Transcript Slide 1
UNIVERSIDADE FEDERAL DO CEARÁ
PRÓ-REITORIA DE PESQUISA E PÓS-GRADUAÇÃO
PROGRAMA DE MESTRADO EM LOGÍSTICA E PESQUISA OPERACIONAL
A GENETIC ALGORITHM FOR PERIOD VEHICLE
ROUTING PROBLEM WITH PRACTICAL
APPLICATION
JOSÉ LASSANCE DE CASTRO SILVA
FELIPE PINHEIRO BEZERRA
1
CYTEDHAROSA 2012
Outline
Motivating Problem
Problem Definition
Solution Method Aproach
Computational Experiments
Conclusions and Future Research Directions
Motivating Problem
Practical application:
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Wholesaler Distributor
Ice cream and ice pops division
Sales team
Marketing mix:
Product
Pricing
Promotion
Placement
Motivating Problem
Practical application:
SALES TEAM ROUTINE AT CUSTOMER STORE
• Observe visibility and promotion elements
• Inspect equipments (freezers)
• Clean the equipments and rearrange the products inside them
• Remove strange products
• Analyse supply, assortment and prices
• Negotiate improvements and orders
• Place order
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Motivating Problem
Practical application: Current solution method
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Motivating Problem
Practical application: Current solution method
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Advantages:
Out of route serving
Intuitive inclusion of new customers
Sales representative´s familiarity with territory
Motivating Problem
Practical application: Current solution method
Drawbacks:
No tour definition
Replanning cost (time)
Learning curve
Unable to handle customer with multiple service
frequence demand
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Motivating Problem
Practical application: Considerations
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Predefined frequence a regularity
Route optimization
Save travel time
Increase sales oportunity
Minimize travel costs and risks
Fast and easy to use
Operational restrictions
Team size
Daily workload
The Periodic Vehicle Routing Problem (PVRP)
Given:
a set of customers with known demands and visit frequencies;
a set of schedule options for each customer;
a planning period of multiple days;
a homogeneous fleet of vehicles with limited capacity;
the location of the customers and the central depot (where all trips must start and end);
the complete network wiht known arc costs.
Find:
A set of routes over the plannig period.
Objective:
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Minimize the global visiting cost.
The Periodic Vehicle Routing Problem (PVRP)
(BALDACCI et al., 2011)
1 vehicle
30 units of capacity
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The Periodic Vehicle Routing Problem (PVRP)
Three simultaneous decisions:
Select a visit schedule for each customer;
Define the customers that should be visited by each
vehicle on each day;
Route the vehicles for each day.
It´s a generalization of the VRP: NP-Hard.
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Solution Method Aproach
Genetic Algorithms: Concepts
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Holland (1975)
Metaheuristic
Natural selection
Population based
Cromossomes/individuals
Recombinations
Fitness
Solution Method Aproach
Genetic Algorithms: Basic pseudocode
Begin
generate initial population
evaluate fitness of each individual
While stop criteria is not true do
proceed crossovers
proceed mutations
evaluate new individuals
select individuals to replace and their replacements
update stop criteria
End
return best solution
End
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Solution Method Aproach
Genetic Algorithms: Key points
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Solution representation
Fitness function
Population control
Selection method
Genetic operators
Use of hibridization
Stop criteria
Parameters definition
Solution Method Aproach
Proposed genetic algorithm:
Solution representation
Grand Tour
No trip delimiters
Prins (2004), Chu et al. (2004) e Vidal et al. (2012)
(VIDAL et al. 2012)
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Solution Method Aproach
Proposed genetic algorithm:
Individuals evaluation: Split algorithm (PRINS 2004)
(PRINS, 2004)
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Solution Method Aproach
Proposed genetic algorithm:
Original crossover operator
Customer
1
2
3
4
5
6
7
8
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Service freq.
3
2
1
1
1
3
2
1
Schedule combinations
{Day1, Day3, Day4}, {Day2, Day3, Day4}
{Day1,Day3}, {Day2, Day4}
{Day1}, {Day4}
{Day1}
{Day1}, {Day2}
{Day2, Day3, Day4}, {Day1, Day2, Day3}, {Day1, Day2, Day4}
{Day1,Day3}, {Day2, Day4}
{Day2}, {Day3}
Computational experiments
Benchmark instances testing:
Results on benchmark instances.
NOME
TB
p01
p02
CGL
ALP
HDH
BDC
VDL (z*)
LB
524,61
531,02
524,61
524,61
524,61
590,90
1.443,10
1.337,20
1.330,09
1.324,74
1.332,01
1.322,87
1.322,87
1.373,15
546,70
524,60
524,61
537,37
528,97
524,61
524,61
619,22
p04
843,90
860,90
837,93
845,97
847,48
835,26
835,26
988,10
2.187,30
2.089,00
2.061,36
2.043,75
2.059,74
2.027,99
2.024,96
2.089,17
p06
938,20
881,10
840,30
840,10
884,69
835,26
835,26
1.057,21
p07
839,20
832,00
829,45
829,65
829,92
825,14
826,14
862,78
2.281,80
2.151,30
2.075,10
2.054,90
2.052,21
2.058,36
2.034,15
2.022,47
2.098,81
875,00
829,90
829,45
829,65
834,92
826,14
826,14
881,42
1.833,70
878,50
1.674,00
847,30
1.633,20
791,30
1.629,58
817,56
1.621,21
782,17
1.629,76
791,18
1.593,45
779,06
1.593,43
770,89
1.697,88
825,14
p12
1.237,40
1.239,58
1.230,95
1.258,46
1.186,47
1.308,86
p13
3.629,80
3.602,76
3.835,90
3.492,89
p08
2.192,50
p09
p10
p11
p14
954,81
954,81
954,81
954,81
954,81
954,81
954,81
p15
1.862,60
1.862,63
1.862,63
1.862,63
1.862,63
1.862,63
1.864,52
p16
2.875,20
2.875,24
2.875,24
2.875,24
2.875,24
2.875,24
2.891,50
p17
1.614,40
1.597,75
1.597,75
1.601,75
1.597,75
1.597,75
1.597,75
p18
3.217,70
3.159,22
3.157,00
3.147,00
3.136,69
3.131,09
3.183,93
p19
4.846,50
4.902,64
4.846,49
4.851,41
4.834,34
4.834,34
4.945,63
p20
8.367,40
8.367,40
8.412,02
8.367,40
8.367,40
8.776,81
p21
2.216,10
2.184,04
2.173,58
2.180,33
2.170,61
2.170,61
2.200,90
p22
4.436,40
4.307,19
4.330,59
4.218,46
4.193,95
4.193,95
4.416,00
p23
6.769,00
6.620,50
6.813,45
6.644,93
6.420,71
7.113,13
p24
3.773,00
3.704,11
3.702,02
3.704,60
3.687,46
3.687,46
3.748,45
p25
3.826,00
3.781,38
3.781,38
3.781,38
3.777,15
3.777,15
3.781,38
p26
3.834,00
3.795,32
3.795,33
3.795,32
3.795,32
3.795,32
3.810,61
p27
23.401,60
23.017,45
22.561,33
22.153,31
21.912,85
21.833,87
22.378,36
p28
23.105,10
22.569,40
22.562,44
22.418,52
22.242,51
22.242,51
22.693,78
p29
24.248,20
24.012,92
23.752,15
22.864,23
22.543,76
22.543,75
23.021,93
p30
80.982,10
77.179,33
76.793,99
75.579,23
74.464,26
73.875,19
76.639,43
p31
80.279,10
79.382,35
77.944,79
77.459,14
76.322,04
76.001,57
78.309,61
p32
83.838,70
80.908,95
81.055,52
79.487,97
78.072,88
77.598,00
80.756,82
2,9%
1,8%
1,6%
1,6%
0,1%
0,0%
5,4%
DESVIO
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CGW
524,60
p03
p05
1.481,30
CB
547,40
12,4%
6,2%
STATE-OF-THE-ART METHODS
Tan and Beasley (1984)
- TB
Christofides and Beasley (1984) - CB
Chao et al. (1995)
- CGW
Cordeau et al. (1997)
- CGL
Alegre et al. (2007)
- ALP
Hemmelmayr et al. (2007)
- HDR
Baldacci et al.(2011)
- BLD
Vidal et al. (2012)
- VDL
Computational experiments
Benchmark instances testing:
Average computational cost in minutes
Time (min)
CGL
ALP
HDR
CGW
VDL
LB
4,28
3,64
3,34
10,36
5,56
3,00
Source: Vidal et al. (2012)
STATE-OF-THE-ART METHODS
Cordeau et al. (1997)
Alegre et al. (2007)
Hemmelmayr et al. (2007)
Chao et al. (1995)
Vidal et al. (2012)
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CGL
ALP
HDR
CGW
VDL
Computational experiments
Benchmark instances testing:
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Fair results
Low computational costs
Computational experiments
Practical application: Solution method applied
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Briefing
629 Stores
7 sales representatives
Weekly visits, from monday through friday
5 schedule options, except for 36 customers
Service time: 15 minutes
Maximum daily workload: 8 hours (480 minutes)
Travel speed: 30km/h
Computational experiments
Practical application: Solution method applied
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Computational experiments
Practical application: Solution method applied
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Adjustments:
Demand = service time
Restrictions = daily workload in mimutes
Travel time
Penalties for not using every “vehicle” daily
Computational experiments
Practical application: Solution method applied
Distance savings over planning period
Current
method
Daily workload considered (min)
Total distance (km)
Savings (km)
Savings (%)
Proposed
method A
480,00
1.337,40
-
480,00
956,80
380,60
28,46
Proposed
method B
425,00
1.188,84
148,56
11,11
Average daily workload composition per salesman (minutes).
Current
method
Daily workload considered
Daily workload proposed
Total service time
Total travel time
Total downtime
Minimum daily workload
Maximum daily workload
Standart deviation
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480,00
346,00
269,57
76,42
134,00
195,46
550,28
75,41
Proposed
method A
480,00
324,25
269,57
54,67
155,75
15,39
464,42
167,49
Proposed
method B
425,00
337,51
269,57
67,93
142,49
35,65
409,86
87,02
Computational experiments
Practical application: Solution method applied
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Initial findings:
Downtime awareness
Trade-off between savings and workload balancing
“How much does the workload balancing cost?”
Computational experiments
Practical application: Solution method applied
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Estimated savings
Time limit used
Saving per day and salesman (min)
Total savings per year (min)
Total savings per year (h)
Travel cost considering R$ 4,8/h
Labor cost considering R$ 7,5/h
Opportunity cost considering R$ 135,00/h
Estimated annual savings (R$)
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Proposed
method A
480,00
21,75
39.585,73
659,76
3.166,86
4.948,22
89.067,89
97.182,96
Proposed
method B
425,00
8,49
15.453,98
257,57
1.236,32
1.931,75
34.771,46
37.939,53
Computational experiments
Practical application: Solution method applied
Comparisons between current solution method and proposed solution method
Week day
monday
tuesday
wednesday
thursday
friday
Total
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Current method
Distance Workload
(Km)
(Min)
252,55
2.545,11
246,03
2.427,06
284,17
2.323,34
277,66
2.445,33
277,02
2.369,04
1.337,44 12.109,87
Proposed method
Distance Workload
(Km)
(Min)
228,51
2.197,03
221,08
2.542,16
235,75
2.256,50
254,90
2.384,80
248,59
2.432,19
1.188,84 11.812,68
Savings
Distance
10%
10%
17%
8%
10%
11%
Workload
14%
-5%
3%
2%
-3%
2%
Computational experiments
Practical application: Solution method applied
MONDAY
CURRENT
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PROPOSED
Computational experiments
Practical application: Solution method applied
TUESDAY
CURRENT
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PROPOSED
Computational experiments
Practical application: Solution method applied
WEDNESDAY
CURRENT
30
PROPOSED
Computational experiments
Practical application: Solution method applied
THURSDAY
CURRENT
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PROPOSED
Computational experiments
Practical application: Solution method applied
FRIDAY
CURRENT
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PROPOSED
Conclusions
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Good solution method for the PVRP
Good results for the practical case:
Route optimization
Reliable procedure
Service level guaranteed
Cost control
Easy set-up
Decision making tool
Future Research Directions
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Testing another insertion methods (i.e. GENI)
Population diversity control
Apply more mutation operators
Multicriteria analisys for fitness evaluation
Automatic and/or dynamic calibration
Meta-AGs
AI
Future Research Directions
Direct aproach for balancing
Spatial route clustering for each vehicle during
planning period
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UNIVERSIDADE FEDERAL DO CEARÁ
PRÓ-REITORIA DE PESQUISA E PÓS-GRADUAÇÃO
PROGRAMA DE MESTRADO EM LOGÍSTICA E PESQUISA OPERACIONAL
THANK YOU!
JOSÉ LASSANCE DE CASTRO SILVA <[email protected]>
FELIPE PINHEIRO BEZERRA <[email protected]>
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CYTEDHAROSA 2012