Milk-run routing problem with progress-lane in the collection of automobile parts

  • Zhaofang Mao
  • Dian Huang
  • Kan FangEmail author
  • Chengbo Wang
  • Dandan Lu
S.I.: RealCaseOR


In recent years, the automotive industry has faced an unprecedented crisis. In particular, the zero-inventory approach, which has been widely pursued by many automobile companies, seems to be impractical in some real production contexts since it requires an inventory of all parts but in low amounts. In this paper, we investigate a new logistics method which collects automobile parts by integrating the progress-lane (P-LANE) into the corresponding vehicle routing problem. We propose a mixed integer programming formulation for this new model, which can simultaneously determines the trip routes to collect automobile parts, as well as the P-LANE that each collected part should be assigned to, so as to minimize the total costs of the production and inbound logistics. The comparison with the zero-inventory model shows that the use of the P-LANE within the milk-run system could significantly decrease the total costs and also improve the transportation efficiency. To be specific, for small and large size instances, the total costs of the zero-inventory model are about 10% and 30% higher than the ones with P-LANE, respectively, which suggests that the periodic part collection model with P-LANE could be more appropriate for automobile manufacturing.


Milk-run system Vehicle routing problem Progress-lane Lean logistics 



The authors are grateful to the anonymous referees for their constructive comments and suggestions.


  1. Alnahhal, M., Ridwan, A., & Noche, B. (2014). In-plant milk run decision problems. Facilities, 35(22), 25–45.Google Scholar
  2. Benjamin, A. M., & Beasley, J. E. (2010). Metaheuristics for the waste collection vehicle routing problem with time windows, driver rest period and multiple disposal facilities. Computers & Operations Research, 37(12), 2270–2280.CrossRefGoogle Scholar
  3. Berman, O., & Wang, Q. (2006). Inbound logistic planning: Minimizing transportation and inventory cost. Transportation Science, 40(3), 287–299.CrossRefGoogle Scholar
  4. Bilgen, B., & Ozkarahan, I. (2004). Strategic tactical and operational production-distribution models: A review. International Journal of Technology Management, 28(2), 151–171.CrossRefGoogle Scholar
  5. Boysen, N., Emde, S., Hoeck, M., & Kauderer, M. (2015). Part logistics in the automotive industry: Decision problems, literature review and research agenda. European Journal of Operational Research, 242(1), 107–120.CrossRefGoogle Scholar
  6. Bramel, J., & Simchi-Levi, D. (1995). A location based heuristic for general routing problems. Operations Research, 43(4), 649–660.CrossRefGoogle Scholar
  7. Brar, G. S., & Saini, G. (2011). Milk run logistics: Literature review and directions. Proceedings of the World Congress on Engineering, 1, 6–8.Google Scholar
  8. Chen, C., Tian, Z., & Yao, B. (2019). Optimization of two-stage location-routing-inventory problem with time-windows in food distribution network. Annals of Operations Research, 273(1–2), 111–134.Google Scholar
  9. Chuah, K. H., & Yingling, J. C. (2005). Routing for a just-in-time supply pickup and delivery system. Transportation Science, 39(3), 328–339.CrossRefGoogle Scholar
  10. Du, T., Wang, F. K., & Lu, P.-Y. (2007). A real-time vehicle-dispatching system for consolidating milk runs. Transportation Research Part E: Logistics and Transportation Review, 43(5), 565–577.CrossRefGoogle Scholar
  11. El Fallahi, A., Prins, C., & Calvo, R. W. (2008). A memetic algorithm and a tabu search for the multi-compartment vehicle routing problem. Computers & Operations Research, 35(5), 1725–1741.CrossRefGoogle Scholar
  12. Federgruen, A., Queyranne, M., & Zheng, Y.-S. (1992). Simple power-of-two policies are close to optimal in a general class of production/distribution networks with general joint setup costs. Mathematics of Operations Research, 17(4), 951–963.CrossRefGoogle Scholar
  13. Gallego, G., & Simchi-Levi, D. (1990). On the effectiveness of direct shipping strategy for the one-warehouse multi-retailer R-systems. Management Science, 36(2), 240–243.CrossRefGoogle Scholar
  14. Gao, S., Qi, L., & Lei, L. (2015). Integrated batch production and distribution scheduling with limited vehicle capacity. International Journal of Production Economics, 160, 13–25.CrossRefGoogle Scholar
  15. Gendreau, M., Guertin, F., Potvin, J.-Y., & Séguin, R. (2006). Neighborhood search heuristics for a dynamic vehicle dispatching problem with pick-ups and deliveries. Transportation Research Part C: Emerging Technologies, 14(3), 157–174.CrossRefGoogle Scholar
  16. Henke, T., Speranza, M. G., & Wäscher, G. (2015). The multi-compartment vehicle routing problem with flexible compartment sizes. European Journal of Operational Research, 246(3), 730–743.CrossRefGoogle Scholar
  17. Hosseini, S. D., Shirazi, M. A., & Karimi, B. (2014). Cross-docking and milk run logistics in a consolidation network: A hybrid of harmony search and simulated annealing approach. Journal of Manufacturing Systems, 33(4), 567–577.CrossRefGoogle Scholar
  18. Jiang, Z., Huang, Y., & Wang, J. (2010). Routing for the milk-run pickup system in automobile parts supply. In Proceedings of the 6th CIRP-sponsored international conference on digital enterprise technology (pp. 1267–1275). SpringerGoogle Scholar
  19. Kilic, H. S., Durmusoglu, M. B., & Baskak, M. (2012). Classification and modeling for in-plant milk-run distribution systems. The International Journal of Advanced Manufacturing Technology, 62(9–12), 1135–1146.CrossRefGoogle Scholar
  20. Lahyani, R., Coelho, L. C., Khemakhem, M., Laporte, G., & Semet, F. (2015). A multi-compartment vehicle routing problem arising in the collection of olive oil in Tunisia. Omega, 51, 1–10.CrossRefGoogle Scholar
  21. Lapierre, S. D., & Ruiz, A. B. (2007). Scheduling logistic activities to improve hospital supply systems. Computers & Operations Research, 34(3), 624–641.CrossRefGoogle Scholar
  22. Lapierre, S. D., Ruiz, A. B., & Soriano, P. (2004). Designing distribution networks: Formulations and solution heuristic. Transportation Science, 38(2), 174–187.CrossRefGoogle Scholar
  23. Li, K., Jia, Z.-H., & Leung, J. Y.-T. (2015). Integrated production and delivery on parallel batching machines. European Journal of Operational Research, 247(3), 755–763.CrossRefGoogle Scholar
  24. Montoya-Torres, J. R., Franco, J. L., Isaza, S. N., Jiménez, H. F., & Herazo-Padilla, N. (2015). A literature review on the vehicle routing problem with multiple depots. Computers & Industrial Engineering, 79, 115–129.CrossRefGoogle Scholar
  25. Nemoto, T., Hayashi, K., & Hashimoto, M. (2010). Milk-run logistics by Japanese automobile manufacturers in Thailand. Procedia Social and Behavioral Sciences, 2(3), 5980–5989.CrossRefGoogle Scholar
  26. Nguyen, P. K., Crainic, T. G., & Toulouse, M. (2017). Multi-trip pickup and delivery problem with time windows and synchronization. Annals of Operations Research, 253(2), 899–934.CrossRefGoogle Scholar
  27. Patel, D., Patel, M. B., & Vadher, J. A. (2014). Implementation of milk run material supply system in vehicle routing problem with simultaneous pickup and delivery. International Journal of Application or Innovation in Engineering & Management, 3(11), 122–124.Google Scholar
  28. Qu, W. W., Bookbinder, J. H., & Iyogun, P. (1999). An integrated inventory-transportation system with modified periodic policy for multiple products. European Journal of Operational Research, 115(2), 254–269.CrossRefGoogle Scholar
  29. Sadjadi, S. J., Jafari, M., & Amini, T. (2009). A new mathematical modeling and a genetic algorithm search for milk run problem (an auto industry supply chain case study). The International Journal of Advanced Manufacturing Technology, 44(1–2), 194.CrossRefGoogle Scholar
  30. Sarmiento, A. M., & Nagi, R. (1999). A review of integrated analysis of production-distribution systems. IIE Transactions, 31(11), 1061–1074.Google Scholar
  31. Sitek, P., & Wikarek, J. (2019). Capacitated vehicle routing problem with pick-up and alternative delivery (CVRPPAD): Model and implementation using hybrid approach. Annals of Operations Research, 273(1–2), 257–277.CrossRefGoogle Scholar
  32. Staab, T., Klenk, E., Galka, S., & Günthner, W. A. (2016). Efficiency in in-plant milk-run systems—The influence of routing strategies on system utilization and process stability. Journal of Simulation, 10(2), 137–143.CrossRefGoogle Scholar
  33. Talbi, E.-G. (2009). Metaheuristics: From design to implementation (Vol. 74). New York: Wiley.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Management and EconomicsTianjin UniversityTianjinChina
  2. 2.Business SchoolOxford Brookes UniversityOxfordUK

Personalised recommendations