Skip to main content
Springer Nature Link
Log in

Online coupon consumption problem

  • Published:
Journal of Combinatorial Optimization Aims and scope Submit manuscript

Abstract

Nowadays, it is popular that the dealer makes profits by selling a kind of discount coupons, which can be used as money to purchase commodities with total cost less than or equal to the face value of the coupon. We can purchase a coupon at a price of 0<s≤1 times its face value and the number of potential purchasable coupons is a given integer l. The customer has the option to buy the goods by cash completely or by a discount coupon. However, each piece of goods can only use one coupon and the coupon used must have enough balance for the goods. The objective is to minimize the total cost for purchasing all the goods. In this paper, we reduce the problem to a special bin packing model. We consider the online problems for all 0<s≤1 and 1≤l≤∞. We present optimal online algorithms for all 0<s≤1 when l=∞ and l=1. For 2≤l<∞, we give both a lower bound and an algorithm, and show the algorithm is optimal for l=2.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

  • Basse S (1988) Computer algorithms: Introduction to design and analysis. Addison–Wesley, Reading

    Google Scholar 

  • Coffman EG, Garey MR, Johnson DS (1997) Approximation algorithms for bin packing: A survey. In: Hochbaum D (ed) Approximation algorithms for NP-hard problems. PWS, Boston, pp 46–93

    Google Scholar 

  • Dósa G, He Y (2006) Bin packing problems with rejection penalties and their dual problems. Inf Comput 204:795–815

    Article  MATH  Google Scholar 

  • Epstein L (2007) Bin packing with rejection revisited. In: Proceeding of the 4th workshop on approximation and online algorithms. Lecture notes in computer science, vol 4368. Springer, Berlin, pp 146–159

    Chapter  Google Scholar 

  • Fiat A, Woeginger G (1998) On-line algorithms: the state of art. In: Lecture notes in computer sciences, vol 1442. Springer, Berlin, pp 1–12

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Science, Key Laboratory of Advanced Textile Materials and Manufacturing Technology, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Yiwei Jiang

  2. Department of Mathematics, State Key Lab of CAD & CG, Zhejiang University, Hangzhou, 310027, China

    An Zhang & Zhiyi Tan

Authors
  1. Yiwei Jiang
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. An Zhang
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Zhiyi Tan
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Zhiyi Tan.

Additional information

A preliminary version of this paper appeared in the proceedings of the 1st International Symposium on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies, Lecture Notes in Computer Science.

Y. Jiang supported by Natural Science Foundation of Zhejiang Province (Y605316).

Z. Tan supported by Natural Science Foundation of China (10671177, 60021201).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jiang, Y., Zhang, A. & Tan, Z. Online coupon consumption problem. J Comb Optim 16, 1–15 (2008). https://doi.org/10.1007/s10878-007-9091-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10878-007-9091-3

Keywords