Abstract
We consider how the analytic hierarchy process (AHP) can be used in multiple objective linear programming. In particular, when only qualitative (subjective, judgmental) data is available, the AHP can be used to quantify the qualitative relationships between the row variables and the decision variables. The AHP can also assist a decision maker in specifying the so-called reference direction in an interactive search procedure. The reference direction is a direction, which reflects the desire of the decision maker to improve the values of the objectives starting from the current position. We illustrate our ideas with a numerical example, which is slightly modified from a real application.
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References
Arbel, A. and Oren, S. 1986. Priority-based interactive multicriteria optimization algorithm. In Preprints of VII-th International Conference on Multiple Criteria Decision Making, Kyoto, Japan, August 18–22,1986.
Gass S. 1986. A process for determining priorities and weights for large-scale linear goal programmes. Journal of Operational Research Society 37: 779–785.
Kok, M. and Lootsma, F. 1985. Pairwise-comparison methods in multi-objective programming with applications in a long-term energy-planning model. European Journal of Operational Research 22: 44–55.
Korhonen, P. 1987. The specification of a reference direction using the AHP. Mathematical Modelling 9: 361–368.
Korhonen, P. and Laakso, J. 1986. A visual interactive method for solving the multiple criteria problem. European Journal of Operational Research 24: 277–287.
Korhonen, P. and Lantto, O. 1986. An experimental comparison of some reference direction techniques for MCDM-problems. Working Paper F-142, Helsinki School of Economics.
Korhonen, P. and Wallenius, J. 1988. A Pareto race. Naval Research Logistics 35: 615–623.
Korhonen, P. and Wallenius, J. 1990. Using qualitative data in multiple objective linear programming. European Journal of Operational Research 48: 81–87.
Romero, C., Sutcliffe, C., Board, J. and Cheshire, P. 1985. Naive weighting in non-preemptive goal programming: Viewpoint and reply. Journal of Operational Research Society 36: 647–649.
Saaty, T. 1980. The Analytic Hierarchy Process. McGraw-Hill, New York.
Wierzbicki, A. 1980. The use of reference objectives in multiobjective optimization. Pages 468–486 in G. Fandel and T. Gal. (eds) Multiple Criteria Decision Making, Theory and Application. Springer-Verlag, Berlin.
Wierzbicki, A. 1986. On the completeness and constructiveness of parametric characterizations to vector optimization problems. OR-Spectrum 8: 73–87.
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© 2001 Springer Science+Business Media Dordrecht
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Korhonen, P., Wallenius, J. (2001). On Using the AHP in Multiple Objective Linear Programming. In: Schmoldt, D.L., Kangas, J., Mendoza, G.A., Pesonen, M. (eds) The Analytic Hierarchy Process in Natural Resource and Environmental Decision Making. Managing Forest Ecosystems, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9799-9_3
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DOI: https://doi.org/10.1007/978-94-015-9799-9_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5735-8
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