Strict monotonicity and improved complexity in the standard form projective algorithm for linear programming

1993 ◽  
Vol 62 (1-3) ◽  
pp. 517-535 ◽  
Author(s):  
Kurt M. Anstreicher
Keyword(s):  
Linear Programming ◽  
Standard Form ◽  
Strict Monotonicity ◽  
Projective Algorithm

Essentials of Linear Programming for Managers

2014 ◽  
pp. 96-127
Author(s):  
Hossein Arsham ◽  
M. Bardossy ◽  
D. K. Sharma
Keyword(s):  
Linear Programming ◽  
Standard Form ◽  
Optimal Solution ◽  
Solution Algorithm ◽  
Managerial Decision ◽  
Software Packages ◽  
Time Sensitivity ◽  
Decision Variables ◽  
New Variables ◽  
Critical Overview

This chapter provides a critical overview of Linear Programming (LP) from a manager's perspective. The main objective is to provide managers with the essentials of LP as well as cautionary notes and defenses on common modeling issues and software limitations. The authors illustrate the findings by solving a simple LP directly on the original decision variables and constraints space without adding new variables or translating the model to fit a specific solution algorithm. The aims are the unification of diverse set of topics in their natural states in a manner that are easy to understand and providing useful information to the managers. The advances in computing software have brought LP tools to the desktop for a variety of applications to support managerial decision-making. However, it is already recognized that current LP tools, in ample circumstances, do not answer the managerial questions satisfactorily. For instance, there is a costly difference between the mathematical and managerial interpretations of sensitivity analysis. LP software packages provide one-change-at-a-time sensitivity results; the authors develop the largest sensitivity region, which allows for simultaneous dependent and/or independent changes, based on the optimal solution. The procedures are illustrated by numerical examples including LP in standard-form and LP in non standard-form.

scholarly journals A Centered Projective Algorithm for Linear Programming

1990 ◽  
Vol 15 (3) ◽  
pp. 508-529 ◽  
Author(s):  
Michael J. Todd ◽  
Yinyu Ye
Keyword(s):  
Linear Programming ◽  
Projective Algorithm
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