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Generating the Discrete Efficient Frontier to the Capital Budgeting Problem

Author

Listed:
  • Meir J. Rosenblatt

    (Technion-Israel Institute of Technology, Haifa, Israel, and Washington University, St. Louis, Missouri)

  • Zilla Sinuany-Stern

    (Ben Gurion University of the Negev, Beer Sheva, Israel)

Abstract

In this paper, we characterize the capital budgeting problem by two objective functions. One is maximizing the present value of accepted projects and the other is minimizing their risk. As we assume that the weights assigned to these objectives are unspecified, we utilize a Discrete Efficient Frontier (DEF) approach to represent all the efficient combinations. We found an optimality range for each efficient combination covering the entire possible range of weights (zero to one). Furthermore, we present different properties and characteristics of the DEF, and develop two algorithms for constructing the DEF. The first one is a simple heuristic and the second one is an optimal algorithm. We conducted experiments measuring the effectiveness of the heuristic algorithm and the effect of terminating the optimal algorithm before its completion. We have shown that the heuristic algorithm, which is the first phase of the branch-and-bound algorithm, has an average error of about 2%. Furthermore, we have shown that this average error can be reduced by applying only part of the optimal algorithm and terminating it before its actual completion.

Suggested Citation

  • Meir J. Rosenblatt & Zilla Sinuany-Stern, 1989. "Generating the Discrete Efficient Frontier to the Capital Budgeting Problem," Operations Research, INFORMS, vol. 37(3), pages 384-394, June.
    • Handle: RePEc:inm:oropre:v:37:y:1989:i:3:p:384-394
    DOI: 10.1287/opre.37.3.384
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    Citations

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    Cited by:

    1. Altannar Chinchuluun & Panos Pardalos, 2007. "A survey of recent developments in multiobjective optimization," Annals of Operations Research, Springer, vol. 154(1), pages 29-50, October.
    2. Rong, Aiying & Figueira, José Rui, 2013. "A reduction dynamic programming algorithm for the bi-objective integer knapsack problem," European Journal of Operational Research, Elsevier, vol. 231(2), pages 299-313.
    3. Rong, Aiying & Figueira, José Rui, 2014. "Dynamic programming algorithms for the bi-objective integer knapsack problem," European Journal of Operational Research, Elsevier, vol. 236(1), pages 85-99.
    4. Kathrin Klamroth & Margaret M. Wiecek, 2000. "Dynamic programming approaches to the multiple criteria knapsack problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(1), pages 57-76, February.
    5. Zilla Sinuany-Stern, 2014. "Quadratic model for allocating operational budget in public and nonprofit organizations," Annals of Operations Research, Springer, vol. 221(1), pages 357-376, October.
    6. Marchioni, Andrea & Magni, Carlo Alberto, 2018. "Investment decisions and sensitivity analysis: NPV-consistency of rates of return," European Journal of Operational Research, Elsevier, vol. 268(1), pages 361-372.
    7. Janice E. Carrillo & Cheryl Gaimon, 2004. "Managing Knowledge-Based Resource Capabilities Under Uncertainty," Management Science, INFORMS, vol. 50(11), pages 1504-1518, November.

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