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Comparative Analysis for Clustering Based Optimal Vehicle Routes Planning

클러스터링 기반의 최적 차량 운행 계획 수립을 위한 비교연구

  • Received : 2020.08.05
  • Accepted : 2020.08.25
  • Published : 2020.08.30

Abstract

It takes the most important role the problem of assigining vehicles and desigining optimal routes for each vehicle in order to enhance the logistics service level. While solving the problem, various cost factors such as number of vehicles, the capacity of vehicles, total travelling distance, should be considered at the same time. Although most of logistics service providers introduced the Transportation Management System (TMS), the system has the limitation which can not consider the practical constraints. In order to make the solution of TMS applicable, it is required experts revised the solution of TMS based on their own experience and intuition. In this research, different from previous research which have focused on minimizing the total cost, it has been proposed the methodology which can enhance the efficiency and fairness of asset utilization, simultaneously. First of all, it has been adopted the Cluster-First Route-Second (CFRS) approach. Based on the location of customers, we have grouped customers as clusters by using four different clustering algorithm such as K-Means, K-Medoids, DBSCAN, Model-based clustering and a procedural approach, Fisher & Jaikumar algorithm. After getting the result of clustering, it has been developed the optiamal vehicle routes within clusters. Based on the result of numerical experiments, it can be said that the propsed approach based on CFRS may guarantee the better performance in terms of total travelling time and distance. At the same time, the variance of travelling distance and number of visiting customers among vehicles, it can be concluded that the proposed approach can guarantee the better performance of assigning tasks in terms of fairness.

화물의 수배송을 위한 차량의 배차 및 최적 경로 설계는 물류 서비스의 효율성 향상을 위한 가장 핵심적인 역할을 담당한다. 이 문제는 차량의 대수, 차량별 적재 용량, 차량의 총 이동거리와 같이 다양한 비용 요소를 동시에 고려해야 하기 때문이다. 최근 비용 최소화 및 운영 효율성 향상을 위해 TMS를 도입하는 사례가 증가하고 있으나, 현장에서 필요한 모든 요소를 고려하지 못한다는 한계가 존재한다. 이를 해결하기 위해 현장 전문가가 TMS의 결과를 경험과 직관에 기반하여 수정하는 과정이 필요하다. 본 연구에서는 지금까지 총 비용의 최소화에 집중하고 있는 기존 연구들과 달리 서비스에 투입되는 자원 활용의 효율성과 형평성을 동시에 높일 수 있는 방법을 제안한다. 이를 위해 Cluster-First Route-Second (CFRS)기법을 활용한다. 고객의 위치를 기준으로 네 가지 클러스터링 알고리즘(K-Means, K-Medoids, DBSCAN, Model-based)과 Fisher & Jaikumar 알고리즘을 적용하여 고객들을 군집화하였다. 이 후, 군집별 최적의 차량 경로 계획을 수립하였다. 수치 실험을 통해 본 연구에서 제안하는 CFRS 기법을 적용한 방안이 상대적으로 차량의 전체 이동거리와 평균 이동거리 및 이동시간이 더 절감될 수 있다는 사실을 확인하였다. 또한, 차량별 방문하는 고객의 수에 대한 편차가 더 낮다는 사실로부터 기본적인 차량 경로 배정 유형에 비해 본 연구에서 제안하는 방안이 상대적으로 형평성 있게 업무가 할당되었음을 확인할 수 있었다.

Keywords

References

  1. 김지수(2014). Refuse collection network design and vehicle routing in reverse logistics, 박사학위논문. 한양대학교 대학원.
  2. 나유진, 임현우, 문정민(2016). 시간대별 도로교통 상황을 고려한 도심 식자재 배송서비스 개선 방안에 관한 연구. 로지스틱스연구, 24(4), 79-97. https://doi.org/10.15735/KLS.2016.24.4.006
  3. Ai, T. J. & Kachitvichyanukul, V. (2009). A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery. Computers & Operations Research, 36(5), 1693-1702. https://doi.org/10.1016/j.cor.2008.04.003
  4. Amini, S., Gerostathopoulos, I. & Prehofer, C. (2017). Big data analytics architecture for real-time traffic control., 710-715.
  5. Badeau, P., Guertin, F., Gendreau, M., Potvin, J. & Taillard, E. (1997). A parallel tabu search heuristic for the vehicle routing problem with time windows. Transportation Research Part C: Emerging Technologies, 5(2), 109-122. https://doi.org/10.1016/S0968-090X(97)00005-3
  6. Baker, B. M. & Ayechew, M. (2003). A genetic algorithm for the vehicle routing problem. Computers & Operations Research, 30(5), 787-800. https://doi.org/10.1016/S0305-0548(02)00051-5
  7. Baldacci, R., Mingozzi, A. & Roberti, R. (2012). Recent exact algorithms for solving the vehicle routing problem under capacity and time window constraints. European Journal of Operational Research, 218(1), 1-6. https://doi.org/10.1016/j.ejor.2011.07.037
  8. Bast, H., Delling, D., Goldberg, A., Muller-Hannemann, M., Pajor, T., Sanders, P., Wagner, D. & Werneck, R. F. (2016). Route planning in transportation networks., 19-80.
  9. Beasley, J. E. (1983). Route first-cluster second methods for vehicle routing. Omega, 11(4), 403-408. https://doi.org/10.1016/0305-0483(83)90033-6
  10. Calvete, H. I., Gale, C., Oliveros, M. & Sanchez-Valverde, B. (2007). A goal programming approach to vehicle routing problems with soft time windows. European Journal of Operational Research, 177(3), 1720-1733. https://doi.org/10.1016/j.ejor.2005.10.010
  11. Charrad, M., Ghazzali, N., Boiteau, V., Niknafs, A. & Charrad, M. M. (2014). Package 'NbClust'. J.Stat.Soft, 61, 1-36.
  12. Chen, J. & Wu, T. (2006). Vehicle routing problem with simultaneous deliveries and pickups. Journal of the Operational Research Society, 57(5), 579-587. https://doi.org/10.1057/palgrave.jors.2602028
  13. Chun-Hua, L., Hong, Z. & Jian, Z. (2009). Vehicle routing problem with time windows and simultaneous pickups and deliveries., 685-689.
  14. Cordeau, J., Gendreau, M. & Laporte, G. (1997). A tabu search heuristic for periodic and multi‐depot vehicle routing problems. Networks, 30(2), 105-119. https://doi.org/10.1002/(sici)1097-0037(199709)30:2<105::aid-net5>3.0.co;2-g
  15. Cordeau, J., Gendreau, M., Laporte, G., Potvin, J. & Semet, F. (2002). A guide to vehicle routing heuristics. Journal of the Operational Research society, 512-522.
  16. Dantzig, G., Fulkerson, R. & Johnson, S. (1954). Solution of a large-scale traveling-salesman problem. Journal of the operations research society of America, 2(4), 393-410. https://doi.org/10.1287/opre.2.4.393
  17. Davies, D. L. & Bouldin, D. W. (1979). A cluster separation measure. IEEE Transactions on Pattern Analysis and Machine Intelligence(2), 224-227.
  18. De Jaegere, N., Defraeye, M. & Van Nieuwenhuyse, I. (2014). The vehicle routing problem: state of the art classification and review.
  19. Dempster, A. P., Laird, N. M. & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the royal statistical society.Series B (methodological), 1-38.
  20. Dondo, R. & Cerda, J. (2007). A cluster-based optimization approach for the multi-depot heterogeneous fleet vehicle routing problem with time windows. European Journal of Operational Research, 176(3), 1478-1507. https://doi.org/10.1016/j.ejor.2004.07.077
  21. Ester, M., Kriegel, H., Sander, J. & Xu, X. (1996). A density-based algorithm for discovering clusters in large spatial databases with noise., 96(34), 226-231.
  22. Feng, L., Ong, Y., Chen, C. & Chen, X. (2016). Conceptual modeling of evolvable local searches in memetic algorithms using linear genetic programming: a case study on capacitated vehicle routing problem. Soft Computing, 20(9), 3745- 3769. https://doi.org/10.1007/s00500-015-1971-3
  23. Fisher, M. L. & Jaikumar, R. (1981). A generalized assignment heuristic for vehicle routing. Networks, 11(2), 109-124. https://doi.org/10.1002/net.3230110205
  24. Fraley, C. & Raftery, A. E. (1998). How many clusters? Which clustering method? Answers via model-based cluster analysis. The computer journal, 41(8), 578-588. https://doi.org/10.1093/comjnl/41.8.578
  25. Fraley, C. & Raftery, A. E. (2002). Model-based clustering, discriminant analysis, and density estimation. Journal of the American statistical Association, 97(458), 611-631. https://doi.org/10.1198/016214502760047131
  26. Gendreau, M., Hertz, A. & Laporte, G. (1994). A tabu search heuristic for the vehicle routing problem. Management science, 40(10), 1276-1290. https://doi.org/10.1287/mnsc.40.10.1276
  27. Gendreau, M., Laporte, G., Musaraganyi, C. & Taillard, .. D. (1999). A tabu search heuristic for the heterogeneous fleet vehicle routing problem. Computers & Operations Research, 26(12), 1153-1173. https://doi.org/10.1016/S0305-0548(98)00100-2
  28. Gillett, B. E. & Miller, L. R. (1974). A heuristic algorithm for the vehicle-dispatch problem. Operations research, 22(2), 340-349. https://doi.org/10.1287/opre.22.2.340
  29. Goetschalckx, M. & Jacobs-Blecha, C. (1989). The vehicle routing problem with backhauls. European Journal of Operational Research, 42(1), 39-51. https://doi.org/10.1016/0377-2217(89)90057-X
  30. Gounaris, C. E., Wiesemann, W. & Floudas, C. A. (2013). The robust capacitated vehicle routing problem under demand uncertainty. Operations research, 61(3), 677-693. https://doi.org/10.1287/opre.1120.1136
  31. Grangier, P., Gendreau, M., Lehuede, F. & Rousseau, L. (2016). An adaptive large neighborhood search for the two-echelon multiple-trip vehicle routing problem with satellite synchronization. European Journal of Operational Research, 254(1), 80-91. https://doi.org/10.1016/j.ejor.2016.03.040
  32. Gurobi Optimization, I. (2016). Gurobi Optimizer Reference Manual; 2015. URL http://www.gurobi.com.
  33. Han, J., Pei, J. & Kamber, M. (2011). Data mining: concepts and techniques. Elsevier.
  34. Hernandez, F., Feillet, D., Giroudeau, R. & Naud, O. (2016). Branch-and-price algorithms for the solution of the multi-trip vehicle routing problem with time windows. European Journal of Operational Research, 249(2), 551-559. https://doi.org/10.1016/j.ejor.2015.08.040
  35. Iassinovskaia, G., Limbourg, S. & Riane, F. (2017). The inventory-routing problem of returnable transport items with time windows and simultaneous pickup and delivery in closed-loop supply chains. International Journal of Production Economics, 183, 570-582. https://doi.org/10.1016/j.ijpe.2016.06.024
  36. Imran, A., Salhi, S. & Wassan, N. A. (2009). A variable neighborhood-based heuristic for the heterogeneous fleet vehicle routing problem. European Journal of Operational Research, 197(2), 509-518. https://doi.org/10.1016/j.ejor.2008.07.022
  37. Irnich, S. (2000). A multi-depot pickup and delivery problem with a single hub and heterogeneous vehicles. European Journal of Operational Research, 122(2), 310-328. https://doi.org/10.1016/S0377-2217(99)00235-0
  38. Jepsen, M., Spoorendonk, S. & Ropke, S. (2013). A branch-and-cut algorithm for the symmetric two-echelon capacitated vehicle routing problem. Transportation Science, 47(1), 23-37. https://doi.org/10.1287/trsc.1110.0399
  39. Jin, J., Crainic, T. G. & Lokketangen, A. (2014). A cooperative parallel metaheuristic for the capacitated vehicle routing problem. Computers & Operations Research, 44, 33-41. https://doi.org/10.1016/j.cor.2013.10.004
  40. Karadimas, N. V., Doukas, N., Kolokathi, M. & Defteraiou, G. (2008). Routing optimization heuristics algorithms for urban solid waste transportation management. WSEAS Transaction on Computers, 7(12), 2022-2031.
  41. Kaufman, L. & Rousseeuw, P. (1987). Clustering by means of medoids. North-Holland.
  42. Ko, H. J. & Evans, G. W. (2007). A genetic algorithm-based heuristic for the dynamic integrated forward/reverse logistics network for 3PLs. Computers & Operations Research, 34(2), 346-366. https://doi.org/10.1016/j.cor.2005.03.004
  43. Koc, C. & Karaoglan, I. (2016). The green vehicle routing problem: A heuristic based exact solution approach. Applied Soft Computing, 39, 154-164. https://doi.org/10.1016/j.asoc.2015.10.064
  44. Land, A. H. & Doig, A. G. (2010). An automatic method for solving discrete programming problems. 50 Years of Integer Programming 1958-2008, 105-132.
  45. Li, F., Golden, B. & Wasil, E. (2007). A record-to-record travel algorithm for solving the heterogeneous fleet vehicle routing problem. Computers & Operations Research, 34(9), 2734-2742. https://doi.org/10.1016/j.cor.2005.10.015
  46. Lim, A. & Wang, F. (2005). Multi-depot vehicle routing problem: A one-stage approach. IEEE transactions on Automation Science and Engineering, 2(4), 397-402. https://doi.org/10.1109/TASE.2005.853472
  47. Lysgaard, J. & Wohlk, S. (2014). A branchand- cut-and-price algorithm for the cumulative capacitated vehicle routing problem. European Journal of Operational Research, 236(3), 800-810. https://doi.org/10.1016/j.ejor.2013.08.032
  48. Michael, R. G. & David, S. J. (1979). Computers and intractability: a guide to the theory of NP-completeness. WH Free.Co., San Fr, 90-91.
  49. Mittal, P. & Singh, Y. (2016). Development of intelligent transportation system for improving average moving and waiting time with artificial intelligence. Indian Journal of Science and Technology, 9(3).
  50. Nagy, G. & Salhi, S. (2005). Heuristic algorithms for single and multiple depot vehicle routing problems with pickups and deliveries. European Journal of Operational Research, 162(1), 126-141. https://doi.org/10.1016/j.ejor.2002.11.003
  51. Ombuki, B., Ross, B. J. & Hanshar, F. (2006). Multi-objective genetic algorithms for vehicle routing problem with time windows. Applied Intelligence, 24(1), 17-30. https://doi.org/10.1007/s10489-006-6926-z
  52. Penna, P. H. V., Subramanian, A. & Ochi, L. S. (2013). An iterated local search heuristic for the heterogeneous fleet vehicle routing problem. Journal of Heuristics, 1-32.
  53. Potvin, J., Duhamel, C. & Guertin, F. (1996). A genetic algorithm for vehicle routing with backhauling. Applied Intelligence, 6(4), 345-355. https://doi.org/10.1007/BF00132738
  54. Reed, M., Yiannakou, A. & Evering, R. (2014). An ant colony algorithm for the multi-compartment vehicle routing problem. Applied Soft Computing, 15, 169-176. https://doi.org/10.1016/j.asoc.2013.10.017
  55. Renaud, J., Laporte, G. & Boctor, F. F. (1996). A tabu search heuristic for the multi-depot vehicle routing problem. Computers & Operations Research, 23(3), 229-235. https://doi.org/10.1016/0305-0548(95)O0026-P
  56. Rivera, J. C., Afsar, H. M. & Prins, C. (2016). Mathematical formulations and exact algorithm for the multitrip cumulative capacitated single-vehicle routing problem. European Journal of Operational Research, 249(1), 93-104. https://doi.org/10.1016/j.ejor.2015.08.067
  57. Roodbergen, K. J. & De Koster, R. (2001). Routing order pickers in a warehouse with a middle aisle. European Journal of Operational Research, 133(1), 32-43. https://doi.org/10.1016/S0377-2217(00)00177-6
  58. Rousseeuw, P. J. (1987). Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics, 20, 53-65. https://doi.org/10.1016/0377-0427(87)90125-7
  59. Ryan, D. M., Hjorring, C. & Glover, F. (1993). Extensions of the petal method for vehicle routeing. Journal of the Operational Research Society, 289-296.
  60. Savelsbergh, M. W. (1992). The vehicle routing problem with time windows: Minimizing route duration. ORSA journal on computing, 4(2), 146-154. https://doi.org/10.1287/ijoc.4.2.146
  61. Scott, A. J. & Symons, M. J. (1971). Clustering methods based on likelihood ratio criteria. Biometrics, 387-397.
  62. Subramanian, A., Penna, P. H. V., Uchoa, E. & Ochi, L. S. (2012). A hybrid algorithm for the heterogeneous fleet vehicle routing problem. European Journal of Operational Research, 221(2), 285-295. https://doi.org/10.1016/j.ejor.2012.03.016
  63. Taillard, E., Badeau, P., Gendreau, M., Guertin, F. & Potvin, J. (1997). A tabu search heuristic for the vehicle routing problem with soft time windows. Transportation science, 31(2), 170-186. https://doi.org/10.1287/trsc.31.2.170
  64. Taş, D., Gendreau, M., Dellaert, N., Van Woensel, T. & De Kok, A. (2014). Vehicle routing with soft time windows and stochastic travel times: A column generation and branch-and-price solution approach. European Journal of Operational Research, 236(3), 789-799. https://doi.org/10.1016/j.ejor.2013.05.024
  65. Tibshirani, R., Walther, G. & Hastie, T. (2001). Estimating the number of clusters in a data set via the gap statistic. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 63(2), 411-423. https://doi.org/10.1111/1467-9868.00293
  66. Wei, L., Zhang, Z., Zhang, D. & Leung, S. C. (2017). A simulated annealing algorithm for the capacitated vehicle routing problem with two-dimensional loading constraints. European Journal of Operational Research.
  67. Yao, B., Yu, B., Hu, P., Gao, J. & Zhang, M. (2016). An improved particle swarm optimization for carton heterogeneous vehicle routing problem with a collection depot. Annals of Operations Research, 242(2), 303-320. https://doi.org/10.1007/s10479-015-1792-x
  68. Yu, B., Yang, Z. & Yao, B. (2009). An improved ant colony optimization for vehicle routing problem. European Journal of Operational Research, 196(1), 171-176. https://doi.org/10.1016/j.ejor.2008.02.028