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Solving knapsack problems with S-curve return functions
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DOI：10.1016/j.ejor.2007.10.060.png)
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Abstract
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We 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. (C) 2007 Elsevier B.V. All rights reserved.
Keywords:
Non-linear programming
OR in strategic planning
Dynamic programming
Marketing
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