },
19 "time_window": [1693382400, 1693418400]
20 },
21 {
22 "id": 3,
23 "start_index": 18,
24 "capacity": [20],
25 "costs": {
26 "fixed": 1000
27 },
28 "time_window": [1693382400, 1693418400]
29 },
30 {
31 "id": 4,
32 "capacity": [20],
33 "start_index": 19,
34 "costs": {
35 "fixed": 1000
36 },
37 "time_window": [1693382400, 1693418400]
38 }
39 ]
40}Locations
Next, we define the locations object and add all the locations used in the problem along with a valid id. The locations object with all the points used in this example:
1{
2 "locations": {
3 "id": 1,
4 "location": [
5 "34.083950,-118.318640",
6 "34.054927,-118.323726",
7 "34.075525,-118.361588",
8 "34.076350,-118.338519",
9 "34.090425,-118.338933",
10 "34.037925,-118.459842",
11 "34.004364,-118.421170",
12 "34.000215,-118.318803",
13 "33.945884,-118.325628",
14 "34.000895,-118.204929",
15 "34.076646,-118.376969",
16 "34.094986,-118.300885",
17 "34.018780,-118.317919",
18 "33.996658,-118.261708",
19 "33.916595,-118.240132",
20 "33.946275,-118.385486",
21 "34.057106,-118.361326",
22 "34.016137,-118.253523",
23 "33.940407,-118.265196",
24 "33.974060,-118.246945"
25 ]
26 }
27}Relations
And, lastly, we define the relations between the tasks of our choice. For this example, we will
-
Keep shipment 3, jobs 7,8,9 in same route
-
Keep shipment 2 and job 10, 5 in direct sequence
-
Keep jobs 6, 4, 1 in sequence
-
Jobs 2, 3 and shipment 1 are not part of any relations
The relations object once configured according to the above distribution results in :
1{
2 "relations": [
3 {
4 "type": "in_sequence",
5 "steps": [
6 {
7 "type": "start"
8 },
9 {
10 "type": "job",
11 "id": 6
12 },
13 {
14 "type": "job",
15 "id": 4
16 },
17 {
18 "type": "job",
19 "id": 1
20 },
21 {
22 "type": "end"
23 }
24 ],
25 "vehicle": 1
26 },
27 {
28 "type": "in_direct_sequence",
29 "steps": [
30 {
31 "type": "start"
32 },
33 {
34 "type": "pickup",
35 "id": 2
36 },
37 {
38 "type": "delivery",
39 "id": 2
40 },
41 {
42 "type": "job",
43 "id": 10
44 },
45 {
46 "type": "job",
47 "id": 5
48 },
49 {
50 "type": "end"
51 }
52 ]
53 },
54 {
55 "type": "in_same_route",
56 "steps": [
57 {
58 "type": "start"
59 },
60 {
61 "type": "pickup",
62 "id": 3
63 },
64 {
65 "type": "delivery",
66 "id": 3
67 },
68 {
69 "type": "job",
70 "id": 7
71 },
72 {
73 "type": "job",
74 "id": 8
75 },
76 {
77 "type": "job",
78 "id": 9
79 },
80 {
81 "type": "end"
82 }
83 ]
84 }
85 ]
86}
87Optimization POST Request
Bringing all these attributes together, let’s create the final POST request that we will submit to the optimizer.
1curl --location 'https://api.nextbillion.io/optimization/v2?key=<your_api_key>' \
2--header 'Content-Type: application/json' \
3--data '{
4 "description": "Relations Example",
5 "jobs": [
6 {
7 "id": 1,
8 "location_index":0,
9 "service": 120,
10 "pickup":[0],
11 "time_windows": [
12 [
13 1693386000,
14 1693386900
15 ]
16 ]
17 },
18 {
19 "id": 2,
20 "location_index": 1,
21 "service": 180,
22 "pickup":[0],
23 "time_windows": [
24 [
25 1693387800,
26 1693388700
27 ]
28 ]
29 },
30 {
31 "id": 3,
32 "location_index": 2,
33 "service": 120,
34 "pickup":[0],
35 "time_windows": [
36 [
37 1693389600,
38 1693390500
39 ]
40 ]
41 },
42 {
43 "id": 4,
44 "location_index": 3,
45 "service": 120,
46 "pickup":[0],
47 "time_windows": [
48 [
49 1693391400,
50 1693392300
51 ]
52 ]
53 },
54 {
55 "id": 5,
56 "location_index": 4,
57 "service": 60,
58 "pickup":[0],
59 "time_windows": [
60 [
61 1693393200,
62 1693394100
63 ]
64 ]
65 },
66 {
67 "id": 6,
68 "location_index": 5,
69 "service": 120,
70 "pickup":[0],
71 "time_windows": [
72 [
73 1693396800,
74 1693397700
75 ]
76 ]
77 },
78 {
79 "id": 7,
80 "location_index": 6,
81 "service": 120,
82 "pickup":[0],
83 "time_windows": [
84 [
85 1693398600,
86 1693399500
87 ]
88 ]
89 },
90 {
91 "id": 8,
92 "location_index": 7,
93 "service": 150,
94 "pickup":[0],
95 "time_windows": [
96 [
97 1693401300,
98 1693402200
99 ]
100 ]
101 },
102 {
103 "id": 9,
104 "location_index": 8,
105 "service": 80,
106 "pickup":[0],
107 "time_windows": [
108 [
109 1693404000,
110 1693404900
111 ]
112 ]
113 },
114 {
115 "id": 10,
116 "location_index": 9,
117 "service": 120,
118 "pickup":[0],
119 "time_windows": [
120 [
121 1693405800,
122 1693406700
123 ]
124 ]
125 }
126 ],
127 "shipments": [
128 {
129 "pickup":{
130 "description": "Shipment Pickup 1",
131 "id":1,
132 "location_index":10,
133 "service":120,
134 "time_windows":[[1693395000,1693395900]]
135 },
136 "delivery":{
137 "description": "Shipment Delivery 1",
138 "id":1,
139 "location_index":11,
140 "service":120,
141 "time_windows":[[1693397700,1693398600]]
142 },
143 "amount":[2]
144 },
145 {
146 "pickup":{
147 "description": "Shipment Pickup 2",
148 "id":2,
149 "location_index":12,
150 "service":120,
151 "time_windows":[[1693399500,1693400400]]
152 },
153 "delivery":{
154 "description": "Shipment Delivery 2",
155 "id":2,
156 "location_index":13,
157 "service":120,
158 "time_windows":[[1693402200,1693403100]]
159 },
160 "amount":[2]
161 },
162 {
163 "pickup":{
164 "description": "Shipment Pickup 3",
165 "id":3,
166 "location_index":14,
167 "service":120,
168 "time_windows":[[1693400400,1693401300]]
169 },
170 "delivery":{
171 "description": "Shipment Delivery 3",
172 "id":3,
173 "location_index":15,
174 "service":120,
175 "time_windows":[[1693407600,1693408500]]
176 },
177 "amount":[2]
178 }
179 ],
180 "vehicles": [
181 {
182 "id": 1,
183 "start_index": 16,
184 "capacity":[20],
185 "costs":{
186 "fixed":1000
187 },
188 "time_window": [
189 1693382400,
190 1693418400
191 ]
192 },
193 {
194 "id": 2,
195 "start_index": 17,
196 "capacity":[20],
197 "costs":{
198 "fixed":1000
199 },
200 "time_window": [
201 1693382400,
202 1693418400
203 ]
204 },
205 {
206 "id": 3,
207 "start_index": 18,
208 "capacity":[20],
209 "costs":{
210 "fixed":1000
211 },
212 "time_window": [
213 1693382400,
214 1693418400
215 ]
216 },
217 {
218 "id": 4,
219 "capacity":[20],
220 "start_index": 19,
221 "costs":{
222 "fixed":1000
223 },
224 "time_window": [
225 1693382400,
226 1693418400
227 ]
228 }
229 ],
230 "locations":
231 {
232 "id": 1,
233 "location": ["34.083950,-118.318640", "34.054927,-118.323726","34.075525,-118.361588","34.076350,-118.338519","34.090425,-118.338933","34.037925,-118.459842","34.004364,-118.421170", "34.000215,-118.318803","33.945884,-118.325628","34.000895,-118.204929", "34.076646,-118.376969","34.094986,-118.300885","34.018780,-118.317919","33.996658,-118.261708", "33.916595,-118.240132", "33.946275,-118.385486","34.057106,-118.361326", "34.016137,-118.253523", "33.940407,-118.265196","33.974060,-118.246945"]
234 },
235 "relations":[
236 {
237 "type":"in_sequence",
238 "steps":[
239 {
240 "type":"start"
241 },
242 {
243 "type":"job",
244 "id": 6
245 },
246 {
247 "type":"job",
248 "id": 4
249 },
250 {
251 "type":"job",
252 "id": 1
253 },
254 {
255 "type":"end"
256 }
257 ],
258 "vehicle":1
259 },
260 {
261 "type":"in_direct_sequence",
262 "steps":[
263 {
264 "type":"start"
265 },
266 {
267 "type":"pickup",
268 "id": 2
269 },
270 {
271 "type":"delivery",
272 "id": 2
273 },
274 {
275 "type":"job",
276 "id": 10
277 },
278 {
279 "type":"job",
280 "id": 5
281 },
282 {
283 "type":"end"
284 }
285 ]
286 },
287 {
288 "type":"in_same_route",
289 "steps":[
290 {
291 "type":"start"
292 },
293 {
294 "type":"pickup",
295 "id": 3
296 },
297 {
298 "type":"delivery",
299 "id": 3
300 },
301 {
302 "type":"job",
303 "id": 7
304 },
305 {
306 "type":"job",
307 "id": 8
308 },
309 {
310 "type":"job",
311 "id": 9
312 },
313 {
314 "type":"end"
315 }
316 ]
317 }
318 ]
319}
320'
321Optimization POST Response
Once the request is made, we get a unique ID in the API response:
1{
2 "id": "b6752a169903fd4cd6f820e4c27ff850",
3 "message": "Optimization job created",
4 "status": "Ok"
5}Optimization GET Request
We take the ID and use the Optimization GET request to retrieve the result. Here is the GET request:
1curl --location 'https://api.nextbillion.io/optimization/v2/result?id=b6752a169903fd4cd6f820e4c27ff850
2&key=<your_api_key>'Optimization GET Response
Following is the optimized route plan:
1{
2 "description": "Relations Example",
3 "result": {
4 "code": 0,
5 "summary": {
6 "cost": 16139,
7 "routes": 3,
8 "unassigned": 0,
9 "service": 1910,
10 "duration": 13139,
11 "waiting_time": 15191,
12 "priority": 0,
13 "delivery": [6],
14 "pickup": [6],
15 "distance": 195236.8
16 },
17 "routes": [
18 {
19 "vehicle": 1,
20 "cost": 3006,
21 "steps": [
22 {
23 "type": "start",
24 "arrival": 1693396088,
25 "duration": 0,
26 "service": 0,
27 "waiting_time": 0,
28 "location": [34.057106, -118.361326],
29 "location_index": 16,
30 "load": [0]
31 },
32 {
33 "type": "job",
34 "arrival": 1693396800,
35 "duration": 712,
36 "service": 120,
37 "waiting_time": 0,
38 "location": [34.037925, -118.459842],
39 "location_index": 5,
40 "id": 6,
41 "load": [0]
42 },
43 {
44 "type": "job",
45 "arrival": 1693397904,
46 "duration": 1696,
47 "service": 120,
48 "waiting_time": 0,
49 "location": [34.07635, -118.338519],
50 "location_index": 3,
51 "id": 4,
52 "load": [0],
53 "late_by": 5604
54 },
55 {
56 "type": "job",
57 "arrival": 1693398334,
58 "duration": 2006,
59 "service": 120,
60 "waiting_time": 0,
61 "location": [34.08395, -118.31864],
62 "location_index": 0,
63 "id": 1,
64 "load": [0],
65 "late_by": 11434
66 },
67 {
68 "type": "end",
69 "arrival": 1693398454,
70 "duration": 2006,
71 "service": 0,
72 "waiting_time": 0,
73 "location": [34.08395, -118.31864],
74 "location_index": 0,
75 "load": [0]
76 }
77 ],
78 "service": 360,
79 "duration": 2006,
80 "waiting_time": 0,
81 "priority": 0,
82 "delivery": [0],
83 "pickup": [0],
84 "distance": 31219.500000000004,
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304 }
305 ]
306 },
307 "status": "Ok",
308 "message": ""
309}Following is a visual representation of the initial locations of tasks, vehicles and the routes suggested after optimization as per the given constraints.
Analyzing the Solution
Looking at the result we can observe some interesting insights:
-
From the summary, we can see that all the jobs were assigned and a total of 3 routes were created.
-
The
in_sequencerelation with jobs 6, 4, 1 gets fulfilled through vehicle 1. Job 4 & 1 could not be fulfilled within their time window. -
The
in_direct_sequencerelation with shipment 2 and jobs 10 & 5 get fulfilled through vehicle 2. Job 5 could not be fulfilled within its time window. -
The
in_same_routerelation with shipment 3 and jobs 7, 8, 9 get fulfilled through vehicle 3. -
Rest of all tasks - jobs 2, 3 and shipment 1 - were also taken care of by vehicle 3 on the same route as well.
As we can see, NextBillion.ai’s Route Optimization V2 honors the relation constraints exactly as configured. To explore more readers can change the contents of different relations, assign different vehicles to relations. Or else they can just remove the relations object and contrast the result with the above and see how adding relations impacts the job distribution, number of routes, costs, wait_time etc.
We hope this example was helpful. Check out some more use cases that Route Optimization V2 can handle for you!
