Abstract
In this paper, the problem of robust load planning for trains in intermodal container terminals is studied. The goal of load planning is to choose wagon settings and assign load units to wagons of a train such that the utilization of the train is maximized, and setup and transportation costs in the terminal are minimized. However, in real-world applications, many of the parameters needed for the model are not known exactly. Since feasibility of the resulting load distribution has always to be guaranteed, we decided to use a robust approach. In particular, we apply the concepts of strict and adjustable robustness to enhance the load planning problem. Based on a formulation developed in Bruns and Knust (OR Spectrum 34:511–533, 2012) for the deterministic load planning problem, we propose mixed-integer linear programming formulations for most of the respective robust counterparts, dependent on the type of uncertainty. An experimental study shows that most of the robust problems can be solved within runtimes of a few minutes, which is good enough for real-world applications. Furthermore, our results indicate that robust solutions may improve the planning considerably, and that it is promising to add robustness even to large mixed-integer programs with many and diverse technical constraints.
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References
Alvarez PP, Vera JR (2011) Application of robust optimization to the sawmill planning problem. Ann Oper Res 1–19. doi:10.1007/s10479-011-1002-4
Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust optimization. Princeton University Press, Princeton and Oxford
Ben-Tal A, Goryashko A, Guslitzer E, Nemirovski A (2003) Adjustable robust solutions of uncertain linear programs. Math Program A 99:351–376
Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math Oper Res 23(4):769–805
Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math Program A 88:411–424
Bertsimas D, Goyal V, Sun XA (2011) A geometric characterization of the power of finite adaptability in multistage stochastic and adaptive optimization. Math Oper Res 36(1):24–54
Bertsimas D, Sim M (2004) The price of robustness. Oper Res 52(1):35–53
Bessas A, Kontogiannis S, Zaroliagis C (2011) Robust line planning in case of multiple pools and disruptions. In: Marchetti-Spaccamela A, Segal M (eds) Theory and practice of algorithms in (Computer) systems. Lecture Notes in Computer Science, vol 6595 , Springer, Berlin, pp 33–44
Bontekoning YM, Macharis C, Trip JJ (2004) Is a new applied transportation research field emerging? A review of intermodal rail-truck freight transport literature. Transp Res Part A Policy Pract 38(1):1–34
Boysen N, Fliedner M, Jaehn F, Pesch E (2013) A survey on container processing in railway yards. Transp Sci. doi:10.1287/trsc.1120.0415
Bruns F, Knust S (2012) Optimized load planning of trains in intermodal transportation. OR Spectr 34:511–533
Carrizosa E, Nickel S (2003) Robust facility location. Math Methods Oper Res 58:331–349
Erera AL, Morales JC, Savelsbergh M (2009) Robust optimization for empty repositioning problems. Oper Res 57(2):468–483
Fischetti M, Monaci M (2009) Light robustness. In: Ahuja RK, Möhring RH, Zaroliagis CD (eds) Robust and online large-scale optimization. Lecture notes in computer science, vol 5868. Springer, Berlin, pp 61–84
Garey MR, Johnson DS (1979) Computers and intractability—a guide to the theory of NP-completeness. Freeman, San Francisco
Goerigk M, Knoth M, Müller-Hannemann M, Schmidt M, Schöbel A (2011) The price of robustness in timetable information. In: Caprara A, Kontogiannis S (eds) Proceedings of ATMOS11, vol 20. Open Access Series in Informatics (OASIcs)Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Germany, pp 76–87
Goerigk M, Schöbel A (2010) An empirical analysis of robustness concepts for timetabling. In: Erlebach T, Lübbecke M (eds) Proceedings of ATMOS10, vol 14. OpenAccess Series in Informatics (OASIcs)Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Germany, pp 100–113
Goerigk M, Schöbel A (2012) A note on the relation between strict robustness and adjustable robustness. Institute for Numerical and Applied Mathematics, University of Göttingen, Technical report
Liebchen C, Lübbecke M, Möhring RH, Stiller S (2009) The concept of recoverable robustness, linear programming recoery, and railway applications. In: Ahuja RK, Möhring RH, Zaroliagis CD (eds) Robust and online large-scale optimization. Lecture notes in computer science, vol 5868. Springer, Berlin
Soyster AL (1973) Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper Res 21:1154–1157
Stahlbock R, Voss S (2008) Operations research at container terminals: a literature update. OR Spectr 30(1):1–52
Subramani K (2004) Analyzing selected quantified integer programs. In: David B, Michaël R (eds) Automated Reasoning. Lecture notes in computer science, vol 3097. Springer, Berlin, pp 342–356
WASCOSA AG Luzern, Doppeltaschenwagen T2000. http://www.txlogistik.eu/assets/Uploads/WASCOSA-Doppeltaschenwagen-T2000.pdf. Accessed August 2013.
Acknowledgments
We gratefully acknowledge the help of two anonymous referees who gave several constructive comments to improve the paper. Additionally, we thank Marco Lenk (Deutsche Umschlaggesellschaft Schiene-Straße mbH) for providing information about uncertainties in the practical load planning setting.
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Partially supported by Grant SCHO 1140/3-2 within the DFG programme Algorithm Engineering
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Bruns, F., Goerigk, M., Knust, S. et al. Robust load planning of trains in intermodal transportation. OR Spectrum 36, 631–668 (2014). https://doi.org/10.1007/s00291-013-0341-8
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DOI: https://doi.org/10.1007/s00291-013-0341-8