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Systems Evaluation and Repricing Theorems

Author

Listed:
  • A. Charnes

    (The Technological Institute, Northwestern University)

  • W. W. Cooper

    (Graduate School of Industrial Administration, Carnegie Institute of Technology)

Abstract

When a system is described in terms of a linear programming problem max c T x with Ax \leqq b, x \geqq 0, study of its properties, e.g., sensitivity analyses, etc., focuses on effects of alterations in the triple (A, b, c) on the properties of the system. These effects are non-linear and generally lead one away from a model with convenient special structure to much more complex systems. In this paper, methods ("repricing-reprocessing" theorems) are developed which (under certain assumptions about real world behavior) permit one to assess these effects exactly by means of a model of the same structure which can be prescribed in advance. The proofs of these theorems are accomplished by the "chained construction" methods of Charnes and Cooper. Approximation techniques and exact characterization of the non-linearities are also presented.

Suggested Citation

  • A. Charnes & W. W. Cooper, 1962. "Systems Evaluation and Repricing Theorems," Management Science, INFORMS, vol. 9(1), pages 33-49, October.
    • Handle: RePEc:inm:ormnsc:v:9:y:1962:i:1:p:33-49
    DOI: 10.1287/mnsc.9.1.33
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    Cited by:

    1. Demiröz, Barış Evrim & Altınel, İ. Kuban & Akarun, Lale, 2019. "Rectangle blanket problem: Binary integer linear programming formulation and solution algorithms," European Journal of Operational Research, Elsevier, vol. 277(1), pages 62-83.
    2. İ. Altınel & Bora Çekyay & Orhan Feyzioğlu & M. Keskin & Süleyman Özekici, 2011. "Mission-Based Component Testing for Series Systems," Annals of Operations Research, Springer, vol. 186(1), pages 1-22, June.
    3. Feyzioglu, Orhan & Kuban Altinel, I. & Ozekici, Suleyman, 2006. "The design of optimum component test plans for system reliability," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3099-3112, July.
    4. V. Balachandran & Suresh Jain, 1975. "Optimal Facility Location under Random Demand with General Cost Structure," Discussion Papers 149, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Glover, Fred & Sueyoshi, Toshiyuki, 2009. "Contributions of Professor William W. Cooper in Operations Research and Management Science," European Journal of Operational Research, Elsevier, vol. 197(1), pages 1-16, August.
    6. Kuzʹmin, S. A., 1976. "Introduction to the structure and dynamics of systems; a technical note," ILO Working Papers 991691233402676, International Labour Organization.
    7. Kuban Altinel, I. & Ozekici, Suleyman, 1998. "Optimum component test plans for systems with dependent components," European Journal of Operational Research, Elsevier, vol. 111(1), pages 175-186, November.

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