[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ skip to main content
article

Global Sensitivity Analysis

Published: 01 December 1995 Publication History

Abstract

<P>In applications of operations research models, decision makers must assess the sensitivity of outputs to imprecise values for some of the model's parameters. Existing analytic approaches for classic optimization models rely heavily on duality properties for assessing the impact of local parameter variations, parametric programming for examining systematic variations in model coefficients, or stochastic programming for ascertaining a robust solution. This paper accommodates extensive simultaneous variations in any of an operations research model's parameters. For constrained optimization models, the paper demonstrates practical approaches for determining relative parameter sensitivity with respect to a model's optimal objective function value, decision variables, and other analytic functions of a solution. Relative sensitivity is assessed by assigning a portion of variation in an output value to each parameter that is imprecisely specified. The computing steps encompass optimization, Monte Carlo sampling, and statistical analyses, in addition to model specification. The required computations can be achieved with commercially available off-the-shelf software available for microcomputers and other platforms. The paper uses a broad set of test models to demonstrate the merit of the approaches. The results are easily put to use by a practitioner. The paper also outlines further research developments to extend the applicability of the approaches.</P>

References

[1]
Agresti, A. 1990. Categorical Data Analysis. John Wiley, New York.
[2]
Babbar, M. M. 1955. Distributions of Solutions of a Set of Linear Equations With an Application to Linear Programming. J. Am. Stat. Assoc. 50, 854-869.
[3]
Boor, C. D. 1986. Approximation Theory. In Proceedings of Symposia in Applied Mathematics 36. American Mathematical Society, Providence, R.I.
[4]
Box, G. E. P., and N. R. Draper. 1959. A Basis for Selection of a Response Surface Design. J. Am. Stat. Assoc. 54, 622-654.
[5]
Bradley, S.P., A.C. Hax and T.L. Magnanti. 1977. Applied Mathematical Programming. Addison-Wesley, Reading, Mass.
[6]
Breiman, L., and W. S. Meisel. 1976. General Estimates of the Intrinsic Variability of Data in Nonlinear Regression Models. J. Am. Stat. Soc. 71, 301-307.
[7]
Breiman, L. 1991. The Pi Method for Estimation Multivariate Functions From Noisy Data. Technometrics 33, 125-143.
[8]
Bring, J. 1994. How to Standardize Regression Coefficients. Amer. Statistician 48, 209-213.
[9]
Camm, J. D., and T. H. Burwell. 1991. Sensitivity Analysis in Linear Programming Models With Common Inputs. Dec. Sci. 22, 512-518.
[10]
Casella, G., and E. I. George. 1992. Explaining the Gibbs Sampler. Amer. Statistician 46, 167-174.
[11]
Chevan, A., and M. Sutherland. 1991. Hierarchical Partitioning. Amer. Statistician 45, 90-96.
[12]
Cox, L. A., Jr. 1985. A New Measure of Attributable Risk for Public Health Applications. Opns. Res. 31, 800-813.
[13]
Cuadras, C. M. 1993. Interpreting an Inequality in Multiple Regression. Amer. Statistician 47, 256-258.
[14]
Dantzig, G. B. 1955. Linear Programming Under Uncertainty. Mgmt. Sci. 1, 197-206.
[15]
Dantzig, G. B. 1963. Linear Programming and Extensions. Princeton University Press, Princeton, N.J.
[16]
Dantzig, G. B., and P. W. Glynn. 1990. Parallel Processors for Planning Under Uncertainty. Ann. Opns. Res. 22, 1-21.
[17]
Draper, N. R., and H. Smith. 1981. Applied Regression Analysis. John Wiley, New York.
[18]
Ermoliev, Y. and R. J. B. Wets. 1988. Numerical Techniques for Stochastic Optimization. Springer Verlag, Berlin.
[19]
Eschenbach, T. G. 1992. Spider Plots Versus Tornado Diagrams for Sensitivity Analysis. Interfaces 22, 40-46.
[20]
Ewbank, J. B., B. L. Foote and H. J. Kumin. 1974. A Method for the Solution of the Distribution Problem of Stochastic Linear Programming. SIAM J. Appl. Math. 26, 225-238.
[21]
Farlow, S. J. 1981. The GMDH Algorithm of Ivakhnenko. Amer. Statistician 35, 210-215.
[22]
Farlow, S. J. (ed.) 1984. Self-Organizing Methods in Modeling: GMDH Type Algorithms. Marcel Dekker, New York.
[23]
Fiacco, A. V. 1983. Introduction to Sensitivity and Stability Analysis in Nonlinear Programming. Academic Press, New York.
[24]
Friedman, J. H. 1991. Multivariate Adaptive Regression Splines (With Discussion). Anns. Stat. 19, 1-141.
[25]
Gal, T., and J. Nedoma. 1972. Multiparametric Linear Programming. Mgmt. Sci. 18, 406-422.
[26]
Gal, T. 1979. Postoptimality Analyses, Parametric Programming, and Related Topics. McGraw-Hill, Great Britain.
[27]
Gass, S. I., and T. L. Saaty. 1954. The Parametric Objective Function, Part I. Opns. Res. 2, 316-319.
[28]
Gass, S. I., and T. L. Saaty. 1955. The Parametric Objective Function, Part II. Opns. Res. 3, 395-401.
[29]
Gassmann, H. 1990. A Computer Code for the Multi-Stage Stochastic Linear Programming Problem. Math. Prog. 47, 407-423.
[30]
Gelfand, A. E., and A. F. M. Smith. 1990. Sampling-Based Approaches to Calculating Marginal Densities. J. Am. Stat. Assoc. 85, 398-409.
[31]
Greenberg, H. J. 1993. How to Analyze the Results of Linear Programs--Part 2: Price Interpretation. Interfaces 23, 97-114.
[32]
Griffin, J. M. 1977. Long-run Production Modeling With Pseudo-Data: Electric Power Generation. Bell J. Econ. 8, 112-127.
[33]
Hamilton, D. 1987. Sometimes R2 > ryx12 + ryx22 Correlated Variables Are Not Always Redundant. Amer. Statistician 41, 129-132.
[34]
Hawkins, D. M. 1990. FIRM. Books Underground, University of Minnesota, St. Paul, Minn.
[35]
Hornik, K., M. Stinchcombe and H. White. 1989. Multilayer Feedforward Networks are Universal Approximators. Neural Networks 2, 359-366.
[36]
Infanger, G. 1994. Planning Under Uncertainty. Boyd & Fraser, Danvers, Mass.
[37]
Inman, R. L., and J. C. Helton. 1988. An Investigation of Uncertainty and Sensitivity Analysis Techniques for Computer Models. Risk Anal. 8, 71-90.
[38]
Jansen, B., C. Roos and T. Terlaky. 1992. An Interior Point Approach to Postoptimal and Parametric Analysis in Linear Programming. Technical Report 92-21. Faculty of Technical Mathematics and Informatics/Computer Science, Delft University of Technology, Delft, The Netherlands.
[39]
Jongen, H. T., and G. W. Weber. 1990. On Parametric Nonlinear Programming. Anns. Opns. Res. 27, 253-284.
[40]
Kendall, Sir M., and A. Stuart. 1979. The Advanced Theory of Statistics, Vols. 2 and 3. Charles Griffin & Company, London.
[41]
Kruskal, W. 1987. Relative Importance by Averaging Over Orderings. Amer. Statistician 41, 6-10.
[42]
Kruskal, W., and R. Majors. 1989. Concepts of Relative Importance in Recent Scientific Literature. Amer. Statistician 43, 2-6.
[43]
Kuhn, H. W., and A. W. Tucker. 1950. Nonlinear Programming. In Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, J. Neyman (ed.). University of California Press, Berkeley, Calif., 481-492.
[44]
Madansky, A. 1960. Inequalities for Stochastic Linear Programming Problems. Mgmt. Sci. 6, 197-204.
[45]
Madansky, A. 1962. Methods of Solution of Linear Programs Under Uncertainty. Opns. Res. 10, 463-471.
[46]
Manne, A. S. 1953. Notes on Parametric Linear Programming. RAND Corporation, Report No. P-468.
[47]
Manne, A. S. 1958. Programming of Economic Lot Sizes. Mgmt. Sci. 4, 115-135.
[48]
Mantel, N. 1970. Why Stepdown Procedures in Variable Selection. Technometrics 12, 621-625.
[49]
Mulvey, J. M., R. J. Vanderbei and S. A. Zenios. 1995. Robust Optimization of Large-Scale Systems, Opns. Res. 43, 264-281.
[50]
Owen, A. B. 1992. A Central Limit Theorem for Latin Hypercube Sampling. J. Roy. Stat. Soc. Series B 54, 541-555.
[51]
Palisade Corporation. 1991. @Risk: Risk Analysis and Simulation Add-In for Lotus 1-2-3. New York.
[52]
Pratt, J. W. 1987. Dividing the Indivisible: Using Simple Symmetry to Partition Variance Explained. In Proceedings Second International Tampere Conference in Statistics, T. Pukkila and S. Puntanen eds. University of Tampere, Finland, 245-260.
[53]
Prekopa, A. 1966. On the Probability Distribution of the Optimum of a Random Linear Program. SIAM J. Control 4, 211-222.
[54]
Ravi, N., and R. E. Wendell. 1985. The Tolerance Approach to Sensitivity Analysis of Matrix Coefficients in Linear Programming General Perturbations. Opns. Res. 33, 943-950.
[55]
Ravi, N., and R. E. Wendell. 1989. The Tolerance Approach to Sensitivity Analysis of Matrix Coefficients in Linear Programming. Mgmt. Sci. 35, 1106-1119.
[56]
Rubin, D. S., and H. M. Wagner. 1990. Shadow Prices: Tips and Traps for Managers and Instructors. Interfaces 20, 150-157.
[57]
Sacks, J., W. J. Welch, T. J. Mitchel and H. P. Wynn. 1989. Design and Analysis of Computer Experiments. Stat. Sci. 4, 409-435.
[58]
Schenkerman, S. 1993. Sensitivity of Linear Programs to Related Changes in Multiple Inputs. Dec. Sci. 24, 879-891.
[59]
SPSS Statistical Algorithms. 1991. SPSS Inc., Chicago, Ill.
[60]
SPSS® for Windows¿. 1993. Chicago, Ill.
[61]
Sunset Software. 1992. XA: Professional Linear Programming System. San Marino, Cal.
[62]
Talon Development Corporation. 1992. @BRAIN. Milwaukee, Wis.
[63]
Theil, H., and C. F. Chung. 1988. Information-Theoretic Measures of Fit for Univariate and Multivariate Linear Regressions. Amer. Statistician 42, 249-252.
[64]
Wagner, H. M. 1958. On the Distribution of Solutions in Linear Programming Problems. J. Am. Stat. Assoc. 53, 161-163.
[65]
Wagner, H. M. 1975. Principles of Operations Research. Prentice Hall, Englewood Cliffs, N.J.
[66]
Wagner, H. M., N. Kathuria and V. Vargas. 1992. Aggregate Planning Models. In Perspectives on Operations Management in Honor of E. S. Buffa, R. K. Sarin (ed.). Kluwer Academic Publishers, Boston, 359-388.
[67]
Wagner, H. M., and T. M. Whitin. 1957. Dynamic Problems in the Theory of the Firm. In The Theory of Inventory Management, T. M. Whitin. Princeton University Press, Princeton, N.J., 299-327.
[68]
Wagner, H. M., and T. M. Whitin. 1958. Dynamic Version of the Economic Lot Size Model. Mgmt. Sci. 5, 89-96.
[69]
Ward, J. E., and R. E. Wendell. 1990. Approaches to Sensitivity Analysis in Linear Programming. Anns. Opns. Res. 27, 3-38.
[70]
Wendell, R. E. 1984. Using Bounds on the Data in Linear Programming: The Tolerance Approach to Sensitivity Analysis. Math. Prog. 29, 304-322.
[71]
Wendell, R. E. 1985. The Tolerance Approach to Sensitivity Analysis in Linear Programming. Mgmt. Sci. 31, 564-578.
[72]
Wendell, R. E. 1992. Sensitivity Analysis Revisited and Extended. Dec. Sci. 23, 1127-1142.
[73]
Wets, R. J.-B. 1989. Stochastic Programming. In Handbook of Operations Research and Management Science, G. L. Nemhauser, A. H. G. Kan, and M. J. Todd (eds.). North-Holland, Amsterdam, 573-629.
[74]
Wilks, S. S. 1962. Mathematical Statistics. John Wiley, New York.
[75]
Wondolowski, F. R., Jr. 1991. A Generalization of Wendell's Tolerance Approach to Sensitivity Analysis in Linear Programming. Dec. Sci. 22, 792-810.
[76]
Zelen, M., and N. C. Severo. 1964. Probability Functions. In Handbook of Mathematical Functions, M. Abramowitz and I. A. Stegun (eds.). National Bureau of Standards, Washington, D.C., 927-995.

Cited By

View all

Recommendations

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Operations Research
Operations Research  Volume 43, Issue 6
December 1995
160 pages

Publisher

INFORMS

Linthicum, MD, United States

Publication History

Published: 01 December 1995

Author Tags

  1. estimation
  2. fitting value of optimal objective function
  3. linear
  4. programming
  5. sensitivity analysis
  6. statistics

Qualifiers

  • Article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)0
  • Downloads (Last 6 weeks)0
Reflects downloads up to 09 Jan 2025

Other Metrics

Citations

Cited By

View all
  • (2024)An annotated timeline of sensitivity analysisEnvironmental Modelling & Software10.1016/j.envsoft.2024.105977174:COnline publication date: 1-Mar-2024
  • (2023)Information Density in Decision AnalysisDecision Analysis10.1287/deca.2022.046520:2(89-108)Online publication date: 1-Jun-2023
  • (2022)Sensitivity analysis of agent-based models: a new protocolComputational & Mathematical Organization Theory10.1007/s10588-021-09358-528:1(52-94)Online publication date: 1-Mar-2022
  • (2021)Sensitivity Analysis on Constraints of Combinatorial Optimization ProblemsLearning and Intelligent Optimization10.1007/978-3-030-92121-7_30(394-408)Online publication date: 20-Jun-2021
  • (2020)Faster KrigingOperations Research10.1287/opre.2019.186068:1(233-249)Online publication date: 1-Jan-2020
  • (2020)Decomposing Dynamic Risks into Risk ComponentsManagement Science10.1287/mnsc.2019.352266:12(5738-5756)Online publication date: 1-Dec-2020
  • (2020)Sensitivity analysis in constrained evolutionary optimizationProceedings of the 2020 Genetic and Evolutionary Computation Conference10.1145/3377930.3390222(894-902)Online publication date: 25-Jun-2020
  • (2019)Metamodel-assisted sensitivity analysis for controlling the impact of input uncertaintyProceedings of the Winter Simulation Conference10.5555/3400397.3400696(3681-3692)Online publication date: 8-Dec-2019
  • (2019)Solving Large Batches of Linear ProgramsINFORMS Journal on Computing10.1287/ijoc.2018.083831:2(302-317)Online publication date: 15-Apr-2019
  • (2019)Enhanced Morris method for global sensitivity analysis: good proxy of Sobol’ indexStructural and Multidisciplinary Optimization10.1007/s00158-018-2071-759:2(373-387)Online publication date: 15-Feb-2019
  • Show More Cited By

View Options

View options

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media