Solving knapsack problems with S-curve return functions

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 scal...

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Bibliographic Details
Published in:European journal of operational research Vol. 193; no. 2; pp. 605 - 615
Main Authors: Ağralı, Semra, Geunes, Joseph
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.03.2009
Elsevier
Elsevier Sequoia S.A
Series:European Journal of Operational Research
Subjects:
Algorithms
Allocations
Applied sciences
Approximation
Dynamic programming
Exact sciences and technology
Firm modelling
Flows in networks. Combinatorial problems
Integer programming
Knapsack problem
Marketing
Non-linear programming
Non-linear programming OR in strategic planning Dynamic programming Marketing
Operational research and scientific management
Operational research. Management science
OR in strategic planning
Return on investment
Studies
OR in strategic planning
Dynamic programming
Non-linear programming
Marketing
Polynomial approximation
Strategic planning
Non linear programming
Polynomial method
Approximation algorithm
Modeling
Knapsack problem
Polynomial time
Return to scale
Efficiency
NP hard problem
Problem solving
Budget
Advertising
Investment
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary: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.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2007.10.060