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The Application of Optimum-Seeking Techniques to Simulation Studies: A Preliminary Evaluation**

Published online by Cambridge University Press:  19 October 2009

Robert C. Meier
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Extract

The origins of the application of quantitative methods to the determination of optimum solutions to managerial problems can be traced back at least as far as 50 years when calculus techniques were first suggested for solution of economic lot size problems. However, the great increase in applications of optimizing techniques occurred after the Second World War with the popularization of the operations research concept and development of a wide variety of mathematical tools — among them linear programming, queuing theory, dynamic programming, and network flow theory. The development of digital computers in the late 1940's substantially reduced computational problems associated with the use of many mathematical methods and also made possible the use of simulation techniques which, without digital computers, are not ordinarily practical because of the large amount of computation involved.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 2 , Issue 1 , March 1967 , pp. 31 - 51
Copyright
Copyright © School of Business Administration, University of Washington 1967

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References

1 For an extensive discussion of some of these methods, see Wilde, Douglass J., Optimum Seeking Methods, Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1964.Google Scholar

2 For a review of some of the techniques and applications, see Hunter, William G. and Kittrell, J. R., “Evolutionary Operation: A Review,” Technometrics, Vol. 8, No. 3, August, 1966Google Scholar. Also see Baasel, William D., “Exploring Response Surfaces to Establish Optimum Conditions,” Chemical Engineering, October 25, 1965.Google Scholar

3 The reader should not confuse this name with the simplex method of linear programming which also derives its name from the geometric configuration called a simplex.

4 A complete discussion of the simplex method is contained in Carpenter, B. H. and Sweeny, H. C., “Process Improvement with ‘Simplex’ Self- Directing Evolutionary Operation,” Chemical Engineering, July 5, 1965.Google Scholar

5 A description of the application of the basic simplex procedure to deterministic simulation is contained in Healea, Gary F., Evolutionary Methods as Applied to Simulation Models, Unpublished Master of Business Administration Research Report, University of Washington, 1966Google Scholar. Mr Healea's work was invaluable as a starting point for the research of the author reported in this article.

6 Grant, Eugene L., Statistical Quality Control (3rd Edition), New York: McGraw-Hill, 1964Google Scholar, Appendix, Table B.

7 The decision rules are expressed in terms of a minimization problem.

8 The simulation program is described in detail in Meier, Robert C. and Newell, William T., Inventory Simulation Program: ISP2, Technical Report Series, No. 1, Seattle: Graduate School of Business Administration, University of Washington, 1966.Google Scholar

9 An excellent discussion of this type of inventory management system is contained in Fetter, Robert B. and Dalleck, Winston C., Decision Models for Inventory Management, Homewood, Ill.: Richard D. Irwin, Inc., 1961.Google Scholar

10 In addition to the data shown in Table 4, the complete printout tabulates location of vertices, individual simulation run results, ranges of criterion at the vertices and centroid, limits of significant differences, and results of tests of significance of differences and application of the decision rules.