The purpose of this paper is to describe the development, implementation, and availability of a computer program for generating a variety of feasible network problems together with a set of benchmarked problems derived from it. The code "NETGEN" can generate capacitated and uncapacitated transportation and minimum cost flow network problems, and assignment problems. In addition to generating structurally different classes of network problems the code permits the user to vary structural characteristics within a class. Problems benchmarked on several codes currently available are provided in this paper since NETGEN will also allow other researchers to generate identical problems. In particular, the latter part of the paper contains the solution time and objective function value of 40 assignment, transportation, and network problems varying in size from 200 nodes to 8,000 nodes and from 1,300 arcs to 35,000 arcs.

This paper presents an in-depth computational comparison of the basic solution algorithms for solving transportation problems. The comparison is performed using "state of the art" computer codes for the dual simplex transportation method, the out-of-kilter method, and the primal simplex transportation method (often referred to as the Row-Column Sum Method or M O D I method). In addition, these codes are compared against a state of the art large scale LP code, O P H E L I E/LP. The study discloses that the most efficient solution procedure arises by coupling a primal transportation algorithm (embodying recently developed methods for accelerating the determination of basis trees and dual evaluators) with a version of the Row Minimum start rule and a "modified row first negative evaluator" rule. The resulting method has been found to be at least 100 times faster than OPHELIE, and 9 times faster than a streamlined version of the SHARE out-of-kilter code. The method's median solution time for solving 1000 \times 1000 transportation problems on a CDC 6600 computer is 17 seconds with a range of 14 to 22 seconds. Some of the unique characteristics of this study are (1) all of the fundamental solution techniques are tested on the same machine and the same problems, (2) a broad spectrum of problem sizes are examined, varying from 10 \times 10 to 1000 \times 1000; (3) a broad profile of nondense problems are examined ranging from 100 percent to 1 percent dense; and (4) additional tests using the best of the codes have been made on three other machines (IBM 360/65, UNIVAC 1108, and CDC 6400), providing surprising insights into conclusions based on comparing times on different machines and compilers.

An in-depth study of the influence of problem structure on the computational efficiency of the primal simplex transportation algorithm is presented. The input for the study included over 1000 randomly generated problems with 185 different combinations of the number of sources, the number of destinations, and the number of variables. Objective function coefficients were generated using three different probability distributions to study the effects of variance and skewness in these parameters. Every problem was solved using three different starting procedures, and the following data were collected for each problem: (1) time required to obtain an optimal solution; (2) time required to obtain an initial basic solution; (3) number of artificial variables in the initial basic solution; (4) number of basis changes; (5) average time to perform a change of basis; (6) average number of basic variables in the "stepping stone path" in each change of basis; (7) average number of variables considered before selecting one to enter the basis. These measures of performance provide numerous insights into the effects of problem parameters on computation time.

We present a procedure for finding the shortest routes between all pathconnected ordered pairs of nodes in a network. Furthermore, our approach is quite simple and highly efficient for a special class of network problems. In particular, this class of networks subsumes a number that appear in real world applications. For instance, the Polish government and the Texas Water Resources Developmental Board have developed water resource analysis models that are in this class.

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