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Solution of the Lorie-Savage and Similar Integer Programming Problems by the Generalized Lagrange Multiplier Method

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  • Seymour Kaplan

    (New York University, New York)

Abstract

A specific type of all-integer integer programming problem which seems to arise frequently in capital budgeting and other areas involves a zero-one restriction on the problem variables. Approaches to solutions to such problems by the General Lagrange Multiplier Method are discussed. This procedure, because of its relative simplicity, has certain advantages over other direct methods such as the use of integer programming algorithms, especially in areas such as capital budgeting where the constraints are usually not binding to the degree indicated by the problem statement. Throughout this paper, the Lorie-Savage problem in capital budgeting is used as a basis for the discussion.

Suggested Citation

  • Seymour Kaplan, 1966. "Solution of the Lorie-Savage and Similar Integer Programming Problems by the Generalized Lagrange Multiplier Method," Operations Research, INFORMS, vol. 14(6), pages 1130-1136, December.
    • Handle: RePEc:inm:oropre:v:14:y:1966:i:6:p:1130-1136
    DOI: 10.1287/opre.14.6.1130
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    Cited by:

    1. Tobin, Roger L., 1999. "A fast interactive solution method for large capital expenditure selection problems," European Journal of Operational Research, Elsevier, vol. 116(1), pages 1-15, July.
    2. Myerson, Robert J., 1978. "The Landau-Ginzburg-Wilson model in 2 and 2+ϵ dimensions at low temperatures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 90(3), pages 431-449.
    3. Tobin, Roger L., 2002. "Relief period optimization under budget constraints," European Journal of Operational Research, Elsevier, vol. 139(1), pages 42-61, May.
    4. Betsuyaku, H., 1981. "Monte Carlo realization of Kadanoff block transformation in the 2d plane-rotator model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 106(1), pages 311-325.
    5. Rogiers, J. & Betts, D.D., 1976. "Application of the renormalization group method to the s = 12XY model on the triangular lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 85(3), pages 553-565.
    6. Freville, Arnaud, 2004. "The multidimensional 0-1 knapsack problem: An overview," European Journal of Operational Research, Elsevier, vol. 155(1), pages 1-21, May.

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