Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 7-Day Trial for You or Your Team.

Learn More →

A Computation Study on Start Procedures, Basis Change Criteria, and Solution Algorithms for Transportation Problems

A Computation Study on Start Procedures, Basis Change Criteria, and Solution Algorithms for... 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 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 10 to 1000 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Management Science INFORMS

A Computation Study on Start Procedures, Basis Change Criteria, and Solution Algorithms for Transportation Problems

Glover, Fred; Karney, D.; Klingman, D.; Napier, A.
Management Science , Volume 20 (5): 21 – Jan 1, 1974
Download PDF
22 pages

Loading next page...
 
/lp/informs/a-computation-study-on-start-procedures-basis-change-criteria-and-l0gOJ58XiD

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
INFORMS
Copyright
Copyright © INFORMS
Subject
Research Article
ISSN
0025-1909
eISSN
1526-5501
DOI
10.1287/mnsc.20.5.783
Publisher site
See Article on Publisher Site

Abstract

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 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 10 to 1000 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.

Journal

Management Science – INFORMS

Published: Jan 1, 1974

There are no references for this article.