John J. Jarvis

Set partitioning based heuristics for interactive routing

The set partitioning model is used as the basis for an interactive approach for solving a broad class of routing problems. A pricing mechanism is developed which can be used with a variety of methods in generating improving solutions. A version of the approach for delivery problems has been implemented via a colorgraphics display. The human aided optimization procedure was tested on the standard 50-point, 75-point, and 100-point test problems of Eilon, Watson-Gandy, and Christofides [6]. In the case of the first two test problems, the procedure was able to generate the best known solutions. In the 100-point problem, a better solution was generated than the current best known solution.

Optimal Design of Regional Wastewater Systems: A Fixed-Charge Network Flow Model

A regional wastewater quality management system was modeled as a fixed-charge network flow problem. The model included alternative trunk-line connections, methods of treatment, and variation in system boundaries. The paper describes the model, development of the input data, the network flow analysis method, simplifications, and results. Particular emphasis is put on modification and simplification of the basic fixed-charge model to produce a fixed-charge network flow model of tractable size.

Generalized Penalty-Function Concepts in Mathematical Optimization

Given a mathematical program, this paper constructs an alternate problem with its feasibility region a superset of the original mathematical program. The objective function of this new problem is constructed so that a penalty is imposed for solutions outside the original feasibility region. One attempts to choose an objective function that makes the optimal solutions to the new problem the same as the optimal solutions to the original mathematical program.

Maximal Flow with Gains through a Special Network

This paper uses the special structure at a directed acyclic network with positive gains to develop an extremely simple and powerful algorithm for maximal flow. Finiteness of the algorithm is achieved through a theorem characterizing basic solutions for this special network.

Graphic matroids and the multicommodity transportation problem

A necessary and sufficient condition for unimodularity in the multicommodity transportation problem is established, and the constructive proof yields an equivalent, single commodity network flow problem for the class of problems satisfying the condition. The concept of a graphic matroid is used to establish the transformation.

Network topology and integral multicommodity flow problems

In this paper we investigate the nature of integer solutions to multicommodity network flow problems from a graphtheoretic viewpoint. A sufficient condition for unimodularity is developed that is based upon the topological characteristics of the associated graph, and the results are applied to certain well-structured examples.

A decomposition algorithm for locating a shortest path between two nodes in a network

A decomposition algorithm for locating a shortest path between two nodes of a network with circuits (directed cycles) and arbitrary arc distances (with the customary assumption of no negative circuits) is introduced. Unlike similar decomposition algorithms by Hu [12, 13], Yen [23], and Glover, Klingman, and Napier [10], this algorithm finds only the shortest distance between two specified nodes. Computational complexity of this algorithm is shown to be better than the previous decomposition algorithms.

Decomposition algorithms for locating minimal cuts in a network

This paper provides decomposition algorithms for locating minimal cuts in a large directed network. The main theorem provides several cases for the algorithms. In the worst case, it is shown that the efficiency of one of the proposed algorithms is of the same order as a no-decomposition algorithm. As in linear programming, the obvious advantage of the proposed decomposition procedure is its ability to potentially handle larger problems than a no-decomposition algorithm.

A Network Flow Model for Forecasting and Evaluating Criminal Displacement

In this article, the characteristics of crime patterns in geographic areas over time are described by a network flow model. A method forforecastingfuture crime patterns with the network model is discussed along with procedures for evaluating future displacement by component randomization. An illustrative example of the model building and output analysis from actual arrest data is presented.

An out-of-kilter based heuristic for the integer multicommodity transportation problem

Abstract A new formulation of the multicommodity transportation problem is introduced whereby all supply and demand constraints and in addition, a subset of the capacity constraints are incorporated into an equivalent single commodity, uncapacitated network. Solution of this network problem generally yields stronger lower bounds than one obtains by solving the individual single commodity transportation problems independently. A heuristic algorithm using this formulation is developed for the integer problem and limited computational experience indicates that the new formulation does provide a significant advantage over the unconstrained approach and solutions that are generally within seven percent of the lower bound. The application of this formulation in solving the continuous problem is also discussed.