David S. Rubin

Vertex Generation Methods for Problems with Logical Constraints

Recent work has shown how to use vertex generation methods to solve linear complementarity problems and cardinality constrained linear programs. These problems can be characterized as linear programs with additional logical constraints. These logical constraints can be incorporated into Chernikovas vertex generating algorithm in a natural and straightforward fashion. This study examines the extension of this technique to other linear programs with logical constraints, and discusses its use as a solution procedure for the 0–1 integer programming problem.

Evaluating best-case and worst-case variances when bounds are available

This paper describes procedures for computing the tightest possible best-case and worst-case bounds on the variance of a discrete, bounded, random variable when lower and upper bounds are available for its unknown probability mass function. An example from the application of the Monte Carlo method to the estimation of network reliability illustrates the procedures and, in particular, reveals considerable tightening in the worst-case bound when compared to the trivial worst-case bound based exclusively on range.

Bounding the variance in Monte Carlo experiments

This paper describes a method for obtaining a worst-case bound on variance in a Monte Carlo experiment by using available lower and upper bounds on outcomes within disjoint strata in the corresponding sample space. This worst-case bound can be used to determine a worst-case sample size to meet a specified variance criterion.

Best- and worst-case variances when bounds are available for the distribution function

Consider a discrete random variable, X, taking on values {1,2,…,t} and with lower and upper bounds on its unknown distribution function (d.f.). Within these constraints, this paper derives the forms of the d.f.s that lead to the largest possible (worst-case) variance and to the smallest possible (best-case) variance for any monotone function of X. The paper also describes Algorithms NLPW and NLPB for computing these worst- and best-case variances, each in O(t) time. A network reliability example illustrates how these techniques can be used to bound sample size in a Monte Carlo experiment.

LPMPS: A student oriented preprocessor for MPS/360

Abstract Even though linear programming is one of the most widely taught and used management science techniques, the commercial LP computer packages are not extensively used in the classroom. This is due to their cumbersome data input and control language requirements. This paper describes a student oriented FORTRAN preprocessor, LPMPS, that facilitates the use of one of these large scale packages, IBMs MPS/360. The use and implementation of LPMPS are discussed and compared with the use of MPS/360.

Polynomial algorithms for m × (m + 1) integer programs and m × (m + k) diophantine systems

Recent results of Kannan and Bachem (on computing the Smith Normal Form of a matrix) and Lenstra (on solving integer inequality systems) are used with classical results by Smith to obtain polynomial-time algorithms for solving m x (m + 1) equality constrained integer programs and m x (m + k) systems of diophantine equations for fixed k.