a genetic algorithm for period vehicle routing problem with practical application josÉ lassance de...

A GENETIC ALGORITHM FOR PERIOD VEHICLE ROUTING PROBLEM WITH PRACTICAL

APPLICATION

JOSÉ LASSANCE DE CASTRO SILVA

FELIPE PINHEIRO BEZERRA

CYTEDHAROSA 20121

UNIVERSIDADE FEDERAL DO CEARÁ

PRÓ-REITORIA DE PESQUISA E PÓS-GRADUAÇÃO

PROGRAMA DE MESTRADO EM LOGÍSTICA E PESQUISA OPERACIONAL

Outline

Motivating Problem Problem Definition Solution Method Aproach Computational Experiments Conclusions and Future Research Directions

Motivating Problem

Practical application:

Wholesaler Distributor

Ice cream and ice pops division

Sales team

Marketing mix:

Product

Pricing

Promotion

Placement3

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


Advantages:

Out of route serving

Intuitive inclusion of new customers

Sales representative´s familiarity with territory

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Motivating Problem


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

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 workload8

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: Minimize the global visiting cost.

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(BALDACCI et al., 2011)

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1 vehicle30 units of capacity

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.

Three simultaneous decisions:

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It´s a generalization of the VRP: NP-Hard.

Solution Method Aproach

Genetic Algorithms: Concepts

Holland (1975)

Metaheuristic

Natural selection

Population based

Cromossomes/individuals

Recombinations

Fitness12


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 solutionEnd

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Genetic Algorithms: Key points

Solution representation

Fitness function

Population control

Selection method

Genetic operators

Use of hibridization

Stop criteria

Parameters definition14


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)15



Individuals evaluation: Split algorithm (PRINS 2004)

(PRINS, 2004)

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Original crossover operatorCustomer Service freq. Schedule combinations

1 3 {Day1, Day3, Day4}, {Day2, Day3, Day4}2 2 {Day1,Day3}, {Day2, Day4}3 1 {Day1}, {Day4}4 1 {Day1}5 1 {Day1}, {Day2}6 3 {Day2, Day3, Day4}, {Day1, Day2, Day3}, {Day1, Day2, Day4}7 2 {Day1,Day3}, {Day2, Day4}8 1 {Day2}, {Day3}

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Computational experiments

Benchmark instances testing:NOME TB CB CGW CGL ALP HDH BDC VDL (z*) LB

p01 547,40 524,60 524,61 531,02 524,61 524,61 524,61 590,90

p02 1.481,30 1.443,10 1.337,20 1.330,09 1.324,74 1.332,01 1.322,87 1.322,87 1.373,15

p03 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

p05 2.192,50 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

p08 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

p09 875,00 829,90 829,45 829,65 834,92 826,14 826,14 881,42

p10 1.833,70 1.674,00 1.633,20 1.629,58 1.621,21 1.629,76 1.593,45 1.593,43 1.697,88p11 878,50 847,30 791,30 817,56 782,17 791,18 779,06 770,89 825,14

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

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

DESVIO 12,4% 6,2% 2,9% 1,8% 1,6% 1,6% 0,1% 0,0% 5,4%

STATE-OF-THE-ART METHODSTan and Beasley (1984) - TBChristofides and Beasley (1984) - CBChao et al. (1995) - CGWCordeau et al. (1997) - CGLAlegre et al. (2007) - ALPHemmelmayr et al. (2007) - HDRBaldacci et al.(2011) - BLDVidal et al. (2012) - VDL

Results on benchmark instances.

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Benchmark instances testing:

CGL ALP HDR CGW VDL LB

Time (min) 4,28 3,64 3,34 10,36 5,56 3,00

STATE-OF-THE-ART METHODS

Cordeau et al. (1997) CGLAlegre et al. (2007) ALPHemmelmayr et al. (2007) HDRChao et al. (1995) CGWVidal et al. (2012) VDL

Source: Vidal et al. (2012)

Average computational cost in minutes

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Benchmark instances testing:

Fair results

Low computational costs

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Practical application: Solution method applied

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

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Adjustments:

Demand = service time

Restrictions = daily workload in mimutes

Travel time

Penalties for not using every “vehicle” daily

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Current method

Proposed method A

Proposed method B

Daily workload considered (min) 480,00 480,00 425,00

Total distance (km) 1.337,40 956,80 1.188,84

Savings (km) - 380,60 148,56

Savings (%) - 28,46 11,11

Current method

Proposed method A

Proposed method B

Daily workload considered 480,00 480,00 425,00

Daily workload proposed 346,00 324,25 337,51

Total service time 269,57 269,57 269,57

Total travel time 76,42 54,67 67,93

Total downtime 134,00 155,75 142,49

Minimum daily workload 195,46 15,39 35,65

Maximum daily workload 550,28 464,42 409,86

Standart deviation 75,41 167,49 87,02

Distance savings over planning period

Average daily workload composition per salesman (minutes).

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Initial findings:

Downtime awareness

Trade-off between savings and workload balancing

“How much does the workload balancing cost?”

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Estimated savingsProposed method A

Proposed method B

Time limit used 480,00 425,00

Saving per day and salesman (min) 21,75 8,49

Total savings per year (min) 39.585,73 15.453,98

Total savings per year (h) 659,76 257,57

Travel cost considering R$ 4,8/h 3.166,86 1.236,32

Labor cost considering R$ 7,5/h 4.948,22 1.931,75

Opportunity cost considering R$ 135,00/h 89.067,89 34.771,46

Estimated annual savings (R$) 97.182,96 37.939,53

.

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Current method Proposed method Savings

Week dayDistance

(Km)Workload

(Min)Distance

(Km)Workload

(Min)Distance Workload

monday 252,55 2.545,11 228,51 2.197,03 10% 14%

tuesday 246,03 2.427,06 221,08 2.542,16 10% -5%

wednesday 284,17 2.323,34 235,75 2.256,50 17% 3%

thursday 277,66 2.445,33 254,90 2.384,80 8% 2%

friday 277,02 2.369,04 248,59 2.432,19 10% -3%

Total 1.337,44 12.109,87 1.188,84 11.812,68 11% 2%

Comparisons between current solution method and proposed solution method

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Practical application: Solution method appliedMONDAY

CURRENT PROPOSED

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TUESDAY

CURRENT PROPOSED



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WEDNESDAY

CURRENT PROPOSED



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THURSDAY

CURRENT PROPOSED



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FRIDAY

CURRENT PROPOSED

Conclusions

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

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Future Research Directions

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

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Future Research Directions

Direct aproach for balancing

Spatial route clustering for each vehicle during

planning period

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THANK YOU!

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JOSÉ LASSANCE DE CASTRO SILVA <[email protected]>

FELIPE PINHEIRO BEZERRA <[email protected]>

CYTEDHAROSA 2012

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...

Documents

period vehicle routing

set of customers

plannig period

set of schedule options

e vidal

set of routes

new individuals

visit schedule