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.
| Original language | English |
|---|---|
| Pages (from-to) | 253-283 |
| Number of pages | 31 |
| Journal | Annals of Operations Research |
| Volume | 4 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1985 Dec |
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Keywords
- capital budgeting
- general multiple-choice knapsack problem
- integer programming
- knapsack problem
- Mathematical programming
ASJC Scopus subject areas
- Management Science and Operations Research
- Decision Sciences(all)
Cite this
An efficient alorithm for the general multiple-choice knapsack problem (GMKP). / Mathur, K.; Salkin, H. M.; Morito, S.
In: Annals of Operations Research, Vol. 4, No. 1, 12.1985, p. 253-283.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - An efficient alorithm for the general multiple-choice knapsack problem (GMKP)
AU - Mathur, K.
AU - Salkin, H. M.
AU - Morito, S.
PY - 1985/12
Y1 - 1985/12
N2 - 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.
AB - 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.
KW - capital budgeting
KW - general multiple-choice knapsack problem
KW - integer programming
KW - knapsack problem
KW - Mathematical programming
UR - http://www.scopus.com/inward/record.url?scp=0005061475&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0005061475&partnerID=8YFLogxK
U2 - 10.1007/BF02022043
DO - 10.1007/BF02022043
M3 - Article
AN - SCOPUS:0005061475
VL - 4
SP - 253
EP - 283
JO - Annals of Operations Research
JF - Annals of Operations Research
SN - 0254-5330
IS - 1
ER -