An efficient alorithm for the general multiple-choice knapsack problem (GMKP)

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.