Application of Chaos Theory in Hazardous Material Transportation


1 Ph.D. Candidate, Department of Industrial Engineering, Payam-e-Noor University, Tehran, Iran

2 Professor, Department of Industrial Engineering, Iranian University of Science and Technology, Tehran, Iran


Risk factors are generally defined and assigned to road networks, as constant measures in hazmat routing problems. In fact, they may be dynamic variables depending on traffic volume, weather and road condition, and drivers' behavior. In this research work, risk factors are defined as dynamic variables using the concept of chaos theory. The largest Lyapunov exponent is utilized to determine the presence of chaos for road accident rates. Risk factors with the property of chaotic behavior are considered to solve hazmat routing problem using a developed mathematical model. Evaluation process has been done based on travel distance which mainly represents travel cost, as well as results that show the application of chaos to define dynamic risk factor appropriate method to solve hazmat routing problem, comparing to constant measures of risks.


- Akgun, V., Parekh, A., Batta R. and Rump, C. M. (2007) "Routing of a hazmat truck in the presence of weather systems", Computers and Operation Research Vol. 34, pp. 1351–1373
- Bonvicini, S. and Spadoni, G. (2008) "A hazmat multi-commodity routing model satisfying risk criteria: A case study", Journal of Loss Prevention and Process Industries, Vol. 21, pp. 345–358
- Carotenutoa, P., Giordanib S., Ricciardellib S. andRismondo, S. (2007) "A tabu search approach forscheduling hazmat shipments", Computers and Operation Research, Vol. 34, pp. 1328–1350
- Dadkar, Y., Jones D. and Nozick, L. (2008) "Identifying geographically diverse routes for the transportation of hazardous materials", Transportation Research Part E, Vol. 44, pp. 333–349
- Dadkar, Y., Nozick L. and Jones, D. (2010) "Optimizing facility use restrictions for the movement of hazardous materials", Transportation Research Part B, Vol. 44 Issue 2, pp. 267-281
- Dıaz-Banez, J. M., Gomez, F. and Toussain, G. T. (2005) "Computing shortest paths for transportation of hazardous materials in continuous spaces", Journal of  Food Engineering, Vol 70, pp. 293–298
- Ehsani, A., Azar, A. and Saffarzadeh, M. (2010) "Developing mathematical model for hazmat transport in
Iran, Case study MTBE", Tarbiat Moddares University, Tehran, Iran. (Original on Persian Language, 1389 in local calender)
- Environmental Health & Safety (2011) "Hazardous material classification", NC State University, availablem on
- Erkut, E. and Gzara, F. (2008) "Solving the hazmat transport network design problem", Computer and Operation Research, Vol. 35 pp. 2234 – 2247
- Erkut, E. and Ingolfsson, A. (2005) "Transport risk models for hazardous materials: revisited", Journal of Operation Research, Vol 33, pp. 81 – 89
- Erkuta, E. and Alpb, O. (2007) "Designing a road network for hazardous materials shipments", Computers and Operation Research, Vol 34, pp. 1389–1405
- Frazier, C. and Kockelman K.M. (2004) "Chaos theory and transportation systems: Instructive example", Journal of Transportation Research Board, TRB, National Research Council, Washington, D.C. pp. 9–17
- Gleick, James (1987) "Chaos: making a new science", Open Road Integrated Media, New York, The Enhanced Edition, available on Making-New-Science-ebook/dp/B004Q3RRRI
- Lawrence, W. L., Lin, F.Y. and Huang, Y. C. (2003) "Diagnosis of freeway traffic incidents with chaos theory", Journal of the Eastern Asia Society for Transportation Studies, Vol. 5, pp. 2025-2038
- Loa, S. C. and Cho, H. J. (2005) "Chaos and control of discrete dynamic traffic model", Journal of Franklin Instituation, Vol. 342, pp. 839–851
- Mahmoudabadi, A. (2010) "Comparison of weighted and simple linear regression and artificial neural network models in Freeway Accidents Prediction", Second international conference on Computer and Network Technology, ICCNT, pp. 392-396
- Mingjun, J. and Huanwen, T. (2004) "Application of chaos in simulated annealing", Chaos, Solitons Fractals, Vol. 21, pp. 933–941
- Nielsen, L. R., Pretolani, D. and Andersen, K. A. (2005) "K shortest paths in stochastic time-dependent networks", Logistics/SCM Research Group Working Papers from Aarhus School of Business, Department of Business Studies
- Qiao, Y., Keren N. and Mannan, M. S. (2010) "Utilization of accident databases and fuzzy sets to estimate frequency of HazMat transport accidents", Journal of Hazardous Material, Vol. 184, pp. 647-653
- Serafini, P. (2006) "Dynamic programming and minimum risk paths", European Journal of Operation Research Vol 175, pp. 224-237
- Shariat Mohaymany, A. and Khodadadian, M. (2008) "A routing methodology for hazardous material transportation to reduce the risk of road network", International Journal of Engineering Science Vol. 3 pp. 19-28
- Sugihara, G. and May, R. M. (1990) "Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series", Nature, Vol. 344, pp. 734-741
- Yuan, X. H., Yuan, Y. B. and Zhang, Y. C. (2002) "A hybird chaotic genetic algorithm for short-term hydro system scheduling", Mathematics Computures and Simulation, Vol. 59, pp. 319–27
- Zografos, K. G., Androutsopoulos, K. N. (2004) "A heuristic algorithm for solving hazardous materials distribution problems", European Journal of Operation Research, Vol 152, pp. 507–519