Optimal Risk Reduction in the Railway Industry by Using Dynamic Programming

Authors: Michael Todinov, Eberechi Weli

Abstract:

The paper suggests for the first time the use of dynamic programming techniques for optimal risk reduction in the railway industry. It is shown that by using the concept ‘amount of removed risk by a risk reduction option’, the problem related to optimal allocation of a fixed budget to achieve a maximum risk reduction in the railway industry can be reduced to an optimisation problem from dynamic programming. For n risk reduction options and size of the available risk reduction budget B (expressed as integer number), the worst-case running time of the proposed algorithm is O (n x (B+1)), which makes the proposed method a very efficient tool for solving the optimal risk reduction problem in the railway industry. 

Keywords: Optimisation, railway risk reduction, budget constraints, dynamic programming.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1086935

References:

[1] Elvik, R. (2001). Cost–benefit analysis of road safety measures: applicability and controversies. Accident Analysis and Prevention. vol 33 (2001) pp. 9–17.
[2] J. Li, S. Pollard, G. Kendall, E. Soane, G. Davies. “Optimising risk reduction: An expected utility approach for marginal risk reduction during regulatory decision-making”. Reliability Engineering and System Safety. Elsevier Ltd, (2009).
[3] B. Flyvbjerg, M. Holm, K. Skamris, S.L. Buhl. “How common and how large are Cost Overruns in Transport Infrastructure Projects”, Transport Reviews, volume 23 (1): 71-88, (2003).
[4] An M., Chen, Y., Baker, C.J.(2011). A fuzzy reasoning and fuzzyanalytical hierarchy process based approach to the process of railway risk information: A railway risk management system. Information Sciences 181 (2011) 3946–3966. Elsevier Inc.
[5] Ramanathan, R., Ganesh, L.S. (1995). Using AHP for resource allocation problems. European. Journal of Operational Research, vol. 80, 417.
[6] Saaty, T. (1988). The Analytic Hierarchy Process, McGraw-Hill, New York,
[7] Ghazinoory, S., Aliahmadi A., Namdarzangeneh, S., Ghodsypour, S.H. (2007). “Using AHP and L.P. for choosing the best alternatives based the gap analysis”. Applied Mathematics and Computation vol. 184, pp. 316–321.
[8] Rashid, M., Hayes, D.F. (2011). “Needs-based sewerage prioritization: Alternative to conventional cost-benefit analysis” Md. Journal of Environmental Management, vol. 92, 2427-2440. Elsevier Ltd
[9] Cagno E., Di Giulio, A., Trucco, P. (2001). “An algorithm for the implementation of safety improvement programs”. Safety Science, vol. 37, pp. 59-75. Elsevier Science Ltd.
[10] Persaud, B., Kazakov, A. (1994). “A procedure for allocating a safety improvement budget among treatment types”. Accident Analysis and Prevention. Vol. 26, No. 1, pp. 121-126. Pergamon Press Ltd.
[11] Khisty, C.J., Mohammadi, J., (2001). Fundamentals of System Engineering, with Economics, Probability and Statistics. Prentice Hall, Inc., Upper Saddle River, N.J,pp. 1-57.
[12] Lindhe, A., Rose´n, L., Norberg, T., Bergstedt, O., Pettersson, T.J.R. (2011). “Cost-effectiveness analysis of risk-reduction measures to reach water safety targets”. Water Research 45, pp. 241-253. Elsevier Ltd.
[13] Ozkir, V., Demirel, T. (2012). A fuzzy assessment framework to select among transportation projects in Turkey. Expert Systems with Applications, vol. 39 pp. 74–80. Elsevier Ltd.
[14] Sato, Y. (2012). “Optimal budget planning for investment in safety measures of a chemical company”. International Journal of Production Economics, vol. 140, pp. 579-585. Elsevier B.V.
[15] Caputo, A.C.,Pelagagge, P.M., Palumbo, M. (2011). Economic optimization of industrial safety measures using genetic algorithms.. Journal of Loss Prevention in the Process Industries, vol. 24 pp. 541-551. Elsevier Ltd.
[16] Pirlot, M. (1996). “General local search methods”. European Journal of Operational Research, vol. 92, pp. 493-511.
[17] Olson, D.L. (1988). “Opportunities and Limitations of AHP in Multiobjective Programming”. Math Computing Modelling, Vol. 11, pp. 206- 209
[18] Hey, J.D. (1995). “Experimental investigations of errors in decision making under risk”. European Economic Review, vol. 39, pp. 633-640. Elsevier Science B.V.
[19] Van Laarhoven, P.J.M., Aarts, E.H.L., Lenstra, J.K. (1992). "Jobshop scheduling by simulated annealing". Operations Research, vol. 40, pp. 113-125.
[20] Aven, T., Kørte, J. (2003). “On the use of risk and decision analysis to support decision-making”. Reliability Engineering and System Safety, vol. 79 pp. 289–299. Elsevier Science Ltd.
[21] Fukuba, Y., Ito, K. (1984). “The so-called expected utility theory is inadequate”. Mathematical Social Sciences, vol. 7, pp.1-12. Elsevier Science Publishers B.V.
[22] Basso, A., Peccati, L.A. (2001). “Optimal resource allocation with minimum activation levels and fixed costs – Theory and methodology”. European Journal of Operational Research, vol. 131 pp. 536-549
[23] Horowitz, E., Sahni, S. (1974). "Computing partitions with applications to the Knapsack Problem", Journal of the ACM, vol.21 pp. 277-292.
[24] Bjorndal, M.H. Caprara, A., Cowling, P.I., Croce, F.D., Lourenco, H., Malucelli, F., Orman, A.J., Pisinger, D., Rego, C., Salazar, J.J. (1995).“Some thoughts on combinatorial optimization”. European Journal of Operational Research, vol. 83, pp. 253-270.
[25] Dasgupta, S., Papadimitriou, C., Vazirani, U. (2008). “Algorithms”. McGraw Hill, Boston, 2008.
[26] Bellman R. (1957). “Dynamic programming”. Princeton, N. J., Princeton University Press.