Research Reports from the Department of Operations

Authors

Benjamin Lev

Document Type

Report

Publication Date

9-1-1970

Abstract

Many transportation problems are such that, when origins and destinations are suitably indexed, the cost matrix contains elements along the main diagonal, a band above it, and a band below it, while the other elements of the cost matrix are infinite. A procedure has been developed which yields optimal solution to such tridiagonal problems in n steps for a n-origin, n-destination problem. A second model has been solved for a tridiagonal and a coupling column of the cost matrix. A third model, a four-diagonal one, has been partially solved. We suggested and showed a method to solve any other model which is "close" to a tridiagonal one, by Benders' Algorithm. The algorithm presented here works by eliminating all off diagonal variables in terms of the diagonal ones, and subsequently models and small linear programming problems.

Keywords

Operations research, Algorithms, Programming (Mathematics), Mathematical optimization, Matrices, Transportation problems (Programming), Transportation--Research

Publication Title

Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University

Issue

Technical memorandum no. 198

Rights

This work is in the public domain and may be freely downloaded for personal or academic use

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.