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Economic Models, Estimation and Risk Programming: Essays in Honor of Gerhard Tintner pp 425–455Cite as

Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints

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Part of the book series: Lecture Notes in Operations Research and Mathematical Economics ((LNE,volume 15))

Abstract

Chance constrained programming admits random data variations and permits constraint violations up to specified probability limits. Different kinds of decision rules and optimizing objectives may be used so that, under certain conditions, a programming problem (not necessarily linear) can be achieved that is deterministic--in that all random elements have been eliminated. Existence of such ‘deterministic equivalents’ in the form of specified convex programming problems is here established for a general class of linear decision rules under the following 3 classes of objectives: (1) maximum expected value (‘E model’); (2) minimum variance (‘V model’); and (3) maximum probability (‘P model’). Various explanations and interpretations of these results are supplied along with other aspects of chance constrained programming. For example, the ‘P model’ is interpreted so that H.A. SIMON’S suggestions for ‘satisficing’ can be studied relative to more traditional optimizing objectives associated with ‘E’ and ‘V model’ variants. 2/

Reprinted from Operations Research, XI, No. 1, 18–39 (1963).

Note: This is an extended version of a previous report, “Deterministic Equivalents for Different Objectives in Chance Constrained Programming,” which was released by the authors as ONR. Research Memorandum No. 37 on the projects Temporal Planning and Management Decision under Risk and Uncertainty (Evanston, Ill.: Northwestern University, Dec. 1960) and Planning and Control of Industrial Operations (Pittsburgh: Carnegie Institute of Technology). Both projects are under contract with the U.S. Office of Naval Research. Contract Nonr-1228(10), Project NR 047-021 and Contract Nonr-760(01), Project NR-047011. The authors have benefited from comments by W. Szware, G. L. Thompson and H. A. Simon and they are indebted to the Ford Foundation for faculty fellowships that made time available for these revisions.

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References

  1. BEN-ISRAEL, A., “On Some Problems of Mathematical Programming,” Ph.D. Thesis in Engineering Science ( Evanston, Ill., Northwestern University, June 1962 ).

    Google Scholar 

  2. BEN-ISRAEL, A. AND A. CHARNES, “Constant Level Inventory Policies and Chance- Constrained Programming Models,” ( Evanston, Ill.: Northwestern University, 1961 ).

    Google Scholar 

  3. CHARNES, A., AND W. W. COOPER, “Chance-Constrained Programming,” Management Sci. 6, No. 1, October, 1959.

    Google Scholar 

  4. CHARNES, A., AND W. W. COOPER, Management Models and Industrial Applications of Linear Programming Wiley, New York, 1961.

    Google Scholar 

  5. CHARNES, A., AND W. W. COOPER, “Normal Deviates and Chance Constraints,” J. Am. Stat. Assoc. 57, 134–148 (1962).

    Article  Google Scholar 

  6. CHARNES, A., AND W. W. COOPER, “Programming with Fractional Functionals, I: Linear Fractional Programming,” Naval Res. Log. Quart. (forthcoming).

    Google Scholar 

  7. CHARNES, A., AND W. W. COOPER, “Systems Evaluations and Repricing Theorems,” Management Sci. 9, No. 1 (1962).

    Google Scholar 

  8. CHARNES, A., AND W. W. COOPER, “The Theory of Search: Optimum Distribution of Search Effort, ” Management Sci. 5, No. 1 (1958)

    Google Scholar 

  9. CHARNES, A., AND W. W. COOPER, AND K. KORTANEK, “Duality, Haar Programs and Finite Sequence Spaces,” Proc. National Acad. Sci. 48, 783–786 (1962)

    Article  Google Scholar 

  10. CHARNES, A., AND, “Duality in Semi-Infinite Programs and Some Works of Haar and Caratheodory,” Management Sci. (forthcoming).

    Google Scholar 

  11. CHARNES, A., AND M. H. MILLER, “Application of Linear Programming to Financial Budgeting and the Costing of Funds,” J. Business Univ. of Chicago 32, 20–46 (1959).

    Google Scholar 

  12. CHARNES, A., AND G. H. SYMONDS, “Cost Horizons and Certainty Equivalents: An Approach to Stochastic Programming of Heating Oil Production, ” Management Sci 4, No. 3 (1958).

    Google Scholar 

  13. CHARNES, A., AND G. L. THOMPSON, “Constrained Generalized Medians and Linear Programming under Uncertainty,” Management Sci. (forthcoming).

    Google Scholar 

  14. COOPER, W. W. AND J. D. SAVVAS, “Motivational Cost and Transients in Budgeting the Behavior of Cost and Aspirations,” ONR Memo 83, Pittsburgh: Carnegie Institute of Technology, May 1961.

    Google Scholar 

  15. DANTZIG, G. B., “Linear Programming under Uncertainty,” Management Sci. 1, 197–206 (1955).

    Google Scholar 

  16. DANTZIG, G. B., “Recent Advances in Linear Programming,” Management Sci. 2, 131–144 (1956).

    Google Scholar 

  17. HOLT, C. C., F. MODIGLIANI, J. MUTH, AND H. A. SIMON, Planning Production, Inventory and Work Force, Prentice-Hall, Englewood Cliffs, New Jersey, 1960.

    Google Scholar 

  18. MANDANSKY, A., “Inequalities for Stochastic Linear Programming Problems,” Management Sci. 6, 197–204 (1960).

    Google Scholar 

  19. MARCH, J. G. AND H. A. SIMON, Organizations Wiley, New York, 1958.

    Google Scholar 

  20. MARKOWITZ, H. M., Portfolio Selections: Efficient Diversification of Investment, Wiley, New York, 1959.

    Google Scholar 

  21. NASLUND, B. AND A. W. WHINSTON, “A Model of Multi-Period Investment under Uncertainty, ” Management Sci. 8, 184–200 (1962).

    Article  Google Scholar 

  22. SIMON, H. A., Models of Man, Wiley, New York, 1957.

    Google Scholar 

  23. “Theories of Decision-Making in Economics and Behavioral Science,” Am. Economics Rev. 49, No. 3 (1959).

    Google Scholar 

  24. STEDRY, A., Budget Control and Cost Behavior Prentice-Hall, New York, 1960.

    Google Scholar 

  25. STEDRY, A., AND A. CHARNES, “Exploratory Models in the Theory of Budgetary Control,” ONR Research Memo 43, Mimeo, for project Temporal Planning and Management Decisions under Risk and Uncertainty (Evanston: Northwestern University, January 8, 1962 ).

    Google Scholar 

  26. SYMONDS, G., “Stochastic Scheduling by the Horizon Method,” Management Sci. 8, 138–167 (1962).

    Google Scholar 

  27. THEIL, H., “Some Reflections on Static Programming under Uncertainty,” Weltwirtschaftliches Archiv. 87, 1961 and reprinted as Publication No. 5 of The International Center for Management Science (Rotterdam: The Netherlands School of Economics).

    Google Scholar 

  28. A Note on Stochastic Linear Programming,“ Econometrics 28, 490–495 (1960).

    Google Scholar 

  29. TINTNER, G., “Stochastic Linear Programming with Applications to Agricultural Economics,” Second Symposium on Linear Programming H. A. Antosiewicz, ed. ( Washington: National Bureau of Standards, 1955 ).

    Google Scholar 

  30. VAJDA, S., “Inequalities in Stochastic Linear Programming,” Bull. International Stat. Institute 36, 357–363 (1958).

    Google Scholar 

  31. VAN DE PANNE, C. AND W. POPP, “Minimum-Cost Cattle Feed under Probabilistic Protein Constraints,” Management Sci. (forthcoming).

    Google Scholar 

  32. WEINGARTNER, H. M., “Mathematical Programming and the Analysis of Capital Budgeting,” Ph.D. Thesis, Graduate School of Industrial Administration ( Pittsburgh: Carnegie Institute of Technology, 1961 ).

    Google Scholar 

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Author information

Authors and Affiliations

  1. The University of Texas, USA

    A. Charnes

  2. Carnegie-Mellon University, USA

    W. W. Cooper

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  1. A. Charnes
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  2. W. W. Cooper
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Editor information

Editors and Affiliations

  1. Iowa State University, Ames, USA

    Karl A. Fox (Distinguished Professor of Economics) & Jati K. Sengupta (Professor of Economics and Statistics) (Distinguished Professor of Economics) &  (Professor of Economics and Statistics)

  2. Graduate School of Business Administration, New York University, New York City, USA

    G. V. L. Narasimham (Associate Professor of Economics) (Associate Professor of Economics)

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© 1969 Springer-Verlag Berlin · Heidelberg

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Charnes, A., Cooper, W.W. (1969). Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints. In: Fox, K.A., Sengupta, J.K., Narasimham, G.V.L. (eds) Economic Models, Estimation and Risk Programming: Essays in Honor of Gerhard Tintner. Lecture Notes in Operations Research and Mathematical Economics, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46198-9_19

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  • DOI: https://doi.org/10.1007/978-3-642-46198-9_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04638-7

  • Online ISBN: 978-3-642-46198-9

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