Research Reports from the Department of Operations
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
Recommended Citation
Lev, Benjamin, "Non Iterative Algorithm Form Solving Special Types of Transportation Problems" (1970). Research Reports from the Department of Operations. 337.
https://commons.case.edu/wsom-ops-reports/337