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Solving knapsack problems with S-curve return functions

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  • AgralI, Semra
  • Geunes, Joseph

Abstract

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.

Suggested Citation

  • AgralI, Semra & Geunes, Joseph, 2009. "Solving knapsack problems with S-curve return functions," European Journal of Operational Research, Elsevier, vol. 193(2), pages 605-615, March.
    • Handle: RePEc:eee:ejores:v:193:y:2009:i:2:p:605-615
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    3. Srivastava, Vaibhav & Bullo, Francesco, 2014. "Knapsack problems with sigmoid utilities: Approximation algorithms via hybrid optimization," European Journal of Operational Research, Elsevier, vol. 236(2), pages 488-498.
    4. Westerink-Duijzer, L.E. & Schlicher, L.P.J. & Musegaas, M., 2019. "Fair allocations for cooperation problems in vaccination," Econometric Institute Research Papers EI2019-06, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Lotty E. Westerink‐Duijzer & Loe P. J. Schlicher & Marieke Musegaas, 2020. "Core Allocations for Cooperation Problems in Vaccination," Production and Operations Management, Production and Operations Management Society, vol. 29(7), pages 1720-1737, July.
    6. Vahideh Sadat Abedi, 2017. "Allocation of advertising budget between multiple channels to support sales in multiple markets," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(2), pages 134-146, February.

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