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.
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Bibliographic InfoArticle provided by Elsevier in its journal European Journal of Operational Research.
Volume (Year): 193 (2009)
Issue (Month): 2 (March)
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Web page: http://www.elsevier.com/locate/eor
Non-linear programming OR in strategic planning Dynamic programming Marketing;
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