Redundancy in Mathematical Programming

1. Front Matter

   Pages N2-VII

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2. An Introduction to Redundancy

   • Mark H. Karwan, Vahid Lotfi, Stanley Zionts, Jan Telgen

   Pages 1-13

3. Mathematical Foundations and Notation

   • Mark H. Karwan, Vahid Lotfi, Stanley Zionts, Jan Telgen

   Pages 14-27

4. A Method for Identifying Redundant Constraints and Extraneous Variables in Linear Programming

   • Stanley Zionts, Jyrki Wallenius

   Pages 28-35

5. A Method for Determining Redundant Constraints

   • Tomas Gal

   Pages 36-52

6. Identifying Redundancy in Systems of Linear Constraints

   • Jan Telgen

   Pages 53-59

7. Finding Redundant Constraints in Sets of Linear Inequalities

   • David S. Rubin

   Pages 60-67

8. A Method for Finding Redundant Constraints of a System of Linear Inequalities

   • Theodore H. Mattheiss

   Pages 68-79

9. Some Reduction of Linear Programs Using Bounds on Problem Variables

   • Dieter Klein, Soren J. Holm

   Pages 80-86

10. A Reduction Procedure for Linear and Integer Programming Models

    • H. Paul Williams

    Pages 87-107

11. Preduce — A Probabilistic Algorithm Identifying Redundancy by a Random Feasible Point Generator (RFPG)

    • Arnon Boneh

    Pages 108-134

12. The Noncandidate Constraint Method

    • Awanti P. Sethi, Gerald L. Thompson

    Pages 135-144

13. Structural Redundancy in Large-Scale Optimization Models

    • Gordon H. Bradley, Gerald G. Brown, Glenn W. Graves

    Pages 145-169

14. Programming the Methods and Experimental Design

    • Mark H. Karwan, Vahid Lotfi, Stanley Zionts, Jan Telgen

    Pages 170-179

15. Results of the Sign Test Methods

    • Mark H. Karwan, Vahid Lotfi, Stanley Zionts, Jan Telgen

    Pages 180-207

16. Results of the Other Methods

    • Mark H. Karwan, Vahid Lotfi, Stanley Zionts, Jan Telgen

    Pages 208-233

17. Improvements and Extensions

    • Mark H. Karwan, Vahid Lotfi, Stanley Zionts, Jan Telgen

    Pages 234-251

18. Results of the Improvements and Extensions

    • Mark H. Karwan, Vahid Lotfi, Stanley Zionts, Jan Telgen

    Pages 252-275

19. Conclusions

    • Mark H. Karwan, Vahid Lotfi, Stanley Zionts, Jan Telgen

    Pages 276-278

20. Back Matter

    Pages 279-289

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During the Spring of 1979 one of us (Zionts) was invited to visit Erasmus University in Rotterdam, The Netherlands. It was there that Zionts met another of us (Telgen) who was then in the process of completing a dissertation on redundancy in linear programming. At that time, Telgen proposed an extended visit to Buffalo, during which time he and Zionts would do an extensive study on redundancy. Redundancy, hardly an exciting or new topic, does have numerous applications. Telgen and Zionts planned the project for the Summer of 1980, and enlisted the support of all the contributors as well as the other two members of our team (Karwan and Lotfi). Lotfi was then a Ph. D. student in Industrial Engineering searching for a thesis topic. Redundancy became his topic. Karwan and Zionts served as his thesis co-chairmen, with Telgen serving as an outside reader of the thesis. We initially had hoped to complete the study during Telgen's stay in Buffalo, but that was far too optimistic. Lotfi completed his dissertation during the late Spring-early Summer of 1981. As the project took shape, we decided that we had more than enough for an article, or even several articles. Accordingly, not wanting to produce redundant papers, we decided to produce this volume --- a state-of-the-art review of methods for handling redundancy and comprehensive tests of the various methods, together with extensions and further developments of the most promising methods.

• Optimierung
• Redundanz
• algorithms
• linear optimization
• optimization

• Department of Industrial Engineering, State University of New York at Buffalo, Buffalo, USA

  Mark H. Karwan

• School of Management, State University of New York at Buffalo, Buffalo, USA

  Vahid Lotfi, Stanley Zionts

• Department of Applied Mathematics, Rabobank Nederland, Zeist, The Netherlands

  Jan Telgen

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