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Integer Programming in Capital Budgeting: A Note on Computational Experience

Published online by Cambridge University Press:  19 October 2009

Richard H. Pettway
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Extract

Solving capital budgeting problems with linear and integer programming has been part of the finance literature for some time [21, 22, 23, 7, 14, and 18]. Capital budgeting problems have unique properties that distinguish them from other integer linear problems discussed in the mathematical programming literature. Capital budgeting problems generally have the following characteristics: (1) the matrix tends to be rectangular with more variables than constraints; (2) they are all maximization problems with ≤ constraints and nonnegativity conditions in the general form 0≤xi≤1 in the case of linear programming and xi = 0, 1 in the case of integer problems; and (3) there are often mutually exclusive projects among the variables. The purposes of this note are to illustrate some computational experience using existing integer algorithms to solve a set of capital budgeting problems and to begin to catalog the performance of integer codes on financial problems.

Type
Communications
Information
Journal of Financial and Quantitative Analysis , Volume 8 , Issue 4 , September 1973 , pp. 665 - 672
Copyright
Copyright © School of Business Administration, University of Washington 1973

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References

[1]Balas, Egon. “An Additive Algorithm for Solving the Linear Programs with Zero-One Variables.” Operations Research, July–August 1965, pp. 517–546.CrossRefGoogle Scholar
[2]Cord, J. “A Method for Allocating Funds to Investment Projects When Returns are Subject to Uncertainty.” Management Science, June 1964, pp. 335–341.CrossRefGoogle Scholar
[3]Dyckman, T. R. “Allocating Funds to Investment Projects When Returns are Subject to Uncertainty: A Comment.” Management Science, November 1964, pp. 348–350.CrossRefGoogle Scholar
[4]Geoffrion, A. M.An Improved Implicit Enumeration Approach for Integer Programming. Memo. Rm - 5644 - PR. Santa Monica, Calif.: Rand Corporation, June 1968.Google Scholar
[5]Geoffrion, A. M. “An Improved Implicit Enumeration Approach for Integer Programming.” Operations Research, vol. 17, May–June 1969, pp. 437–454.CrossRefGoogle Scholar
[6]Geoffrion, A. M., and Marsten, R. E.. “Integer Programming Algorithms: A Framework and State-of-the-Art Survey.” Management Science, vol. 18, May 1972, pp. 465–491.CrossRefGoogle Scholar
[7]Glover, Fred. “The Knapsack Problem: Some Relations for an Improved Algorithm.” Management Science Research Report No. 38. Pittsburgh, Pa.: Carnegie Institute of Technology, Graduate School of Industrial Administration, January 1965.Google Scholar
[8]Glover, Fred. “A Multiphase - Dual Algorithm for the Zero-One Integer Programming Problem.” Operations Research, November–December 1965, pp. 879–919.CrossRefGoogle Scholar
[9]Gue, Ronald L.; Liggett, John C.; and Cain, Kenneth C.. “Analysis of Algorithms for Zero-One Programming Problems.” Communications of the ACM, vol. 11, December 1968, pp. 837–844.CrossRefGoogle Scholar
[10]Ignizio, James P. “On the Establishment of Standards for Comparing Algorithm Performance.” Interfaces, vol. 2, 1971, pp. 8–11.CrossRefGoogle Scholar
[11]Lawler, E. L., and Bell, M. D.. “A Method for Solving Discrete Optimization Problems.” Operations Research, November–December 1966, pp. 1098–1112.CrossRefGoogle Scholar
[12]Lemke, C. E., and Spielberg, K.. “Direct Search Algorithms for Zero-One and Mixed-Integer Programming.” Operations Research, September–October 1967, pp. 892–914.CrossRefGoogle Scholar
[13]Lorie, J. H., and Savage, L. J.. “Three Problems in Rationing Capital.” Journal of Business, October 1955, pp. 141–152.Google Scholar
[14]Mao, James C. T.Quantitative Analysis of Financial Decisions. London: The Macmillan Company, 1969.Google Scholar
[15]Operations Research, Issue No. 4. Minneapolis, Minn.: Control Data Corporation, December 1968.Google Scholar
[16]Petersen, C. C. “Computational Experience with Variants of the Balas Algorithm Applied to the Selection of R & D Projects.” Management Science, May 1967, pp. 736–750.CrossRefGoogle Scholar
[17]Plane, Donald R., and McMillan, Claude Jr.Discrete Optimization. Englewood Cliffs, N. J.: Prentice-Hall, Inc., 1971.Google Scholar
[18]Quirin, G. David. The Capital Expenditure Decision. Homewood, Ill.: Richard D. Irwin, Inc., 1967, pp. 175–197.Google Scholar
[19]Trauth, C. A. Jr., and Woolsey, R. E.. “Integer Linear Programming: A Study in Computational Efficiency.” Management Science, vol. 15, May 1969, pp. 481–493.CrossRefGoogle Scholar
[20]Wagner, Harvey M.Principles of Operations Research. Englewood Cliffs, N. J.: Prentice-Hall, Inc., 1969, pp. 459–466.Google Scholar
[21]Weingartner, H. Martin.Mathematical Programming and The Analysis of Capital Budgeting Problems. Englewood Cliffs, N. J.: Prentice Hall, Inc., 1963.Google Scholar
[22]Weingartner, H. Martin. “Capital Budgeting of Interrelated Projects: Survey and Synthesis.” Management Science, vol. 12, March 1966, pp. 485–516.CrossRefGoogle Scholar
[23]Weingartner, H. Martin. “Methods for the Solution of the Multi-dimensional O/l Knapsack Problem.” Operations Research, January–February 1967.CrossRefGoogle Scholar
[24]Woolsey, Gene. “Comment on Briskin's Note.” Management Science, vol. 17, March 1971, pp. 500–501.CrossRefGoogle Scholar
[25]Woolsey, Gene. “On Telling It Like It Is in Integer Programming.” Institute of Operations Research Report No. 1, June 1970.Google Scholar
[26]Woolsey, Gene, and Trauth, C. A. Jr.IPSC, A Machine Independent Integer Linear Program. Sandia Laboratories Research Report SC-RR-66–433, July 1966.Google Scholar