Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2009.1185.1189DingLiliLiuXinminKangWanglin6200996This study provides a new competitive analysis framework for the Bahncard problem through introducing the two-stage discount rate and the risk management. For the online decision-makers, who have not any information about future demand, a new online algorithm is present to help them choose an optimal replacement strategy. Furthermore, when the online decision-makers are willing to increase their risk for some reward, an optimal online risk algorithm is developed, which help them manage risk based on their risk tolerance and forecast.]]>Albers, S. and H. Bals,2003Al-Binali, S.,1999Ding, L.L., Y.F. Xu and S.H. Hu,2005Edmonds, J., S. Datta and P. Dymond,2003Fleischer, R.,2001Fujiwara, H. and K. Iwama,2005Karlin, A., M. Manasse, L. Rudolph and D. Sleator,1988Karlin, A.R., C. Kenyon and D. Randall,2003MacCrimmon, K.R., W.T. Stanbury and D.A. Wehrung,1986Sleator, D. and R. Tarjan,1985Xu, Y.F., W.J. Xu and H.Y. Li,2007