Nancy V. Phillips

A New Polynomially Bounded Shortest Path Algorithm

This paper develops a new polynomially bounded shortest path algorithm, called the partitioning shortest path PSP algorithm, for finding the shortest path from one node to all other nodes in a network containing no cycles with negative lengths. This new algorithm includes as variants the label setting algorithm, many of the label correcting algorithms, and the apparently computationally superior threshold algorithm.

A logistics planning system at W. R. Grace

This paper describes an optimization-based logistics planning system developed for W. R. Grace Company, one of the nations largest suppliers of phosphate-based chemical products. The mathematical model underlying this system includes production, distribution, multiple time periods, and multiple commodities. W. R. Grace initially formulated the model as a linear programming problem with 3,696 constraints and 21,564 variables. We developed an innovative modeling/solution approach to enhance top managements understanding of the model and to make the problem more tractable for the companys DEC 20/60 computer. The key features of this modeling/solution approach are: decomposition of the problem into a generalized network component and a small linear nonnetwork component, transformation of the generalized network component into a pure network, incorporation of most of the nonnetwork component into the pure network via an innovative relaxation approach, and incorporation of the remainder into the objective function via Lagrangian procedures. We solve the resulting model relaxation using highly efficient pure network solution techniques to obtain an advanced starting basis for a basis partitioning algorithm. This approach reduces solution time approximately 10-fold. In addition, W. R. Grace used insights gleaned from the solutions to make multimillion dollar decisions.

A network-related nuclear power model with an intelligent branch-and-bound solution approach

This paper presents a network model with discrete requirements for a nuclear power plant. The model determines the batch size and timing for nuclear unit refueling and how much energy should be produced by nuclear and non-nuclear units for each time period to satisfy forecasted demand with minimum total operating costs over the planning horizon. Efficient modeling and solution strategies are developed which constitute a merger of operations research and artificial intelligence. A branch-and-bound solution approach is combined with a pattern recognition component, involving non-parametric discrimination analyses, to select branching variables and directions. By coupling this approach with network optimization techniques to exploit the underlying network structure of the problem, substantial improvements are obtained both in solution quality and solution efficiency.

Integrating modeling, algorithm design, and computational implementation to solve a large-scale nonlinear mixed integer programming problem

This paper describes the formulation of a nonlinear mixed integer programming model for a large-scale product development and distribution problem and the design and computational implementation of a special purpose algorithm to solve the model. The results described demonstrate that integrating the art of modeling with the sciences of solution methodology and computer implementation provides a powerful approach for attacking difficult problems. The efforts described here were successful because they capitalized on the wealth of existing modeling technology and algorithm technology, the availability of efficient and reliable optimization, matrix generation and graphics software, and the speed of large-scale computer hardware. The model permitted the combined use of decomposition, general linear programming and network optimization within a branch and bound algorithm to overcome mathematical complexity. The computer system reliably found solutions with considerably better objective function values 30 to 50 times faster than had been achieved using general purpose optimization software alone. Throughout twenty months of daily use, the system was credited with providing insights and suggesting strategies that led to very large dollar savings.

An intelligent decision support system for supply, distribution, and marketing planning

The paper focuses on a new and successful application of an optimization-based decision support system (DSS) in the Petroleum Industry. It involves the design, development and implementation of a model and computer system to address the complex short-term planning and operational issues associated with the supply, distribution and marketing of refined petroleum products. This has evolved into an intelligent DSS that uses the tools of Knowledge Engineering and Expert Systems to build an effective, integrated DSS. Several unique modeling features, hitherto untried in any major modeling effort, have been successfully implemented in a Network Optimization framework. The use of a fourth generation modeling language called GENASYS has been instrumental in capturing the intricacies of the network model and facilitates creating new model structures for various parametric changes. Concepts from Knowledge Based Systems and Artificial Intelligence applied in setting up ‘Exception Reports’ through the use of production rules are another major characteristic of this application. The impact of this decision support system on integrated short-term planning and decision making and in stimulating changes in the attitudes and environment of the users and management is extensive.

A modeling/solution approach for optimal deployment of a weapons arsenal

This paper reports a real-world application of a large-scale assignment/allocation mixed-integer program for optimal deployment and targeting of missiles for the U.S. Strategic Air Command. We provide a NETFORM model that reduces the number of zero-one variables of a standard integer programming formulation by more than two orders of magnitude (by factors approaching 500) and a tailored NETFORM software system that solves problems involving 2,400 zero-one variables and 984,000 continuous variables to within 99.9% of optimality in less than one minute on an IBM 4381.

A new variant of the partitioning shortest path algorithm

Abstract This paper proposes a new variant of a label correcting polynomially bounded and computationally efficient shortest path algorithm, called the partitioning shortest path (PSP) algorithm. This variant, called the Extended PSP algorithm, provides a new rule for selecting scan eligible nodes to scan which has promising computational properties, particularly when shortest path algorithms are employed in relaxation strategies. In addition, results are established for this variant which provide a percent of optimality solution procedure.