Robust shortest path problems with two uncertain multiplicative cost coefficients

Naval Research Logistics

Volumn 60, Issue 5, 2013, Pages 375-394

  Kwon, Changhyun ^a   Lee, Taehan ^b   Berglund, Paul ^c  

^a State University of New York   (United States)

^b Chonbuk National University   (South Korea)

^c Norfolk Southern Corporation   (United States)

Author keywords

budgeted uncertainty; hazardous materials transportation; robust shortest path

Indexed keywords

BUDGETED UNCERTAINTY; COST COEFFICIENTS; FINDING ALGORITHM; HAZARDOUS MATERIALS TRANSPORTATION; NUMERICAL EXAMPLE; SHORTEST PATH; SHORTEST PATH PROBLEM; UNCERTAIN FACTORS;

HAZARDOUS MATERIALS; POLYNOMIAL APPROXIMATION;

GRAPH THEORY;

EID: 84879956558     PISSN: 0894069X     EISSN: 15206750     Source Type: Journal    
DOI: 10.1002/nav.21540     Document Type: Article

References (18)

1. M. Abkowitz, P.D. Cheng, Developing a risk/cost framework for routing truck movements of hazardous materials, Accid Anal Prev 20 (1988), 39-51.
2. R.K. Ahuja, K. Mehlhorn, J. Orlin, R.E. Tarjan, Faster algorithms for the shortest path problem, J ACM 37 (1990), 213-223. ISSN 0004-5411. URLhttp://doi.acm.org/10.1145/77600.77615.
3. V. Akgun, A. Parekh, R. Batta, C. Rump, Routing of a hazmat truck in the presence of weather systems, Comput Oper Res 34 (2007), 1351-1373.
4. E. Alp, Risk-based transportation planning practice: Overall methodology and a case example, INFOR 33 (1995), 4-19.
5. R. Batta, S.S. Chiu, Optimal obnoxious paths on a network: Transportation of hazardous materials, Oper Res 36 (1988), 84-92.
6. D. Bertsimas, M. Sim, Robust discrete optimization under ellipsoidal uncertainty sets. Available at: http://citeseerx.ist.psu.edu/viewdoc/summary? doi=10.1.1.207.8139, Accessed on May 21, 2013, 2004.
7. D. Bertsimas, M. Sim, Robust discrete optimization and network flows, Math Program 98 (2003), 49-71.
8. D. Bertsimas, R. Weismantel, Optimization over integers, Vol. 13, Dynamic Ideas Belmont, Belmont, Massachusetts, 2005.
9. D. Chaerani, C. Roos, A. Aman, The robust shortest path problem by means of robust linear optimization, Operations Research Proceedings 2004, Vol. 2004 of Operations Research Proceedings, Chapter 42, in:, H. Fleuren, D. Hertog, P. Kort, (Editors), Springer Berlin Heidelberg, Berlin/Heidelberg, 2005, pp. 335-342.
10. C.A. Floudas, V. Visweswaran, Quadratic optimization, R. Horst, P.M. Paradalos, (Editors), Handbook of Global Optimization, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1995, pp. 217-270.
11. A. Ghouila-Houri, Caractérisation des matrices totalement unimodulaires, CR Acad Sci Paris 254 (1962), 1192-1194.
12. H. Jin, R. Batta, Objectives derived from viewing hazmat shipments as a sequence of independent Bernoulli trials, Trans Sci 31 (1997), 252-261.
13. B.Y. Kara, V. Verter, Designing a road network for hazardous materials transportation, Trans Sci 38 (2004), 188.
14. P. Kouvelis, G. Yu, Robust discrete optimization and its applications (nonconvex optimization and its applications), 1st ed., Kluwer Academic Publishers, Dordrecht, The Netherlands, November 1996.
15. D. Lord, A. Manar, A. Vizioli, Modeling crash-flow-density and crash-flow-v/c ratio relationships for rural and urban freeway segments, Accident Anal Prev 37 (2005), 185-199.
16. J.L. Martin, Relationship between crash rate and hourly traffic flow on interurban motorways, Accident Anal Prev 34 (2002), 619-629.
17. L.N. Vicente, P.H. Calamai, J.J. Júdice, Generation of disjointly constrained bilinear programming test problems, Comput Opt Appl 1 (1992), 299-306.
18. J.Y. Yen, Finding the K shortest loopless paths in a network, Manag Sci 17 (1971), 712-716.