Solving knapsack problems with S-curve return functions
AbstractWe consider the allocation of a limited budget to a set of activities or investments in order to maximize return from investment. In a number of practical contexts (e.g., advertising), the return from investment in an activity is effectively modeled using an S-curve, where increasing returns to scale exist at small investment levels, and decreasing returns to scale occur at high investment levels. We demonstrate that the resulting knapsack problem with S-curve return functions is NP-hard, provide a pseudo-polynomial time algorithm for the integer variable version of the problem, and develop efficient solution methods for special cases of the problem. We also discuss a fully-polynomial-time approximation algorithm for the integer variable version of the problem.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal European Journal of Operational Research.
Volume (Year): 193 (2009)
Issue (Month): 2 (March)
Contact details of provider:
Web page: http://www.elsevier.com/locate/eor
Non-linear programming OR in strategic planning Dynamic programming Marketing;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Andris A. Zoltners & Prabhakant Sinha, 1980. "Integer Programming Models for Sales Resource Allocation," Management Science, INFORMS, vol. 26(3), pages 242-260, March.
- Leonard M. Lodish, 1971. "Callplan: An Interactive Salesman's Call Planning System," Management Science, INFORMS, vol. 18(4-Part-II), pages P25-P40, December.
- Andris A. Zoltners & Prabhakant Sinha & Philip S. C. Chong, 1979. "An Optimal Algorithm for Sales Representative Time Management," Management Science, INFORMS, vol. 25(12), pages 1197-1207, December.
- Ginsberg, William, 1974. "The multiplant firm with increasing returns to scale," Journal of Economic Theory, Elsevier, vol. 9(3), pages 283-292, November.
- Paul H. Zipkin, 1980. "Simple Ranking Methods for Allocation of One Resource," Management Science, INFORMS, vol. 26(1), pages 34-43, January.
- Duncan M. Holthausen, Jr. & Gert Assmus, 1982. "Advertising Budget Allocation under Uncertainty," Management Science, INFORMS, vol. 28(5), pages 487-499, May.
- Gabriel R. Bitran & Arnoldo C. Hax, 1981. "Disaggregation and Resource Allocation Using Convex Knapsack Problems with Bounded Variables," Management Science, INFORMS, vol. 27(4), pages 431-441, April.
- Thomas L. Morin & Roy E. Marsten, 1976. "An Algorithm for Nonlinear Knapsack Problems," Management Science, INFORMS, vol. 22(10), pages 1147-1158, June.
- Bretthauer, Kurt M. & Shetty, Bala, 2002. "The nonlinear knapsack problem - algorithms and applications," European Journal of Operational Research, Elsevier, vol. 138(3), pages 459-472, May.
- Zschocke, Mark S. & Mantin, Benny & Jewkes, Elizabeth M., 2013. "Mature or emerging markets: Competitive duopoly investment decisions," European Journal of Operational Research, Elsevier, vol. 228(3), pages 612-622.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.