Abstract
A common problem frequently faced by business firms and individual investors is to select a few investment opportunities from many available possibilities. This problem, in its simplest form, can be modeled as a 0–1 knapsack problem. In a more general investment scenario, however, we obtain a model which is a general knapsack problem with a multiple-choice constraint. To solve this problem, an efficient enumerative algorithm is developed. The algorithm includes an efficient procedure to solve the LP-relaxed problem, a reduction algorithm which may allow the initial fixing of some of the variables, and various other implicit enumeration criteria derived from the group problem. Extensive computational experience illustrates the efficiency of the algorithm and related results.
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References
M.E. Dyer, An O(n) algorithm for the multiple-choice knapsack linear program, Mathematical Programming 29(1984)57.
H. Everett, Generalized language multiplier method for solving problems of optimum allocation of resources, Oper. Res. 11(1963)399.
F. Glover and D. Kingman, An O(n logn) algorithm for LP knapsacks with GUB constraints, Mathematical Programming 17(1979)345.
H. Greenberg and R. Hegerich, A branch and search algorithm for the knapsack problem, Management Science 16(1970)327.
F.S. Hillier and G.J. Liberman,Introduction to Operations Research (Holden-Day, San Francisco, 1968).
A. Land and A. Doig, An automatic method of solving discrete programming problems, Econometrica 28(1960)497.
K. Mathur, An enumerative algorithm for the general multiple-choice knapsack problem, Ph.D. dissertation, Department of Operations Research, Case Western Reserve University, Cleveland, Ohio (1980).
R.M. Nauss, The 0–1 knapsack problem with multiple-choice constraints, Eur. J. of Oper. Res. 2(1978)125.
H.M. Salkin,Integer Programming (Addison-Wesley, Reading, MA, 1975).
P. Sinha and A.A. Zoltner, The multiple-choice knapsack problem, Oper. Res. 27(1979)503.
E. Zemel, The linear multiple-choice knapsack problem, Oper. Res. 28(1980)1412.
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Mathur, K., Salkin, H.M. & Morito, S. An efficient alorithm for the general multiple-choice knapsack problem (GMKP). Ann Oper Res 4, 253–283 (1985). https://doi.org/10.1007/BF02022043
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DOI: https://doi.org/10.1007/BF02022043