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A simulation study of simplification strategies in the development of optimization models

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  • Knolmayer, Gerhard

Abstract

A major decision in the development of optimization models concerns the degree of accuracy to be used in the model. In practica, this simplification decision is widely met in an ad hoc fashion. Recently, several ways of Computing (worst-case) bounds for simplifying linear programming (LP) models have been developed. On the other hand, the need for empirical studies of simplification effects has been expressed. This paper discusses LP-models for product-mix planning in a job-shop in which manufacturing options exist. In this decision Situation some simplification (compared to the data used in nonsimultaneous planning) is often necessary to obtain a computa-tionally manageable LP model. Several simplification strategies are defined and applied in the Simulation study. Properties of the solutions obtained after applying the different simplification strategies are compared to those of the "real" Optimum. Significant differences of the objective function values allow ranking of the simplification strategies and giving recom-mendations for practical model development.

Suggested Citation

  • Knolmayer, Gerhard, 1981. "A simulation study of simplification strategies in the development of optimization models," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 96, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    • Handle: RePEc:zbw:cauman:96
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    1. Alvin C. Egbert & Hyung M. Kim, 1975. "Analysis of Aggregation Errors in Linear Programming Planning Models," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 57(2), pages 292-301.
    2. Raine, P. S. & Flavell, R. B. & Salkin, G. R., 1978. "Determining appropriate levels of data aggregation in a linear programming model," European Journal of Operational Research, Elsevier, vol. 2(1), pages 26-31, January.
    3. Paul H. Zipkin, 1980. "Bounds on the Effect of Aggregating Variables in Linear Programs," Operations Research, INFORMS, vol. 28(2), pages 403-418, April.
    4. Stelios H. Zanakis, 1977. "Heuristic 0-1 Linear Programming: An Experimental Comparison of Three Methods," Management Science, INFORMS, vol. 24(1), pages 91-104, September.
    5. A. M. Geoffrion & G. W. Graves, 1974. "Multicommodity Distribution System Design by Benders Decomposition," Management Science, INFORMS, vol. 20(5), pages 822-844, January.
    6. Markku Kallio, 1977. "Computing bounds for the optimal value in linear programming," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 24(2), pages 301-308, June.
    7. A. M. Geoffrion, 1977. "A priori error bounds for procurement commodity aggregation in logistics planning models," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 24(2), pages 201-212, June.
    8. Ward Whitt, 1979. "Approximations of Dynamic Programs, II," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 179-185, May.
    9. Paul H. Zipkin, 1980. "Bounds for Row-Aggregation in Linear Programming," Operations Research, INFORMS, vol. 28(4), pages 903-916, August.
    10. Ward Whitt, 1978. "Approximations of Dynamic Programs, I," Mathematics of Operations Research, INFORMS, vol. 3(3), pages 231-243, August.
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