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Quadratic Binary Programming with Application to Capital-Budgeting Problems

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  • D. J. Laughhunn

    (Southern Illinois University, Carbondale, Illinois)

Abstract

The purpose of this paper is to present an algorithm for solving the quadratic binary programming problem. Although a problem with this structure may arise in many situations, it is particularly common in capital budgeting when a decision-maker is confronted with a set of investment proposals from which he must select a portfolio. If returns of proposals are intercorrelated random variables and if the decision-maker uses as his criterion for selection the mean μ and variance σ 2 of portfolio returns, his decision requires prior identification of the (μ, σ 2 ) efficient set. The algorithm developed to solve the problem and hence necessary to generate the efficient set is based on the concept of implicit enumeration recently introduced by Egon Balas for solution of the binary linear programming problem.

Suggested Citation

  • D. J. Laughhunn, 1970. "Quadratic Binary Programming with Application to Capital-Budgeting Problems," Operations Research, INFORMS, vol. 18(3), pages 454-461, June.
    • Handle: RePEc:inm:oropre:v:18:y:1970:i:3:p:454-461
    DOI: 10.1287/opre.18.3.454
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    Cited by:

    1. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.
    2. Sourour Elloumi & Amélie Lambert & Arnaud Lazare, 2021. "Solving unconstrained 0-1 polynomial programs through quadratic convex reformulation," Journal of Global Optimization, Springer, vol. 80(2), pages 231-248, June.
    3. Billionnet, Alain & Calmels, Frederic, 1996. "Linear programming for the 0-1 quadratic knapsack problem," European Journal of Operational Research, Elsevier, vol. 92(2), pages 310-325, July.
    4. Gary Kochenberger & Jin-Kao Hao & Fred Glover & Mark Lewis & Zhipeng Lü & Haibo Wang & Yang Wang, 2014. "The unconstrained binary quadratic programming problem: a survey," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 58-81, July.
    5. Xiaojin Zheng & Xiaoling Sun & Duan Li & Yong Xia, 2010. "Duality Gap Estimation of Linear Equality Constrained Binary Quadratic Programming," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 864-880, November.
    6. Billionnet, Alain & Faye, Alain & Soutif, Eric, 1999. "A new upper bound for the 0-1 quadratic knapsack problem," European Journal of Operational Research, Elsevier, vol. 112(3), pages 664-672, February.
    7. Syam, Siddhartha S., 1998. "A dual ascent method for the portfolio selection problem with multiple constraints and linked proposals," European Journal of Operational Research, Elsevier, vol. 108(1), pages 196-207, July.
    8. Richard J. Forrester & Warren P. Adams & Paul T. Hadavas, 2010. "Concise RLT forms of binary programs: A computational study of the quadratic knapsack problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(1), pages 1-12, February.
    9. Shenshen Gu & Xinyi Chen, 2020. "The Basic Algorithm for the Constrained Zero-One Quadratic Programming Problem with k -diagonal Matrix and Its Application in the Power System," Mathematics, MDPI, vol. 8(1), pages 1-16, January.
    10. C. Helmberg & F. Rendl & R. Weismantel, 2000. "A Semidefinite Programming Approach to the Quadratic Knapsack Problem," Journal of Combinatorial Optimization, Springer, vol. 4(2), pages 197-215, June.

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