The Bahncard Problem with Interest Rate and Risk

  • Lili Ding
  • Yinfeng Xu
  • Shuhua Hu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3828)


This paper investigated a new framework for the competitive analysis of the Bahncard problem. In contrast to the earlier approach we introduce the interest rate i and the risk tolerance t into the model, in which the traveller can develop the optimal trading strategies based on his risk preference. Set \(\alpha=\frac{1}{1+i}\). We prove that the Bahncard problem with the interest rate is \(1+(1-\beta)\alpha^{{m^*}+1}\,\)-competitive, where m * is the critical point. Then we further design a t-tolerance strategy and present a surprisingly flexible competitive ratio of \(1+\frac{(1-\beta)\alpha^{m^*}}{tr^*-(1-\beta\alpha^{m^*})}\) , where r * is the optimal competitive ratio for the Bahncard problem with the interest rate and β is the percentage of discount.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Lili Ding
    • 1
  • Yinfeng Xu
    • 1
    • 2
  • Shuhua Hu
    • 1
  1. 1.School of ManagementXi’an Jiaotong UniversityShaanxiP.R. China
  2. 2.The State Key Lab for Manufacturing Systems EngineeringXi’anChina

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