Skip to main content
SpringerLink
Log in

Competitive Analysis of Two Special Online Device Replacement Problems

  • Regular Paper
  • Published:
Journal of Computer Science and Technology Aims and scope Submit manuscript

Abstract

When a new investment opportunity of purchasing a new device occurs, the investors must decide whether or not and when to buy this device in an online fashion. That is, the online player must make an investment decision while neither future demand for orders nor future investment opportunities are known. This problem which generalizes the basic leasing problem has been introduced by Azar et al., and then two special cases have been studied by Damaschke. In the so-called equal prices model a 2-competitive algorithm is devised and a 1.618 lower bound is given. Here we make use of an averaging technique and obtain a better tight lower bound of 2, in other words, this lower bound cannot be improved. Furthermore, another special case which only considers two-stage device replacement is studied in this paper. Accounting for the interest rate is an essential feature of any reasonable financial model. Therefore, we explore the two-stage model with and without the interest rate respectively. In addition, we introduce the risk-reward model to analyze this problem and improve the competitive ratio performance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Azar Y, Bartal Y, Feuerstein E et al. On capital investment. Algorithmica, 1999, 25: 22–36.

    Article  MATH  Google Scholar 

  2. El-Yaniv R, Karp R M. Nearly optimal competitive online replacement policies. Mathematics of Operations Research, 1997, 22(4): 814–839.

    Article  MATH  MathSciNet  Google Scholar 

  3. Damaschke P. Nearly optimal strategies for special cases of on-line capital investment. Theoretical Computer Science, 2003, 302: 35–44.

    Article  MATH  Google Scholar 

  4. Johnson R W, Lewellen W G. Analysis of the lease-or-buy decision. Journal of Finance, 1972, 27: 815–824.

    Article  Google Scholar 

  5. Miller M H, Upton C W. Leasing, buying and the cost of capital services. Journal of Finance, 1976, 31: 761–786.

    Article  Google Scholar 

  6. S al-Binali. A risk-reward framework for the competitive analysis of finanicial games. Algorithmica, 1999, 25: 99–115.

    Article  MATH  MathSciNet  Google Scholar 

  7. El-Yaniv R, Kaniel R, Linial N. Competitive optimal on-line leasing. Algorithmica, 1999, 25: 116–140.

    Article  MATH  Google Scholar 

  8. Bower R S. Issues in lease financing. Financial Management, 1973, 2: 25–33.

    Article  Google Scholar 

  9. Fleischer R. On the Bahncard problem. Theoretical Computer Science, 2001, 268(1): 161–174.

    Article  MATH  MathSciNet  Google Scholar 

  10. Karlin A R, Kenyon C, Randall D. Dynamic TCP acknowledgement and other stories about e / (e − 1). Algorithmica, 2003, 36(3): 209–224.

    Article  MATH  MathSciNet  Google Scholar 

  11. Xu Y F, Xu W J. Competitive algorithms for online leasing problem in probabilistic environments. In Proc. ISNN’04, Dalian, China, Lecture Notes in Computer Science, 3174, Springer-Verlag, 2004, pp.725–730.

  12. Ding L L, Xin C L, Chen J. A risk-reward competitive analysis of the Bahncard problem. In Proc. AAIM’05, Xi’an, China, Lecture Notes in Computer Science, 3521, Springer-Verlag, 2005, pp.37–45.

  13. Xu Y F, Xin C L, Yi F L. New results on online replacement problem. In Proc. WINE’05, Hong Kong, Lecture Notes in Computer Science, 3828, Springer-Verlag, 2005, pp.554–563.

  14. Xu Y F, Xu W J, Li H Y. On the on-line rent-or-buy problem in probabilistic environments. Journal of Global Optimization, 2007, 38(1): 1–20.

    Article  MATH  MathSciNet  Google Scholar 

  15. Sleator D D, Tarjan R E. Amortized efficiency of list update and paging rules. Communications of the ACM, 1985, 28: 202–208.

    Article  MathSciNet  Google Scholar 

  16. Karlin A, Manasse M, Rudolph L et al. Competitive snoopy caching. Algorithmica, 1988, 3: 79–119.

    Article  MATH  MathSciNet  Google Scholar 

  17. Sui Y F. Two online algorithms for the ambulance systems. Journal of Computer Science and Technology, 2001, 16(2): 176–181.

    MATH  MathSciNet  Google Scholar 

  18. Jiang Y W, He Y. Semi-online algorithms for scheduling with machine cost. Journal of Computer Science and Technology, 2006, 21(6): 984–988.

    Article  MathSciNet  Google Scholar 

  19. Borodin A, El-Yaniv R. Online Computation and Competitive Analysis. Cambridge University Press, 1998.

  20. Fiat A, Woeginger G J. Online algorithms: The state of the art. Workshop on the Competitive Analysis of On-line Algorithms, Lecture Notes in Computer Science, 1442, Germany: Springer-Verlag, 1998, pp.196–231.

Download references

Author information

Authors and Affiliations

  1. School of Economics and Management, Tsinghua University, Beijing, 100084, China

    Chun-Lin Xin & Lei Yang

  2. School of Economics and Management, Tongji University, Shanghai, 200092, China

    Wei-Min Ma

Authors
  1. Chun-Lin Xin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei-Min Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lei Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chun-Lin Xin.

Additional information

This work is supported by China Postdoctoral Science Foundation (Grant No. 20070420029), the National Science Foundation of China (Grant Nos. 70671004, 70401006, and 70521001), the Beijing Natural Science Foundation Program (Grant No. 9073018) for New Century Excellent Talents in Universities (Grant No. NCET-06-0172) and the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200782).

Electronic Supplementary Material

Below is the link to the electronic supplementary material.

(PDF 87.3 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xin, CL., Ma, WM. & Yang, L. Competitive Analysis of Two Special Online Device Replacement Problems. J. Comput. Sci. Technol. 23, 203–213 (2008). https://doi.org/10.1007/s11390-008-9122-2

Download citation

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11390-008-9122-2

Keywords

Search

Navigation