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Planning Service Areas and Vehicle
Routes in a Packaging Waste Collection System
Tânia Rodrigues Pereira Ramos
Instituto Universitário de Lisboa, ISCTE-IUL
Centro de Estudos de Gestão, IST – UTL
Maria Isabel Gomes
Centro de Matemática e Aplicações, FCT-UNL
Ana Paula Barbosa Póvoa
Centro de Estudos de Gestão, IST – UTL
1st International EIMPack Congress, 29-30 November 2012, Lisbon
Agenda
2
• Problem Description
• Work Purpose
• Solution Approach
• Application to the Case Study
• Discussion and Further Work
Problem Description
3
Recyclable waste collection system
Separation Dropping in special containers
Sorting Station Mono-Material
Collection Depots/Transfer Stations
Packaging Waste Glass
Paper
Plastic/Metal
Problem Description
4 Source: SPV, 2011
31 Recyclable Waste Collection Systems
The majority of them has more than one depot (where vehicles are
based)
It is a current practice to manage each depot independently
• Service areas by depot
• Fixed vehicles at each depot
• Closed routes
Problem Description
5
7 municipalities
• Service areas equal for the three materials
• Fixed vehicles at each depot
• Closed routes
231
233
235
232
234
38 Collection Sites
27 Collection Sites
84 Collection Sites
38 Collection Sites
43 Collection Sites
5 Depots
651 bins
513 bins
458 bins
Located at 230 different localities (collection sites)
(one of them is the sorting station)
• Service areas respect the municipalities boundaries
e.g.
Work Purpose
6
Respect municipalities boundaries
Study the impact on the collection cost of four
practices that are commonly used in the packaging
waste collection systems operating in Portugal
Service areas by depot
Fixed vehicles at the depot
Close routes
Plan Service Areas, Vehicle Routes and Route Scheduling
breaking up with the four practices
Approach
7
Definition of the service areas for each depot
Definition of the collection routes for each recyclable material
Tactical and Operational
Decisions
Inbound
Collection Sites Depots Sorting Station
Outbound
Objective:
Minimization of the Total Distance Travelled
Definition of the day when each route will be performed (different collection frequencies by material)
8
1
2
3
Multi-Product
Multi-Depot
Periodic
Vehicle Routing Problem
Approach
Planning Horizon 1 2 3 4 5 6 7 8 9 10 …
Scenario 1
Break:
Maintain:
• Service areas respect the municipalities boundaries
• Service areas equal for the three materials
• Vehicles fixed at each depot
• Closed routes
9
Multi-Depot
Periodic
Vehicle Routing Problem
Approach
Planning Horizon 1 2 3 4 5 6 7 8 9 10 …
Scenario 2
Break:
Maintain:
• Service areas respect the municipalities boundaries • Service areas equal for the three materials
• Vehicles fixed at each depot
• Closed routes
1
2
3
1
2
3
10
Multi-Depot
Periodic
Vehicle Routing Problem
With Shared Resources
Approach
Planning Horizon 1 2 3 4 5 6 7 8 9 10 …
Scenario 3
Break:
Maintain:
• Service areas respect the municipalities boundaries • Service areas equal for the three materials • Vehicles fixed at each depot
• Closed routes
1
2
3
1
2
3
11
Multi-Depot
Periodic
Vehicle Routing Problem
With Inter-Depot Routes
Approach
Planning Horizon 1 2 3 4 5 6 7 8 9 10 …
Scenario 4
Break: • Service areas respect the municipalities boundaries • Service areas equal for the three materials • Vehicles fixed at each depot • Closed routes
1
2
3
1
2
3
Approach
12
Scenario 1: Multi-Product, MDPVRP
Break
- Respect Municipalities
Boundaries
Maintain
- Service Areas by
Depot
- Vehicle Fixed
- Closed Routes
Scenario 2: MDPVRP Break
- Respect Municipalities
Boundaries
- Service Areas by Depot
Maintain
- Vehicle Fixed
- Closed Routes
Scenario 3: MDPVRP with Shared Resources
Break
- Respect Municipalities
Boundaries
- Service Areas by Depot
- Vehicle Fixed
Break
- Respect Municipalities Boundaries
- Service Areas by Depot
- Vehicle Fixed
- Closed Routes
Maintain
- Closed Routes
Scenario 4: MDPVRP with
Inter-Depot Routes
13
Development of a Solution Methodology
Approach
Define Service Areas
Define Final Vehicle Routes
Define Vehicle Schedules
m=1
1. Single-Product, MDVRP-OR(with Capacity and Duration Constraints)
Are all routes closed?
2. Single-Product, MDVRP(for each Open Route)
m=|M|?
3. Multi-Product, MDVRP(for the Doubtful sites)
4. Vehicle Routing Problem (with Capacity and Duration Constraints)
No
Yes
m=m+1
Yes
No
5. Routes Scheduling (Routes from module 4)
Service Areas by Depot ?
Yes
No
Share Resources
?
No
Yes
Open Routes
?
No
Yes
6. Routes Scheduling with Shared Resources (Routes from module 4)
7. Routes Selection and Scheduling with Shared Resources
(Routes from module 1, 2, 4)
Scenarios 1 and 2
Scenario 3
Scenario 4
7 modules
Mathematical Formulations
14
Development of a Solution Methodology
Approach
Scenario 1 m=1
1. Single-Product, MDVRP-OR(with Capacity and Duration Constraints)
Are all routes closed?
2. Single-Product, MDVRP(for each Open Route)
m=|M|?
3. Multi-Product, MDVRP(for the Doubtful sites)
4. Vehicle Routing Problem (with Capacity and Duration Constraints)
No
Yes
m=m+1
Yes
No
5. Routes Scheduling (Routes from module 4)
Service Areas by Depot ?
Yes
No
Share Resources
?
No
Yes
Open Routes
?
No
Yes
6. Routes Scheduling with Shared Resources (Routes from module 4)
7. Routes Selection and Scheduling with Shared Resources
(Routes from module 1, 2, 4)
Scenarios 1 and 2
Scenario 3
Scenario 4
Scenario 2 m=1
1. Single-Product, MDVRP-OR(with Capacity and Duration Constraints)
Are all routes closed?
2. Single-Product, MDVRP(for each Open Route)
m=|M|?
3. Multi-Product, MDVRP(for the Doubtful sites)
4. Vehicle Routing Problem (with Capacity and Duration Constraints)
No
Yes
m=m+1
Yes
No
5. Routes Scheduling (Routes from module 4)
Service Areas by Depot ?
Yes
No
Share Resources
?
No
Yes
Open Routes
?
No
Yes
6. Routes Scheduling with Shared Resources (Routes from module 4)
7. Routes Selection and Scheduling with Shared Resources
(Routes from module 1, 2, 4)
Scenarios 1 and 2
Scenario 3
Scenario 4
15
Development of a Solution Methodology
Approach
Scenario 3 m=1
1. Single-Product, MDVRP-OR(with Capacity and Duration Constraints)
Are all routes closed?
2. Single-Product, MDVRP(for each Open Route)
m=|M|?
3. Multi-Product, MDVRP(for the Doubtful sites)
4. Vehicle Routing Problem (with Capacity and Duration Constraints)
No
Yes
m=m+1
Yes
No
5. Routes Scheduling (Routes from module 4)
Service Areas by Depot ?
Yes
No
Share Resources
?
No
Yes
Open Routes
?
No
Yes
6. Routes Scheduling with Shared Resources (Routes from module 4)
7. Routes Selection and Scheduling with Shared Resources
(Routes from module 1, 2, 4)
Scenarios 1 and 2
Scenario 3
Scenario 4
Scenario 4 m=1
1. Single-Product, MDVRP-OR(with Capacity and Duration Constraints)
Are all routes closed?
2. Single-Product, MDVRP(for each Open Route)
m=|M|?
3. Multi-Product, MDVRP(for the Doubtful sites)
4. Vehicle Routing Problem (with Capacity and Duration Constraints)
No
Yes
m=m+1
Yes
No
5. Routes Scheduling (Routes from module 4)
Service Areas by Depot ?
Yes
No
Share Resources
?
No
Yes
Open Routes
?
No
Yes
6. Routes Scheduling with Shared Resources (Routes from module 4)
7. Routes Selection and Scheduling with Shared Resources
(Routes from module 1, 2, 4)
Scenarios 1 and 2
Scenario 3
Scenario 4
16
Single-Product, MDVRP with Open Routes
Module 1
Multi-Product, Multi-Depot VRP
1
2
3
Single-Product, Multi-Depot VRP
with Open Routes Allowed
1
2
3
Relaxation
Approach
17
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
-9 -8,9 -8,8 -8,7 -8,6 -8,5 -8,4 -8,3 -8,2 -8,1 -8
49
124
125
102 109
110
111
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
-9 -8,9 -8,8 -8,7 -8,6 -8,5 -8,4 -8,3 -8,2 -8,1 -8
135 116
133 117
122
119
120 118
Unfeasible Routes for MDVRP Feasible Routes for MDVRP
Depot
Single-Product, MDVRP with Inter-Depot Routes
Module 1
Single-Product, MDVRP Module 2
Depot
Depot
Approach
18
Single-Product, MDVRP with Open Routes
Module 1
Single-Product, MDVRP Module 2
18
1
2
1
2
1
2
Are run for all materials
Service Area for Paper Service Area for Plastic/Metal Service Area for Glass = =
Multi-Product, MDVRP Module 3 1
2
Unclear Sites
Approach
19 19
Vehicle Routing Problem Module 4
1
2
Service area for each depot is defined:
Definition of the final collection routes for each recyclable material
Approach
20 20
Scheduling Modules 5, 6 and 7
Set of Final Routes
# 1
Paper Routes
# 2
# 21
# 22
# 23
# 70
# 71
# 72
# 102
...
Plastic Routes
Glass Routes
...
...
11 12 13 14 15
6 7 8 9 10
16 17 18 19 20
Vehicle 1
1 2 3 4 5
11 12 13 14 15
6 7 8 9 10
16 17 18 19 20
Vehicle 2
1 2 3 4 5
Vehicle 3
...
• Collection Frequency • Paper Routes: 4x/month • Plastic Routes: 2x/month • Glass: 1x/month
• Minimal and Maximum Time Interval Between Consecutives Collections
• Number of working hours per day
Approach
Assigns routes to days and vehicles
21 21
Scheduling Modules 5, 6 and 7
Set of Final Routes
# 1
Paper Routes
# 2
# 21
# 22
# 23
# 70
# 71
# 72
# 102
...
Plastic Routes
Glass Routes
...
...
11 12 13 14 15
6 7 8 9 10
16 17 18 19 20
Vehicle 1
1 2 3 4 5
11 12 13 14 15
6 7 8 9 10
16 17 18 19 20
Vehicle 2
1 2 3 4 5
Vehicle 3
...
# 1
# 1
# 1
# 1
# 2
# 2
# 2
# 2
# 22
# 22
# 23
# 23
# 71
# 72
Approach
• Collection Frequency • Paper Routes: 4x/month • Plastic Routes: 2x/month • Glass: 1x/month
• Minimal and Maximum Time Interval Between Consecutives Collections
• Number of working hours per day
Assigns routes to days and vehicles
22 22
Approach
Seven Modules Seven Mathematical Formulations based on the Two-Commodity Flow Formulation
Objective Function: Min Total Distance
hj
Vi Vj Vh
ij
Vi
i
Vi Vj
ijij dQT
fryfrScfrdxMin
c f sc
22
1
Outbound Distance Inbound Distance Module 1 and 4
Module 2
c f j sc Vi Vj Mm Bk Vh
hjm
mijmk
Mm Vi
mim
Vi Vj Mm Kk
mijijmk dQT
fryfrScfrdxMin 2..
2
1Module 3
c f jVi Vj Vsh Bk
hjm
mijmk
Vci
i
Vi Vj Kk
ijijk dQT
fryfrScfdxMin 2..
2
1
110
,1
22/2/
gi
kj
ki
ds d m
gj
s d m Gg
StEn
Kk Tt Vji
ijktg
Vj Vi Mm Kk Tt Gg
ijmkktgkiki
Vj Vi Mm Kk Tt Gg
ijmkktgki
Kk Tt Gg
ktgk ddQTLoEnStdQTLoEndisMin
Module 5, 6, 7
23
Application to a case study
231
233
235
232
234
38 Collection Sites
27 Collection Sites
84 Collection Sites
38 Collection Sites
43 Collection Sites
5 Depots
230 Collection Sites
1 Sorting Station
3 Packaging Materials
Planning Horizon: 20 days 5 days x 4 weeks(1 month)
Glass: 1x/month
Paper: 4x/month
Plastic/Metal: 2x/month
Different Collection
Frequencies
Interval between consecutive collec. Glass: 20 days
Paper: Min 4 days, Max 5 days
Plastic/Metal: Min 9 days, Max 10 days
24
Scenario 1
Application to a case study
231
233
235
232
234
18 Collection Sites
0 Collection Sites
156 Collection Sites
53 Collection Sites
3 Collection Sites
New Service Areas by Depot
Depot 231
Depot 232
Depot 233
Depot 234
Depot 235
1
0
2
1
5Number of Vehicles Required:
New Collection Routes:
32 Routes to Collect Glass (1x/Month) = 3659 km
21 Routes to Collect Paper (4x/Month) = 11744 km
49 Routes to Collect Plastic/Metal (2x/Month)= 9002 km
24 405 km
Service Areas by Depot without respecting municipalities boundaries
25
Scenario 1
Application to a case study
Vehicle Schedules 1 2 3 4 5
188m
188m
399m 370m
399m 152m
360m 399m
11 12 13 14 15
6 7 8 9 10
370m
188m 399m
16 17 18 19 20
55m
55m 356m 381m
Depot 231 (Veh.1)
1 2 3 4 5
355m
361m
370m
479m 152m
171m
11 12 13 14 15
6 7 8 9 10
16 17 18 19 20
55m
140m 349m 280m
Depot 233 (Veh.2)
474m 416m
122m
360m
77m 110m
Depot 233 (Veh.3)
215m 211m 227m 74m
349m 74m
361m
399m
1 2 3 4 5
110m
399m 474m
6 7 8 9 10
463m
399m 474m
11 12 13 14 15
211m 294m 337m
399m 474m
16 17 18 19 20
122m
211m
1 2 3 4 5
149m 133m
360m 399m
11 12 13 14 15
6 7 8 9 10
370m16 17 18 19 20
Depot 234 (Veh.4)
476m
294m
370m
375m
163m
Depot 235 (Veh.5)
Depot 235 (Veh.6)
396m
477m
133m
133m
149m 282m
1 2 3 4 5
6 7 8 9 10
16 17 18 19 20
11 12 13 14 15
375m 377m 396m 391m
434m 396m 163m
360m 375m 386m 383m
375m 396m 344m
468m
263m
370m
448m
315m
419m
439m
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
413m 452m 419m 444m
315m 439m 456m
314m 472m 452m 444m
461m 406m 326m
338m
314m
370m
435m
403m
Depot 235 (Veh.8)
Depot 235 (Veh.9)
145m
314m
1 3 4 5
6 8 9 10
11 12 13 14 15
363m 403m 383m 418m
403m 392m 418m
363m 403m 426m
422m 190m 367m
314m
459m
370m
369m
376m
407m
314m
1 3 4 5
6 8 9 10
11 12 13 14 15
472m 476m 407m 433m
478m 407m 433m
314m 471m 467m 433m
341m 407m 433m
16 17 18 19 20 16 18 19 20
Depot 235 (Veh.7)
206m
281m
370m
471m
312m
392m
278m
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
449m 312m 392m 389m
312m 429m 389m
129m 413m 312m 389m
463m 392m 389m
16 17 18 19 20
2
7
16 17 18 19 20
17
2
7
168m
Day
11
360 m
Workload
(in minutes)
Max
Workload:
480 m
Usage Rate: 5632 m =
20 days x 480 m
9600 m 59%
44%
41%
10%
76%
85%
74%
74%
86%
Service Areas by Depot without respecting municipalities boundaries
26
Scenario 2
Application to a case study
231
233
235
232
234
13 Collection Sites
7 Collection Sites
149 Collection Sites
39 Collection Sites
12 Collection Sites
231
233
235
232
234
16 Collection Sites
0 Collection Sites
122 Collection Sites
39 Collection Sites
3 Collection Sites
231
233
235
232
234
15 Collection Sites
18 Collection Sites50 Collection
Sites
68 Collection Sites
31 Collection Sites
Glass Paper Plastic/Metal
Service Areas by Recyclable Materials
27
Scenario 2
Application to a case study
Number of Vehicles Required:
New Collection Routes:
32 Routes to Collect Glass (1x/Month) = 3536 km
21 Routes to Collect Paper (4x/Month) = 11595 km
49 Routes to Collect Plastic/Metal (2x/Month)= 8163 km
23 294 km
Depot 231
Depot 232
Depot 233
Depot 234
Depot 235
1
2
1
4
1
Service Areas by Recyclable Materials
28
Scenario 2
Application to a case study
Vehicle Schedules 268m 471m
479m
431m 471m
11 12 13 14 15
6 7 8 9 10
335m
479m
16 17 18 19 20
80m
55m392m
Depot 231 (Veh.1)
1 2 3 4 5
277m 370m
277m
11 12 13 14 15
6 7 8 9 10
16 17 18 19 20
306m
Depot 232 (Veh.2)
413m
122m
360m
381m 381m
Depot 233 (Veh.3)
201m 85m
85m
474m
1 2 4 5
474m 413m
6 7 8 9 10
122m
474m 413m 211m 458m
474m 413m
16 17 18 19 20
303m
383m
Depot 233 (Veh.4)
Depot 234 (Veh.5)
Depot 235 (Veh.6)
190m
Depot 235 (Veh.8)
Depot 235 (Veh.9)
Depot 235 (Veh.7)
1 2 3 4 5
188m
188m
188m
80m
93m
151m 201m
11 12 13 14 15
255m
3
133m 291m 74m
2 3 4 5
421m 314m
360m 399m
12 13 14 15
6 7 8 9 10
370m16 17 18 19 20
74m
421m 314m
1
317m
133m 148m 74m11
317m
296m
464m
370m
392m
440m
389m
459m
1 2 3 4 5
6 7 8 9 10
16 17 18 19 20
11 12 13 14 15
392m 397m 389m 355m
440m 389m 468m
386m 392m 397m 341m
392m 389m 390m
380m
380m
370m
472m
314m
341m
380m
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
426m 314m 341m 477m
314m 341m 457m
380m 392m 314m 265m
293m 459m 449m
16 17 18 19 20
479m
465m
370m
358m
455m
451m
475m
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
471m 455m 451m 425m
455m 314m 477m
280m 452m 455m 336m
460m 300m
16 17 18 19 20
314m
465m
457m
370m
472m
433m
455m
267m
1 3 4 5
6 8 9 10
12 13 14 15
318m 433m 455m 398m
433m 469m 398m
318m 433m 398m
318m 351m 398m
2
7
16 17 18 19 20465m
11
392m 370m
250m
140m
1 3 4 5
6 8 9 10
11 12 13 14 15
341m
381m 196m 381m
392m 341m 178m
250m 244m 324m
16 18 19 2017
2
7417m
133m 190m 291m 74m
61%
42%
18%
44%
34%
83%
78%
87%
85%
Service Areas by Recyclable Materials
29
Scenario 3
Application to a case study
Same Service Areas as in Scenario 2
Number of Vehicles Required:
Same Collection Routes as in Scenario 2
BUT
Depot 231
Depot 232
Depot 233
Depot 234
Depot 235
1 1 1
4
1
Depot 231
Depot 232
Depot 233
Depot 234
Depot 235
1 1 1
4
0
8 vehicles 7 vehicles
Distance Travelled: 23421 km Distance Travelled: 24198 km
Shared Resources (vehicles can perform routes from other depots)
30
Scenario 3
Application to a case study
Shared Resources (vehicles can perform routes from other depots)
Vehicle Schedules (7 vehicles) 152m
335m
152m
11 12 13 15
6 7 8 9
399m
163m
479m
55m456m
Depot 231 (Veh.1)
Depot 233 (Veh.2)
184m
122m
360m
239m 207m
Depot 234 (Veh.3)
323m
1 2 4 5
444m 75m
6 7 8 9 10
350m
133m 211m 310m
222m 75m
16 17 18 19 20
111m
184m
Depot 235 (Veh.4)
Depot 235 (Veh.5)
Depot 235 (Veh.6)
Depot 235 (Veh.7)
188m
456m
188m
479m
11 12 13 14 15
111m
3
475m
454m
370m
457m
397m460m
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
414m 397m 472m 433m
397m 471m 433m
475m
425m 464m 433m
464m
476m
370m
449m
463m
398m
443m
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
479m 463m 398m 392m
463m 398m 392m
478m 479m 463m 392m
449m 398m 392m
16 17 18 19 20
355m
472m
370m
468m
380m
465m
446m
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
477m 380m 452m 336m
470m 461m 306m
469m 477m 380m 300m
468m 358m
16 17 18 19 20
468m
457m
437m
370m
447m
389m
478m
477m
1 3 4 5
6 8 9 10
12 13 14 15
432m 432m 478m 457m
389m 341m 455m
432m 432m 457m
479m 341m 455m
2
7
16 17 18 19 20458m
11
399m
1 2 3 4 5
429m
204m
10
14
429m16 17 18 19 20
458m
478m
370m
463m
474m
413m
478m
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
469m 477m 413m 474m
474m 413m 474m
383m 473m 477m 474m
463m 413m 474m
16 17 18 19 20
310m
239m
392m16 17 18 19 20
414m 397m 433m
37%
51%
95%
87%
91%
91%
91%
31
Scenario 3
Application to a case study
Shared Resources (vehicles can perform routes from other depots)
231
233
Days 4 and 14:
Routes Duration
Direct route 231-233 24 m
Route 104 381 m
Direct route 233-231 24 m
Total 429 m
32
Scenario 4
Application to a case study
Number of Vehicles Required:
Depot 231
Depot 232
Depot 233
Depot 234
Depot 235
1 1 1
4
1
Depot 231
Depot 232
Depot 233
Depot 234
Depot 235
1 1 1
4
0
8 vehicles 7 vehicles
Distance Travelled: 23181 km Distance Travelled: 23687 km
Open Routes between Depots
362m
268m
204m
11 12 13 15
6 7 8 9
399m
268m
399m
55m268m
Depot 231 (Veh.1)
Depot 233 (Veh.2)
282m
122m
270m 460m
Depot 234 (Veh.3)
281m
458m
281m 211m 392m
184m
16 17 18 19 20310m
Depot 235 (Veh.4)
Depot 235 (Veh.5)
Depot 235 (Veh.6)
Depot 235 (Veh.7)
479m
11 12 13 14 15
468m
451m
370m
428m
392m451m
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
445m 392m 438m 453m
392m 328m 479m
477m
465m 446m 332m
435m
455m
370m
447m
433m
477m
455m
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
436m 433m 477m 403m
433m 475m 476m
456m 436m 433m 418m
479m 314m 336m
16 17 18 19 20
389m
389m
370m
457m
380m
398m
389m
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
439m 380m 398m 441m
380m 398m 391m
389m 465m 380m 399m
422m 476m
16 17 18 19 20
398m
428m
463m
370m
397m
341m
436m
455m
1 3 4 5
6 8 9 10
12 13 14 15
397m 453m 436m 455m
341m 480m 455m
397m 453m 455m
397m 480m 455m
2
7
16 17 18 19 20463m
11
399m
1 2 3 4 5
80m
10
14
16 17 18 19 20
467m
381m
370m
455m
413m
474m
498m
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
446m 461m 474m 398m
413m 474m 461m
361m 449m 413m 473m
455m 474m 461m
16 17 18 19 20
443m
460m
427m16 17 18 19 20
421m 392m 480m
188m
340m
188m
163m 72m
102m 310m
1 2 53
6 7 8 10
320m
4
9
281m
33
Application to a case study
Vehicle Schedules (7 vehicles)
47%
42%
92%
85%
90%
89%
91%
Scenario 4 Open Routes between Depots
34
Application to a case study
Scenario 4 Open Routes between Depots
Days 1 and 11:
Routes Duration
Route 46 74 m
Route 43 150 m
Route 88 57 m
Total 281 m
232
234
#88
#43
#46
35
Application to a case study
Scenario 1 Scenario 2 Scenario 3a Scenario 3b Scenario 4a Scenario 4b
Distance 24 405 km 23 294 km 23 421 km 24 198 km 23 181 km 23 687 km
(Deviation) -5% +0.5% +4% -1% -2%
N.Vehicles 9 9 8 7 8 7
Cost-Analysis
• Fuel Cost: 0,5€/km
• Vehicle Depreciation: 20000€/year
• Driver Cost: 12600€/year
36
Application to a case study
Cost-Analysis
0
50000
100000
150000
200000
250000
300000
350000
400000
450000
500000
Scenario 1 Scenario 2 Scenario 3a Scenario 3b Scenario 4a Scenario 4b
Driver Cost
Vehicle Cost
Fuel Cost
440430€ 433164€
401326€
373388€ 399886€
370322€
-2%
-7%
-14% -0.4%
-0.8%
Annual Cost (€)
Scenario 4b vs.
Scenario 1
-16%
37
Discussion
• Significant savings can be obtained when the depots are managed in an integrated way, but...
it is more complex to manage since three different service areas, shared vehicles and open routes have to be addressed
Demands a decision support system to help managing a more complex solution
• Four current practices
• Respect municipalities boundaries
• Service areas by depot
• Fixed vehicles at the depot
• Close routes
Higher impact: -14%
38
Further Work
• Applying the solution methodology developed to other packaging waste collection systems
• Tackle the periodic issue in an integrated way with service areas and vehicle routes definition (instead of in a sequential way)
• Objective Function: Minimize Total Collection Cost (Distance + N. Vehicles)
• Introduce the objective of balance the schedules (total working hours over the planning horizon) among vehicles
Planning Service Areas and Vehicle
Routes in a Packaging Waste Collection System
Tânia Rodrigues Pereira Ramos
Maria Isabel Gomes
Ana Paula Barbosa Póvoa
1st International EIMpack Congress, 29-30 November 2012, Lisbon
