Glenn W. Graves

Scheduling Parallel Production Lines with Changeover Costs: Practical Application of a Quadratic Assignment/LP Approach

Production orders for a number of products must be scheduled on a number of similar production lines so as to minimize the sum of product-dependent changeover costs, production costs, and time-constraint penalties. We treat the problem by a quadratic assignment algorithm with a linear programming adjustment, and describe a successful practical application for chemical reactor scheduling.

The factorization approach to large-scale linear programming

A unifying concept for large-scale linear programming is developed. This approach, calledfactorization, allows one to isolate the effect of different types of constraints and variables in the algebraic representation of the tableau. Two different factorizations based on a double representation of the tableau are developed. These factorizations are applied to obtain the essential structure of efficient algorithms for generalized upper bounding, coupled block-diagonal problems, set partitioning LPs, minimum cost network flows, and other classes of problems.

Structural Redundancy in Large-Scale Optimization Models

This paper discusses automatic detection and exploitation of structural redundancy in large-scale mathematical programming models. From our perspective, such redundancy represents embedded special structure which can give significant insight to the model proponent as well as greatly reduce solution effort. We report experiments with real-life linear programming (LP) and mixed-integer (MIP) models in which various methods are developed and tested as integral modules in an optimization system of advanced design. We seek to understand the modeling implications of these embedded redundancies as well as to exploit them during actual optimization. The latter goal places heavy emphasis on efficient, as well as effective, identification techniques for economic application to large models. Several (polynomially bounded) heuristic detection algorithms are presented from our work. In addition, bounds are reported for a maximum row dimension of the more complex structures. These bounds are useful for objectively estimating the quality of heuristically derived assessments of structural redundancy. Finally, some additional suggestions are made for analyzing nonlinear programming (NLP) models.

Optimization of a reverse osmosis system using nonlinear programming

Abstract This report develops a mathematical model of a reverse osmosis system for desalination of brackish water. The system is similar to the Coalinga Pilot Plant. A nonlinear programming problem was formulated with the objectives of maximizing product flux and determining the optimal arrangement of assemblies with respect to fabrication temperature. The solution of this problem pointed out a number of important things; most significant of which is that by using modern computing machines and optimization techniques, substantial gains can be made in reducing the size of reverse osmosis systems and thus reducing the cost of the water produced.