Skip to main content
Log in

Integrated planning of loaded and empty container movements

  • Regular Article
  • Published:
OR Spectrum Aims and scope Submit manuscript

Abstract

Efficiently planning drayage operations is an important task for transportation companies since these operations constitute a large part of the cost of an intermodal transport. In this paper, a full truckload vehicle routing problem for transporting loaded and empty containers in drayage operations is studied. For empty container transports, either the origin or the destination is not predefined. The problem is formulated as an asymmetric multiple vehicle Travelling Salesman Problem with Time Windows (am-TSPTW). Two solution approaches are proposed: a sequential and an integrated approach. For both approaches, a single- and a two-phase deterministic annealing algorithm are presented. Results show that the proposed algorithms are able to find good quality solutions in a small amount of computation time. The integrated approach clearly outperforms the sequential one and the results confirm the advantage of using a two-phase algorithm for vehicle routing problems with hierarchical objectives. Finally, it is shown that the proposed integrated solution method improves previous results on a similar problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Baldacci R, Bodin L, Mingozzi A (2006) The multiple disposal facilities and multiple inventory locations rollon-rolloff vehicle routing problem. Comput Oper Res 33(9): 2667–2702

    Article  Google Scholar 

  • Bent R, Van Hentenryck P (2006) A two-phase hybrid algorithm for pickup and delivery vehicle routing problems with time windows. Comput Oper Res 33(4): 875–893

    Article  Google Scholar 

  • Braekers K, Janssens GK, Caris A (2010) A deterministic annealing algorithm for simultaneous routing of loaded and empty containers. In: Proceedings of the Industrial Simulation Conference, Budapest, Hungary, pp 172–176

  • Braekers K, Janssens GK, Caris A (2011) Challenges in managing empty container movements at multiple planning levels. Transport Rev 31(6): 681–708

    Article  Google Scholar 

  • Bräysy O, Berger J, Barkaoui M, Dullaert W (2003) A threshold accepting metaheuristic for the vehicle routing problem with time windows. Cent Eur J Oper Res 11(4): 369–387

    Google Scholar 

  • Bräysy O, Dullaert W, Hasle G, Mester D, Gendreau M (2008) An effective multistart deterministic annealing metaheuristic for the fleet size and mix vehicle routing problem with time windows. Transport Sci 42(3): 371–386

    Article  Google Scholar 

  • Caris A, Janssens GK (2009) A local search heuristic for the pre- and end-haulage of intermodal container terminals. Comput Oper Res 36(10): 2763–2772

    Article  Google Scholar 

  • Caris A, Janssens GK (2010) A deterministic annealing algorithm for the pre- and end-haulage of intermodal container terminals. Int J Comput Aided Eng Tech 2(4): 340–355

    Article  Google Scholar 

  • Chang H, Jula H, Chassiakos A, Ioannou P (2008) A heuristic solution for the empty container substitution problem. Transport Res E-Log 44(2): 203–216

    Article  Google Scholar 

  • Chu Q (1995) Dynamic and stochastic models for container allocation. PhD thesis, Department of Ocean Engineering, Massachusetts Institute of Technology

  • Cordeau JF, Laporte G, Savelsbergh MWP, Vigo D (2007) Vehicle routing. In: Barnhart C, Laporte G (eds) Transportation, Handbooks in Operations Research and Management Science, vol 14. Elsevier, Amsterdam, pp 367–428

  • Crainic TG, Gendreau M, Dejax P (1993) Dynamic and stochastic models for the allocation of empty containers. Oper Res 41(1): 102–126

    Article  Google Scholar 

  • Currie RH, Salhi S (2004) A tabu search heuristic for a full-load, multi-terminal, vehicle scheduling problem with backhauling and time windows. J Math Model Algorithm 3(3): 225–243

    Article  Google Scholar 

  • Deidda L, Di Francesco M, Olivo A, Zuddas P (2008) Implementing the street-turn strategy by an optimization model. Marit Pol Manag 35(5): 503–516

    Article  Google Scholar 

  • Dejax PJ, Crainic TG (1987) A review of empty flows and fleet management models in freight transportation. Transport Sci 21(4): 227–248

    Article  Google Scholar 

  • Desaulniers G, Lavigne J, Soumis F (1998) Multi-depot vehicle scheduling problems with time windows and waiting costs. Eur J Oper Res 111(3): 479–494

    Article  Google Scholar 

  • Desrosiers J, Sauvé M, Soumis F (1988) Lagrangian relaxiation methods for solving the minimum fleet size multiple traveling salesman problem with time windows. Manage Sci 34(8): 1005–1022

    Article  Google Scholar 

  • Di Francesco M, Manca A, Olivo A, Zuddas P (2006) Optimal management of heterogeneous fleets of empty containers. In: Proceedings of the International Conference on Information Systems, Logistics and Supply Chain. Lyon, France, pp 922–931

  • Dueck G, Scheuer T (1990) Threshold accepting: a general purpose optimization algorithm appearing superior to simulated annealing. J Comput Phys 90(1): 161–175

    Article  Google Scholar 

  • Erera AL, Smilowitz K (2008) Intermodal drayage routing and scheduling. In: Ioannou P (ed) Intelligent freight transportation, automation and control engineering series. CRC Press, Boca Raton, pp 171–188

    Google Scholar 

  • Escudero A, Muñuzuri J, Arango C, Onieva L (2011) A satellite navigation system to improve the management of intermodal drayage. Adv Eng Inform 25(3): 427–434

    Article  Google Scholar 

  • Ford LR, Fulkerson DR (1956) Solving the transportation problem. Manage Sci 3(1): 24–32

    Article  Google Scholar 

  • Francis P, Zhang G, Smilowitz K (2007) Improved modeling and solution methods for the multi-resource routing problem. Eur J Oper Res 180(3): 1045–1059

    Article  Google Scholar 

  • Gronalt M, Hirsch P (2007) Log-truck scheduling with a tabu search strategy. In: Doerner K, Gendreau M, Greistorfer P, Guthjahr W, Hartl R, Reimann M (eds) Metaheuristics—progress in complex systems optimization. Springer, New York, pp 64–88

    Google Scholar 

  • Gronalt M, Hartl RF, Reimann M (2003) New savings based algorithms for time constrained pickup and delivery of full truckloads. Eur J Oper Res 151(3): 520–535

    Article  Google Scholar 

  • Hadjar A, Soumis F (2009) Dynamic window reduction for the multiple depot vehicle scheduling problem with time windows. Comput Oper Res 36(7): 2160–2172

    Article  Google Scholar 

  • Homberger J, Gehring H (2005) A two-phase hybrid metaheuristic for the vehicle routing problem with time windows. Eur J Oper Res 162(1): 220–238

    Article  Google Scholar 

  • Huth T, Mattfeld DC (2009) Integration of vehicle routing and resource allocation in a dynamic logistics network. Transport Res C-Emer 17(2): 149–162

    Article  Google Scholar 

  • Ileri Y, Bazaraa M, Gifford T, Nemhauser G, Sokol J, Wikum E (2006) An optimization approach for planning daily drayage operations. Cent Eur J Oper Res 14(2): 141–156

    Article  Google Scholar 

  • Imai A, Nishimura E, Current J (2007) A Lagrangian relaxation-based heuristic for the vehicle routing with full container load. Eur J Oper Res 176(1): 87–105

    Article  Google Scholar 

  • Jula H, Chassiakos A, Ioannou P (2003) Empty container interchange report: methods for modeling and routing of empty containers in the Los Angeles and Long Beach port area. Final report, Center for the Commercial Deployment of Transportation Technologies. California State University, Long Beach

    Google Scholar 

  • Jula H, Dessouky M, Ioannou P, Chassiakos A (2005) Container movement by trucks in metropolitan networks: modeling and optimization. Transport Res E-Log 41(3): 235–259

    Article  Google Scholar 

  • Koo PH, Lee WS, Jang DW (2004) Fleet sizing and vehicle routing for container transportation in a static environment. OR Spectrum 26(2): 193–209

    Article  Google Scholar 

  • Law A (2007) Simulation modeling and analysis, 4th edn. McGraw-Hill, New York

    Google Scholar 

  • Mes M, van der Heijden M, van Harten A (2007) Comparison of agent-based scheduling to look-ahead heuristics for real-time transportation problems. Eur J Oper Res 181(1): 59–75

    Article  Google Scholar 

  • Mes M, van der Heijden M, Schuur P (2010) Look-ahead strategies for dynamic pickup and delivery problems. OR Spectr 32(2): 395–421

    Article  Google Scholar 

  • Mingozzi A, Bianco L, Ricciardelli S (1995) An exact algorithm for combining vehicle trips. In: Daduna J, Branco I, Paixao J (eds) Computer-aided Transit Scheduling. Lecture Notes in Economics and Mathematical Systems, vol 430, pp 145–172. Springer, Berlin

  • Mitrović-Minić S, Krishnamurti R (2006) The multiple tsp with time windows: vehicle bounds based on precedence graphs. Oper Res Lett 34(1): 111–120

    Article  Google Scholar 

  • Namboothiri R, Erera AL (2008) Planning local container drayage operations given a port access appointment system. Transport Res E-Log 44(2): 185–202

    Article  Google Scholar 

  • Nikolakopoulos A, Sarimveis H (2007) A threshold accepting heuristic with intense local search for the solution of special instances of the traveling salesman problem. Eur J Oper Res 177(3): 1911–1929

    Article  Google Scholar 

  • Olivo A, Zuddas P, Di Francesco M, Manca A (2005) An operational model for empty container management. Marit Pol Manag 7(3): 199–222

    Google Scholar 

  • Palmgren M, Rönnqvist M, Värbrand P (2003) A solution approach for log truck scheduling based on composite pricing and branch and bound. Int Trans Oper Res 10(5): 433–447

    Article  Google Scholar 

  • Potvin JY, Rousseau JM (1995) An exchange heuristic for routeing problems with time windows. J Oper Res Soc 46(12): 1433–1446

    Google Scholar 

  • Smilowitz K (2006) Multi-resource routing with flexible tasks: an application in drayage operations. IIE Trans 38(7): 568–577

    Article  Google Scholar 

  • Tarantilis C, Kiranoudis C, Vassiliadis V (2004) A threshold accepting metaheuristic for the heterogeneous fixed fleet vehicle routing problem. Eur J Oper Res 152(1): 148–158

    Article  Google Scholar 

  • Wang X, Regan AC (2002) Local truckload pickup and delivery with hard time window constraints. Transport Res B-Meth 36(2): 97–112

    Article  Google Scholar 

  • Zhang G, Smilowitz K, Erera A (2011) Dynamic planning for urban drayage operations. Transport Res E-Log 47(5): 764–777

    Article  Google Scholar 

  • Zhang R, Yun WY, Moon IK (2009) A reactive tabu search algorithm for the multi-depot container truck transportation problem. Transport Res E-Log 45(6): 904–914

    Article  Google Scholar 

  • Zhang R, Yun WY, Kopfer H (2010) Heuristic-based truck scheduling for inland container transportation. OR Spectr 32(3): 787–808

    Article  Google Scholar 

  • Zhang R, Yun WY, Moon IK (2011) Modeling and optimization of a container drayage problem with resource constraints. Int J Prod Econ 133(1): 351–359

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kris Braekers.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Braekers, K., Caris, A. & Janssens, G.K. Integrated planning of loaded and empty container movements. OR Spectrum 35, 457–478 (2013). https://doi.org/10.1007/s00291-012-0284-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00291-012-0284-5

Keywords

Navigation