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Mathematical models and solution methods for optimal container terminal yard layouts

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Abstract

In this paper, we introduce an integer linear program for planning the layout of container yards. We concentrate on a special layout class of container yards which we call yard layout with transfer lanes. For those layouts typically rubber tired gantry cranes are used for stacking operations and trucks for horizontal transports. We show that the optimization model can be formulated as a special type of a resource constrained shortest path problem for which the LP relaxation always has at least one integer optimal solution. This model is restricted to a rectangular storage yard which allows a linear formulation. For an arbitrary shaped container yard we adopt the model and develop a variable neighborhood descent (VND) heuristic for solving non-rectangular instances. Concerning the rectangular case, we show that the VND heuristic achieves optimal solutions for 38% of the realistic test instances.

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References

  • Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows: theory, algorithms, and applications. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Beasley JE, Christofides N (1989) An algorithm for the resource constrained shortest path problem. Networks 19: 379–394

    Article  Google Scholar 

  • Dekker R, Voogd P, van Asperen E (2006) Advanced methods for container stacking. OR Spectr 28(4): 563–586

    Article  Google Scholar 

  • Drira A, Pierreval H, Hajri-Gabouj S (2007) Facility layout problems: A survey. Annu Rev Control 31(2): 255–267

    Google Scholar 

  • Duinkerken M, Dekker R, Kurstjens S, Ottjes J, Dellaert N (2006) Comparing transportation systems for inter-terminal transport at the maasvlakte container terminals. OR Spectr 28(4): 469–493

    Article  Google Scholar 

  • Handler GY, Zang I (1980) A dual algorithm for the constrained shortest path problem. Networks 10(4): 293–309

    Article  Google Scholar 

  • Hansen P, Mladenovic N (2001) Variable neighborhood search: Principles and applications. Eur J Oper Res 130(3): 449–467

    Article  Google Scholar 

  • Imai A, Sasaki K, Nishimura E, Papadimitriou S (2006) Multi-objective simultaneous stowage and load planning for a container ship with container rehandle in yard stacks. Eur J Oper Res 171(2): 373–389

    Article  Google Scholar 

  • Irnich S, Desaulniers G (2005) Shortest path problems with resource constraints. In: Column generation. Springer, Berlin, pp 33–65

  • Kim KH (1997) Evaluation of the number of rehandles in container yards. Comput Ind Eng 32(4): 701–711

    Article  Google Scholar 

  • Kim KH, Kim HB (1999) Segregating space allocation models for container inventories in port container terminals. Int J Prod Econ 59: 415–423

    Article  Google Scholar 

  • Kim KH, Park Y-M, Jin M-J (2008) An optimal layout of container yards. OR Spectr 30(4): 675–695

    Article  Google Scholar 

  • Liu C, Jula H, Vukadinovic K, and Ioannou P (2000) Comparing different technologies for containers movement in marine container terminals. In: IEEE intelligent transportation systems conference proceedings

  • Liu C-I, Jula H, Ioannou P (2002) Design, simulation, and evaluation of automated container terminals. IEEE Trans Intell Trans Syst 3: 12–26

    Article  Google Scholar 

  • Liu C-I, Jula H, Vukadinovic K, Ioannou P (2004) Automated guided vehicle system for two container yard layouts. Transpo Res C 12: 349–368

    Article  Google Scholar 

  • Mladenovic N, Hansen P (1997) Variable neighborhood search. Comput Oper Res 24(11): 1097–1100

    Article  Google Scholar 

  • MOPS (2009) Mops—mathematical optimization system: About mops. MOPS Optimierungssysteme GmbH and Co. KG. http://www.mops-optimizer.com. Accessed 08 Mar 2009

  • Petering MEH (2009) Effect of block width and storage yard layout on marine container terminal performance. Transp Res E Logist Transp Rev 45: 591–610

    Article  Google Scholar 

  • Petering MEH, Murty KG (2009) Effect of block length and yard crane deployment systems on overall performance at a seaport container transshipment terminal. Comput Oper Res 36(5): 1711–1725

    Article  Google Scholar 

  • Saanen YA, Valkengoed MV (2005) Comparison of three automated stacking alternatives by means of simulation. In: WSC ’05: Proceedings of the 37th conference on winter simulation, pp 1567–1576. Winter simulation conference

  • Singh S, Sharma R (2006) A review of different approaches to the facility layout problems. Int J Adv Manuf Technol 30(5): 425–433

    Article  Google Scholar 

  • Stahlbock R, Voß S (2008) Operations research at container terminals: a literature update. OR Spectr 30(1): 1–52

    Article  Google Scholar 

  • Steenken D, Voß S, Stahlbock R (2004) Container terminal operation and operations research—a classification and literature review. OR Spectrum 26: 3–49

    Article  Google Scholar 

  • Suhl UH (1994) Mops—mathematical optimization system. Eur J Oper Res 72(2): 312–322

    Article  Google Scholar 

  • UNCTAD (2008) Review of Maritime Transport 2008. UNCTAD.

  • Vis IFA (2006) A comparative analysis of storage and retrieval equipment at a container terminal. Int J Prod Econ 103(2): 680–693

    Article  Google Scholar 

  • Vis IFA, de Koster R (2003) Transshipment of containers at a container terminal: An overview. Eur J Oper Res 147(1): 1–16

    Article  Google Scholar 

  • Vis IFA, Harika I (2004) Comparison of vehicle types at an automated container terminal. OR Spectr 26(1): 117–143

    Article  Google Scholar 

  • Wiese J, Kliewer N, Suhl L (2009) A survey of container terminal characteristics and equipment types. Technical Report 0901, DS&OR Lab, University of Paderborn. http://dsor.upb.de/uploads/tx_dsorpublications/DSOR_WP_0901.pdf

  • Wiese J, Suhl L, Kliewer N (2010) Mathematical programming and simulation based layout planning of container terminals. Manuscript. Int J Simul Process Modell (to appear)

  • Yang C, Choi Y, Ha T (2004) Simulation-based performance evaluation of transport vehicles at automated container terminals. OR Spectr 26(2): 149–170

    Article  Google Scholar 

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Correspondence to Jörg Wiese.

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Wiese, J., Suhl, L. & Kliewer, N. Mathematical models and solution methods for optimal container terminal yard layouts. OR Spectrum 32, 427–452 (2010). https://doi.org/10.1007/s00291-010-0203-6

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