Blockage-Free Route Planning for In-Plant Milk-Run Material Delivery Systems

  • Grzegorz BocewiczEmail author
  • Izabela Nielsen
  • Zbigniew Banaszak
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 241)


In this chapter, two kinds of intertwined decisions regarding the movement of vehicles in an in-plant milk-run delivery system are considered: routing decisions, which determine the set of sequences of stations visited by each tugger train, and scheduling decisions, which plan congestion free movement of the tugger trains. The problem under study, called the Multi Trip and Multi Cycle Pick-up and Delivery Problem with Time Windows and Congestion Free Traffic, can be viewed as an extension of the pick-up and delivery problem with time windows in which multiple tugger trains travel along closed-loop congestion-free routes in different cycles. A declarative model of the investigated milk-run delivery principle makes it possible to formulate a vehicle routing and scheduling problem the solution to which determines the route, the time schedule, and the type and number of parts that the different trucks must carry to fulfill orders from various customers/recipients. Due to the requirement of congestion-free milk-run traffic, a scheduling period slicing principle allowing to synchronize cyclic flows of different periods is applied. Its implementation, resulting in a cyclic schedule composed of quasi cyclic sub-schedules, implies a recursive formulation of a well-known constraint satisfaction problem. The goal is to find solutions that can minimize both vehicle downtime and the takt time of the production flow. Computer experiments illustrate the possibility of using the present approach in real-life systems.


  1. 1.
    Badica, A., Badica, C., Leon, F., Luncean, L.: Declarative representation and solution of vehicle routing with pickup and delivery problem. Proc. Comput.Sci. 108, 958–967 (2017)CrossRefGoogle Scholar
  2. 2.
    Bocewicz G., Nielsen P., Banaszak Z., Thibbotuwawa A.: Routing and scheduling of Unmanned Aerial Vehicles subject to cyclic production flow constraints. In: Proceedings of 15th International Conference on Distributed Computing and Artificial Intelligence (2018)Google Scholar
  3. 3.
    Bocewicz, G., Nielsen, P., Banaszak, Z.: Declarative modeling of milk-run vehicle routing problem for split and merge supply streams scheduling. Adv. Intell. Syst. Comput. 853, 157–172 (2019)Google Scholar
  4. 4.
    Bocewicz, G., Banaszak, Z., Nielsen, I.: Delivery-flow routing and scheduling subject to constraints imposed by vehicle flows in fractal-like networks. Arch. Control Sci. 27(2), 135–150 (2017)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Bocewicz G., Nielsen P., Banaszak Z., Wojcik R.: An analytical modeling approach to cyclic scheduling of multiproduct batch production flows subject to demand and capacity constraints. In: Świątek, J., Borzemski, L., Wilimowska, Z. (eds.) Information Systems Architecture and Technology: Proceedings of 38th International Conference on Information Systems Architecture and Technology — ISAT 2017. Springer, Cham (2017)Google Scholar
  6. 6.
    Carić, T., Galić, A., Fosin, J., Gold, H., Reinholz, A.: A Modelling and Optimization Framework for Real-World Vehicle Routing Problems Vehicle Routing Problem. In: Caric, T., Gold, H. (eds.) Vehicle Routing Problem, pp. 15–34. I-Tech, Vienna, Austria (2008)CrossRefGoogle Scholar
  7. 7.
    Goetschalck, M., Jacobs-Blecha, C.: The vehicle routing problem with backhauls. Eur. J. Oper. Res. 42(1), 39–51 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Gola, A., Kłosowski, G.: Application of fuzzy logic and genetic algorithms in automated works transport organization. In: Omatu, S., Rodríguez, S., Villarrubia, G., Faria, P., Sitek, P., Prieto, J. (eds.) Distributed Computing and Artificial Intelligence, 14th International Conference DCAI 2017, pp. 29–36. Springer, Cham (2018)Google Scholar
  9. 9.
    Güner, A.R., Murat, A., Chinnam, R.B.: Dynamic routing for milk-run tours with time windows in stochastic time-dependent networks. Transp. Res. Part E: Logist. Transp. Rev. 97, 251–267 (2017)CrossRefGoogle Scholar
  10. 10.
    Gyulaia D., Pfeiffer A., Sobottka T., Váncza J.: Milkrun Vehicle Routing Approach for Shop-floor Logistics. In: Forty Sixth CIRP Conference on Manufacturing Systems 2013, Procedia CIRP, vol. 7, pp. 127–132 (2013)CrossRefGoogle Scholar
  11. 11.
    Kitamura T., Okamoto K.: Automated route planning for milk-run transport logistics with NuSMV model checker. IEICE Trans. Inf. Syst. E96-D(12), 2555–2564 (2013)Google Scholar
  12. 12.
    Levner E., Kats V., Alcaide D., Pablo L. Cheng T.C.E: Complexity of cyclic scheduling problems: a state-of-the-art survey. Comput. Ind. Eng. 59(2), 352–361 (2010)CrossRefGoogle Scholar
  13. 13.
    Lau, H., Sim, M., Teo, K.: Vehicle routing problem with time windows and a limited number of vehicles. Eur. J. Oper. Res. 148(3), 559–569 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Lenstra J.K., Rinnooy Kan A.H.G: Complexity of vehicle and scheduling problems. Networks 11(2), 221–227 (1981)CrossRefGoogle Scholar
  15. 15.
    Nguyen, P.K., Crainic, T.G., Toulouse, M.: Multi-trip pickup and delivery problem with time windows and synchronization. Ann. Oper. Res. 253(2), 899–934 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Ong, J.O.: Suprayogi: vehicle routing problem with backhaul, multiple trips and time window. Jurnal Teknik Industri 13(1), 1–10 (2011)CrossRefGoogle Scholar
  17. 17.
    Patel, D., Patel, M.B., Vadher, J.A.: Implementation of milk run material supply system in vehicle routing problem with simultaneous pickup and delivery. Int. J. Appl. Innov. Eng. Manag. 3(11), 122–124 (2014)Google Scholar
  18. 18.
    Perronnet F., Abbas-Turki A., El Moudni A.: Vehicle routing through deadlock-free policy for cooperative traffic control in a network of intersections: reservation and congestion. In: 17th International IEEE Conference on Intelligent Transportation Systems (ITSC), Qingdao, 8–11 Octomber 2014, pp. 2233–2238. IEEE (2014)Google Scholar
  19. 19.
    Pillac, V., Gendreau, M., Guéret, C., Medaglia, A.L.: A review of dynamic vehicle routing problems. Eur. J. Oper. Res. 225(1), 1–11 (2013)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Polak, M., Majdzik, P., Banaszak, Z., Wójcik, R.: The performance evaluation tool for automated prototyping of concurrent cyclic processes. Fundam. Inf. 60(1), 269–289 (2004)MathSciNetzbMATHGoogle Scholar
  21. 21.
    Sun S., Gu C., Wan Q., Huang H., Jia X.: CROTPN based collision-free and deadlock-free path planning of AGVs in logistic center. In: Procedings of the 15th International Conference on Control, Automation, Robotics and Vision (ICARCV), Singapore, 18–21 Nov 2018, pp. 1685–1691. IEEE (2018)Google Scholar
  22. 22.
    Schmidt T., Meinhardt I., Schulze F.: New design guidelines for in-plant milk-run systems (2016). Accessed 29 Mar 2019
  23. 23.
    Setiani P., Fiddieny H., Setiawan E.B., Cahyanti D.E.: Optimizing delivery route by applying milkrun method. In: Conference on Global Research on Sustainable Transport (GROST 2017). Advances in Engineering Research, vol. 147, pp. 748–757 (2017)Google Scholar
  24. 24.
    Sitek P., Wikarek J.: Capacitated vehicle routing problem with pick-up and alternative delivery (CVRPPAD): model and implementation using hybrid approach. Ann. Oper. Res. 273, 257–277 (2001)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Suprayogi, Priyandari Y.: Vehicle routing problem with multiple trips, time windows, and simultaneous delivery and pickup services. Asia Pac. Ind. Eng. Manag. Syst. 8, 1543–1552 (2009)Google Scholar
  26. 26.
    Witczak, M., Majdzik, P., Stetter, R., Bocewicz, G.: Interval max-plus fault-tolerant control under resource conflicts and redundancies: application to the seat assembly. International Journal of Control (2019). in printGoogle Scholar
  27. 27.
    Wysk, R.A., Yang, N.-S., Joshi, S.: Resolution of deadlocks in flexible manufacturing systems: avoidance and recovery approaches. J. Manuf. Syst. 13(2), 128–138 (1994)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Faculty of Electronics and Computer ScienceKoszalin University of TechnologyKoszalinPoland
  2. 2.Department of Materials and ProductionAalborg UniversityAalborg ØstDenmark

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