Research Reports from the Department of Operations
Document Type
Report
Publication Date
7-1-1970
Abstract
A considerable amount of work has been done in recent years on adapting the simplex method for linear programming to solving II large-scale specially structured linear programs. One class of methods which has proved to be quite useful in practice is the class of compact inverse methods ([16], Chapter 6). In these S methods, the special structure of the constraint matrix is 8 exploited to obtain a representation of the basis inverse matrix 1 which is more compact than the explicit inverse used in the revised simplex method. .Early proposals for this type of algorithm are found in [1] and [5]. The product form of the inverse, which is used in commercially available linear programming packages and the modifications of it for variables with upper bounds [4] are the most widely used compact inverse methods. In 1964 Dantzig and Van Slyke [7] developed the generalized upper bounding algorithm for problems "with M+L equations, L of which have the property that each variable has at most one nonzero coefficient in them" [7] . This algorithm has been programmed in commercially available packages and has proved to be attractive for some problems [9].
Keywords
Operations research, Linear programming, Algorithms, Poisson processes, Doubly stochastic, Production scheduling, Matrices
Publication Title
Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 196
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Hartman, James K., "A Primal Method for Linear Programs with Coupling Rows and Columns" (1970). Research Reports from the Department of Operations. 435.
https://commons.case.edu/wsom-ops-reports/435