Generalized Equivalent Integer Programs and Canonical Problems

The theory of equivalent integer programs is generalized so that a set of minimal canonical problems always exists within each equivalence class. An example is used to demonstrate how highly computation time depends on the particular canonical problem chosen to be solved by implicit enumeration algorithms.

An Integer Programming Algorithm for Portfolio Selection

A mean-variance portfolio selection model suitable for the small investor is formulated as a sequence of quadratic integer programming problems. The special structure of these quadratic problems is exploited in a partial enumeration algorithm which uses cutting planes to accelerate convergence. Computational experience is reported on problems ranging in size from fifteen to fifty variables.

The Linear Fractional Portfolio Selection Problem

A simplified portfolio selection criterion suggested by Sharpe and Mao involves choosing at most n securities from a universe of m securities in order to maximize the portfolio's excess-return-to-beta ratio. This paper examines alternative solution procedures to achieve this objective, including a gradient procedure whose continuous Knapsack subproblems in m bounded variables are solved in O(m) time. The effect on the optimal portfolio of increasing n is discussed, as well as the relationship between the excess-return-to-beta ratio of an individual security and that of the optimal portfolio. The paper concludes with computational experience on problems with n ranging from 10 to 200 and m from 500 to 1,245.finance: portfolio, programming: fractional