1. A GENETIC ALGORITHM FOR PERIOD VEHICLE ROUTING PROBLEM WITH PRACTICAL APPLICATION JOSÉ LASSANCE DE CASTRO SILVA FELIPE PINHEIRO BEZERRA CYTEDHAROSA 2012 1 UNIVERSIDADE FEDERAL DO CEARÁ PRÓ-REITORIA DE PESQUISA E PÓS-GRADUAÇÃO PROGRAMA DE MESTRADO EM LOGÍSTICA E PESQUISA OPERACIONAL

2. Outline  Motivating Problem  Problem Definition  Solution Method Aproach  Computational Experiments  Conclusions and Future Research Directions

3. Motivating Problem Practical application:  Wholesaler Distributor  Ice cream and ice pops division  Sales team  Marketing mix:  Product  Pricing  Promotion  Placement 3

4. 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 4

5. Motivating Problem Practical application: Current solution method 5

6. Motivating Problem Practical application: Current solution method  Advantages:  Out of route serving  Intuitive inclusion of new customers  Sales representative´s familiarity with territory 6

7. 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 7

8. 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 workload 8

9. 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. 9

10. The Periodic Vehicle Routing Problem (PVRP) (BALDACCI et al., 2011) 10 1 vehicle 30 units of capacity

11.  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: 11 The Periodic Vehicle Routing Problem (PVRP) It´s a generalization of the VRP: NP-Hard.

12. Solution Method Aproach Genetic Algorithms: Concepts  Holland (1975)  Metaheuristic  Natural selection  Population based  Cromossomes/individuals  Recombinations  Fitness 12

13. 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 13

14. Solution Method Aproach Genetic Algorithms: Key points  Solution representation  Fitness function  Population control  Selection method  Genetic operators  Use of hibridization  Stop criteria  Parameters definition 14

15. 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) 15

16. Solution Method Aproach Proposed genetic algorithm:  Individuals evaluation: Split algorithm (PRINS 2004) (PRINS, 2004) 16

17. Solution Method Aproach Proposed genetic algorithm:  Original crossover operator CustomerService freq.Schedule combinations 13{Day1, Day3, Day4}, {Day2, Day3, Day4} 22{Day1,Day3}, {Day2, Day4} 31{Day1}, {Day4} 41{Day1} 51{Day1}, {Day2} 63{Day2, Day3, Day4}, {Day1, Day2, Day3}, {Day1, Day2, Day4} 72{Day1,Day3}, {Day2, Day4} 81{Day2}, {Day3} 17

18. Computational experiments Benchmark instances testing: NOMETBCBCGWCGLALPHDHBDCVDL (z*)LB p01547,40524,60524,61531,02524,61 590,90 p021.481,301.443,101.337,201.330,091.324,741.332,011.322,87 1.373,15 p03546,70524,60524,61537,37528,97524,61 619,22 p04843,90860,90837,93845,97847,48835,26 988,10 p052.192,502.187,302.089,002.061,362.043,752.059,742.027,992.024,962.089,17 p06938,20881,10840,30840,10884,69835,26 1.057,21 p07839,20832,00829,45829,65829,92825,14826,14862,78 p082.281,802.151,302.075,102.054,902.052,212.058,362.034,152.022,472.098,81 p09875,00829,90829,45829,65834,92826,14 881,42 p101.833,701.674,001.633,201.629,581.621,211.629,761.593,451.593,431.697,88 p11878,50847,30791,30817,56782,17791,18779,06770,89825,14 p121.237,401.239,581.230,951.258,461.186,471.308,86 p133.629,803.602,763.835,903.492,89 p14954,81 p151.862,601.862,63 1.864,52 p162.875,202.875,24 2.891,50 p171.614,401.597,75 1.601,751.597,75 p183.217,703.159,223.157,003.147,003.136,693.131,093.183,93 p194.846,504.902,644.846,494.851,414.834,34 4.945,63 p208.367,40 8.412,028.367,40 8.776,81 p212.216,102.184,042.173,582.180,332.170,61 2.200,90 p224.436,404.307,194.330,594.218,464.193,95 4.416,00 p236.769,006.620,506.813,456.644,936.420,717.113,13 p243.773,003.704,113.702,023.704,603.687,46 3.748,45 p253.826,003.781,38 3.777,15 3.781,38 p263.834,003.795,323.795,333.795,32 3.810,61 p2723.401,6023.017,4522.561,3322.153,3121.912,8521.833,8722.378,36 p2823.105,1022.569,4022.562,4422.418,5222.242,51 22.693,78 p2924.248,2024.012,9223.752,1522.864,2322.543,7622.543,7523.021,93 p3080.982,1077.179,3376.793,9975.579,2374.464,2673.875,1976.639,43 p3180.279,1079.382,3577.944,7977.459,1476.322,0476.001,5778.309,61 p3283.838,7080.908,9581.055,5279.487,9778.072,8877.598,0080.756,82 DESVIO12,4%6,2%2,9%1,8%1,6% 0,1%0,0%5,4% 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 Results on benchmark instances. 18

19. Computational experiments Benchmark instances testing: CGLALPHDRCGWVDLLB Time (min)4,283,643,3410,365,563,00 STATE-OF-THE-ART METHODS Cordeau et al. (1997)CGL Alegre et al. (2007)ALP Hemmelmayr et al. (2007)HDR Chao et al. (1995)CGW Vidal et al. (2012) VDL Source: Vidal et al. (2012) Average computational cost in minutes 19

20. Computational experiments Benchmark instances testing:  Fair results  Low computational costs 20

21. Computational experiments 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 21

22. Computational experiments Practical application: Solution method applied 22

23. Computational experiments Practical application: Solution method applied  Adjustments:  Demand = service time  Restrictions = daily workload in mimutes  Travel time  Penalties for not using every “vehicle” daily 23

24. Computational experiments Practical application: Solution method applied Current method Proposed method A Proposed method B Daily workload considered (min)480,00 425,00 Total distance (km)1.337,40956,801.188,84 Savings (km)-380,60148,56 Savings (%)-28,4611,11 Current method Proposed method A Proposed method B Daily workload considered480,00 425,00 Daily workload proposed346,00324,25337,51 Total service time269,57 Total travel time76,4254,6767,93 Total downtime134,00155,75142,49 Minimum daily workload195,4615,3935,65 Maximum daily workload550,28464,42409,86 Standart deviation75,41167,4987,02 Distance savings over planning period Average daily workload composition per salesman (minutes). 24

25. Computational experiments Practical application: Solution method applied  Initial findings:  Downtime awareness  Trade-off between savings and workload balancing  “How much does the workload balancing cost?” 25

26. Computational experiments Practical application: Solution method applied Estimated savings Proposed method A Proposed method B Time limit used480,00425,00 Saving per day and salesman (min)21,758,49 Total savings per year (min)39.585,7315.453,98 Total savings per year (h)659,76257,57 Travel cost considering R$ 4,8/h3.166,861.236,32 Labor cost considering R$ 7,5/h4.948,221.931,75 Opportunity cost considering R$ 135,00/h89.067,8934.771,46 Estimated annual savings (R$)97.182,9637.939,53. 26

27. Computational experiments Practical application: Solution method applied Current methodProposed methodSavings Week day Distance (Km) Workload (Min) Distance (Km) Workload (Min) DistanceWorkload monday252,552.545,11228,512.197,0310%14% tuesday246,032.427,06221,082.542,1610%-5% wednesday284,172.323,34235,752.256,5017%3% thursday277,662.445,33254,902.384,808%2% friday277,022.369,04248,592.432,1910%-3% Total1.337,4412.109,871.188,8411.812,6811%2% Comparisons between current solution method and proposed solution method 27

28. Computational experiments Practical application: Solution method applied MONDAY CURRENTPROPOSED 28

29. Computational experiments Practical application: Solution method applied 29 TUESDAY CURRENTPROPOSED

30. Computational experiments Practical application: Solution method applied 30 WEDNESDAY CURRENTPROPOSED

31. Computational experiments Practical application: Solution method applied 31 THURSDAY CURRENTPROPOSED

32. Computational experiments Practical application: Solution method applied 32 FRIDAY CURRENTPROPOSED

33. 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 33

34. 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 34

35. Future Research Directions  Direct aproach for balancing  Spatial route clustering for each vehicle during planning period 35

36. THANK YOU! 36 JOSÉ LASSANCE DE CASTRO SILVA FELIPE PINHEIRO BEZERRA CYTEDHAROSA 2012 UNIVERSIDADE FEDERAL DO CEARÁ PRÓ-REITORIA DE PESQUISA E PÓS-GRADUAÇÃO PROGRAMA DE MESTRADO EM LOGÍSTICA E PESQUISA OPERACIONAL