American Institute of Mathematical Sciences

Advanced
January  2010, 6(1): 1-14. doi: 10.3934/jimo.2010.6.1

Competitive risk management for online Bahncard problem

Lili Ding 1, , Xinmin Liu 1, and  Yinfeng Xu 2,

1. 

Economics and Management College, Shandong University of Science and Technology, Qingdao, China, China
2. 

School of Management, Xi’an Jiaotong University, Xi’an, China

Received  July 2008 Revised  June 2009 Published  November 2009

In the Bahncard problem a traveler decides when to buy a Bahncard, i.e., a railway discount card of the German Deutsche Bundesbahn company, in an online setting. This problem is introduced by Fleischer and some optimal deterministic algorithms are presented with a fixed Bahncard price. In practice, however, travelers are trying to manage their risks by using some forms of rewards and their forecasting skills. We extend Fleischer's model to a new one in a risk management framework. For such an extended problem, we provide some flexible results which can be used by a traveler to obtain an optimal risk algorithm based on his risk tolerance and forecast. We further study another extention of the Bahncard problem with a fluctuated Bahncard price. We propose some algorithms and analyze their competitive ratios with and without risk, respectively. It turns out that a traveler can significantly improve his risk management performance by putting reasonable forecasts in conventional competitive analysis.
Keywords: online algorithm., Risk management, competitive analysis.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Lili Ding, Xinmin Liu, Yinfeng Xu. Competitive risk management for online Bahncard problem. Journal of Industrial & Management Optimization, 2010, 6 (1) : 1-14. doi: 10.3934/jimo.2010.6.1
[1]

Jiping Tao, Zhijun Chao, Yugeng Xi. A semi-online algorithm and its competitive analysis for a single machine scheduling problem with bounded processing times. Journal of Industrial & Management Optimization, 2010, 6 (2) : 269-282. doi: 10.3934/jimo.2010.6.269
[2]

Jiping Tao, Ronghuan Huang, Tundong Liu. A $2.28$-competitive algorithm for online scheduling on identical machines. Journal of Industrial & Management Optimization, 2015, 11 (1) : 185-198. doi: 10.3934/jimo.2015.11.185
[3]

Ran Ma, Jiping Tao. An improved 2.11-competitive algorithm for online scheduling on parallel machines to minimize total weighted completion time. Journal of Industrial & Management Optimization, 2018, 14 (2) : 497-510. doi: 10.3934/jimo.2017057
[4]

Andrew P. Sage. Risk in system of systems engineering and management. Journal of Industrial & Management Optimization, 2008, 4 (3) : 477-487. doi: 10.3934/jimo.2008.4.477
[5]

Aude Hofleitner, Tarek Rabbani, Mohammad Rafiee, Laurent El Ghaoui, Alex Bayen. Learning and estimation applications of an online homotopy algorithm for a generalization of the LASSO. Discrete & Continuous Dynamical Systems - S, 2014, 7 (3) : 503-523. doi: 10.3934/dcdss.2014.7.503
[6]

Ruiqi Yang, Dachuan Xu, Yicheng Xu, Dongmei Zhang. An adaptive probabilistic algorithm for online k-center clustering. Journal of Industrial & Management Optimization, 2019, 15 (2) : 565-576. doi: 10.3934/jimo.2018057
[7]

Sanyi Tang, Lansun Chen. Modelling and analysis of integrated pest management strategy. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 759-768. doi: 10.3934/dcdsb.2004.4.759
[8]

Donglei Du, Tianping Shuai. Errata to:''Optimal preemptive online scheduling to minimize $l_{p}$ norm on two processors''[Journal of Industrial and Management Optimization, 1(3) (2005), 345-351.]. Journal of Industrial & Management Optimization, 2008, 4 (2) : 339-341. doi: 10.3934/jimo.2008.4.339
[9]

Ping-Chen Lin. Portfolio optimization and risk measurement based on non-dominated sorting genetic algorithm. Journal of Industrial & Management Optimization, 2012, 8 (3) : 549-564. doi: 10.3934/jimo.2012.8.549
[10]

Serap Ergün, Sirma Zeynep Alparslan Gök, Tuncay Aydoǧan, Gerhard Wilhelm Weber. Performance analysis of a cooperative flow game algorithm in ad hoc networks and a comparison to Dijkstra's algorithm. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1085-1100. doi: 10.3934/jimo.2018086
[11]

Leong-Kwan Li, Sally Shao. Convergence analysis of the weighted state space search algorithm for recurrent neural networks. Numerical Algebra, Control & Optimization, 2014, 4 (3) : 193-207. doi: 10.3934/naco.2014.4.193
[12]

Yazheng Dang, Fanwen Meng, Jie Sun. Convergence analysis of a parallel projection algorithm for solving convex feasibility problems. Numerical Algebra, Control & Optimization, 2016, 6 (4) : 505-519. doi: 10.3934/naco.2016023
[13]

Wenjuan Jia, Yingjie Deng, Chenyang Xin, Xiaodong Liu, Witold Pedrycz. A classification algorithm with Linear Discriminant Analysis and Axiomatic Fuzzy Sets. Mathematical Foundations of Computing, 2019, 2 (1) : 73-81. doi: 10.3934/mfc.2019006
[14]

Jiangchuan Fan, Xinyu Guo, Jianjun Du, Weiliang Wen, Xianju Lu, Brahmani Louiza. Analysis of the clustering fusion algorithm for multi-band color image. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1233-1249. doi: 10.3934/dcdss.2019085
[15]

Yan Tang. Convergence analysis of a new iterative algorithm for solving split variational inclusion problems. Journal of Industrial & Management Optimization, 2020, 16 (2) : 945-964. doi: 10.3934/jimo.2018187
[16]

Santiago Moral, Victor Chapela, Regino Criado, Ángel Pérez, Miguel Romance. Efficient algorithms for estimating loss of information in a complex network: Applications to intentional risk analysis. Networks & Heterogeneous Media, 2015, 10 (1) : 195-208. doi: 10.3934/nhm.2015.10.195
[17]

Tao Zhang, Yue-Jie Zhang, Qipeng P. Zheng, P. M. Pardalos. A hybrid particle swarm optimization and tabu search algorithm for order planning problems of steel factories based on the Make-To-Stock and Make-To-Order management architecture. Journal of Industrial & Management Optimization, 2011, 7 (1) : 31-51. doi: 10.3934/jimo.2011.7.31
[18]

Ning Zhang, Qiang Wu. Online learning for supervised dimension reduction. Mathematical Foundations of Computing, 2019, 2 (2) : 95-106. doi: 10.3934/mfc.2019008
[19]

Sangkyu Baek, Jinsoo Park, Bong Dae Choi. Performance analysis of transmission rate control algorithm from readers to a middleware in intelligent transportation systems. Numerical Algebra, Control & Optimization, 2012, 2 (2) : 357-375. doi: 10.3934/naco.2012.2.357
[20]

Hatim Tayeq, Amal Bergam, Anouar El Harrak, Kenza Khomsi. Self-adaptive algorithm based on a posteriori analysis of the error applied to air quality forecasting using the finite volume method. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020400

2019 Impact Factor: 1.366

Tools

Metrics

  • PDF downloads (44)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences