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Computational Experience with Variants of the Balas Algorithm Applied to the Selection of R&D Projects

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  • Clifford C. Petersen

    (Motorola, Inc., Scottsdale, Arizona)

Abstract

Allocating funds to independent R&D projects is a problem of practical importance for many firms. We formulate the problem as a 0-1 integer programming problem with the objective of selecting projects that will maximize the anticipated dollar contract volume, yet not exceed cost budgets. Our form-mulation accommodates R&D projects extending over several budget periods and permits carryover of unspent funds from one budget period to later periods. Experience in solving such problems by using the Balas [Balas, Egon. 1965. An additive algorithm for solving linear programs with zero-one variables. Oper. Res. 13 (4, July-August) 517-549.] algorithm in its literal form and in reformulated form is summarized. Several other modifications to the algorithm are described and; their effect on efficiency is shown through presentation of computational experience on problems with as many as 50 variables.

Suggested Citation

  • Clifford C. Petersen, 1967. "Computational Experience with Variants of the Balas Algorithm Applied to the Selection of R&D Projects," Management Science, INFORMS, vol. 13(9), pages 736-750, May.
    • Handle: RePEc:inm:ormnsc:v:13:y:1967:i:9:p:736-750
    DOI: 10.1287/mnsc.13.9.736
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    Cited by:

    1. Woiler, Samsão, 1969. "Enumeração implícita aplicada à seleção de investimentos," RAE - Revista de Administração de Empresas, FGV-EAESP Escola de Administração de Empresas de São Paulo (Brazil), vol. 9(4), October.
    2. Lokketangen, Arne & Glover, Fred, 1998. "Solving zero-one mixed integer programming problems using tabu search," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 624-658, April.
    3. José García & Paola Moraga & Matias Valenzuela & Hernan Pinto, 2020. "A db-Scan Hybrid Algorithm: An Application to the Multidimensional Knapsack Problem," Mathematics, MDPI, vol. 8(4), pages 1-22, April.
    4. A. Elfes & C. R. Weisbin & R. Manvi & V. Adumitroaie & W. P. Lincoln & K. Shelton, 2006. "Extending the START framework: Computation of optimal capability development portfolios using a decision theory approach," Systems Engineering, John Wiley & Sons, vol. 9(4), pages 331-357, December.
    5. Hanafi, Said & Freville, Arnaud, 1998. "An efficient tabu search approach for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 659-675, April.
    6. Jafarzadeh, M. & Tareghian, H.R. & Rahbarnia, F. & Ghanbari, R., 2015. "Optimal selection of project portfolios using reinvestment strategy within a flexible time horizon," European Journal of Operational Research, Elsevier, vol. 243(2), pages 658-664.
    7. Yalçın Akçay & Haijun Li & Susan Xu, 2007. "Greedy algorithm for the general multidimensional knapsack problem," Annals of Operations Research, Springer, vol. 150(1), pages 17-29, March.
    8. Matteo Fischetti & Ivana Ljubić & Michele Monaci & Markus Sinnl, 2019. "Interdiction Games and Monotonicity, with Application to Knapsack Problems," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 390-410, April.
    9. Freville, Arnaud, 2004. "The multidimensional 0-1 knapsack problem: An overview," European Journal of Operational Research, Elsevier, vol. 155(1), pages 1-21, May.
    10. Yuji Nakagawa & Ross J. W. James & César Rego & Chanaka Edirisinghe, 2014. "Entropy-Based Optimization of Nonlinear Separable Discrete Decision Models," Management Science, INFORMS, vol. 60(3), pages 695-707, March.
    11. Kunikazu Yoda & András Prékopa, 2016. "Convexity and Solutions of Stochastic Multidimensional 0-1 Knapsack Problems with Probabilistic Constraints," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 715-731, May.

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