Introduction
Decision making typically involves a decision maker selecting a course of action that optimizes some criterion while respecting the resources and other conditions that must be satisfied. When multiple criteria are involved, this class of problems is generally referred to as multiple criteria decision problems. In some circumstances, the number of alternatives is limited and the decision maker identifies a number of (multiple) desirable measureable attributes. Each of the alternatives is assessed with respect to each of the attributes to provide information to the decision maker to aid in selecting the desired alternative. This type of problem is generally termed a multiple attribute decision problem. In other situations, the set of alternatives may be very large and represented as various types and levels of particular actions. The decision maker may be able to determine how various combinations of these alternatives contribute to a particular objective (e.g., completion...
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References
Benayoun, R., de Montgolfier, J., Tergny, J., & Laritchev, O. (1971). Linear programming and multiple objective functions: STEP method (STEM). Mathematical Programming, 1, 366–375.
Branke, J., Deb, K., Miettinen, K., & Slowiński, R. (Eds.). (2008). Multiobjective optimization: Interactive and evolving approaches. Berlin/Heidelburg: Springer-Verlag.
Buchanan, J. T. (1997). A naïve approach for solving MCDM problems: The GUESS method. Journal of the Operational Research Society, 48, 202–206.
Chankong, V., & Haimes, Y. Y. (1978). The interactive surrogate worth trade-off (ISWT) method for multiobjective decision making. In S. Zionts (Ed.), Multi-criteria problem solving (pp. 42–67). Berlin/Heidelberg: Springer-Verlag.
Chankong, V., & Haimes, Y. Y. (1983). Multiobjective decision making: Theory and methodology. New York: Elsevier/North-Holland.
Dyer, J. S. (1972). Interactive goal programming. Management Science, 19, 62–70.
Evans, G. W. (1984). An overview of techniques for solving multiobjective mathematical programs. Management Science, 30, 1268–1282.
Evans, G. W., Stuckman, B., & Mollaghasemi, M. (1991). Multiple response simulation optimization. In Proceedings of 1991 winter simulation conference, Phoenix, Arizona. pp 894–900.
Geoffrion, A. M., Dyer, J. S., & Feinberg, A. (1972). An interactive approach for multicriterion optimization, with an application to the operation of an academic department. Management Science, 19, 357–368.
Jaszkiewicz, A., & Slowiński, R. (1994). The light beam search over a non-dominated surface of a multiple objective programming problem. In G. H. Tzeng, H. F. Wand, U. P. Wen, & P. L. Yu (Eds.), Multiple criteria decision making – Proceedings of the tenth international conference, Springer-Verlag, New York, pp 87–99.
Korhonen, P. (1987). VIG–a visual interactive support system for multiple criteria decision making. Belgian Journal of Operations Research, Statistics, and Computer Science, 27, 3–15.
Korhonen, P., & Laasko, J. (1986). A visual interactive approach for solving the multiple criteria problem. European Journal of Operational Research, 24, 277–287.
Loucks, D. P. (1977). An application of interactive multiobjective water resources planning. Interfaces, 8(1), 70–75.
Mäkelä, M. M. (1993). Issues of implementing a Fortran subroutine package NSOLIB for nonsmooth optimization, Report 5/1993, University of Jyväskylä, Department of Mathematics, Laboratory of Scientific Computing, Jyväskylä.
Miettinen, K. M. (1994). On the methodology of multiobjective optimization with applications, Doctoral thesis, Report 60, University of Jyväskylä, Department of Mathematics, Jyväskylä.
Miettinen, K. M. (1999). Nonlinear multiobjective optimization. Boston/London/Dordrecht: Kluwer Academic.
Miettinen, K. M., & Mäkelä, M. M. (2006). Synchronous approach in interactive multiobjective optimization. European Journal of Operational Research, 170, 909–922.
Mollaghasemi, M., & Pet-Edwards, J. (1997). Making multiple objective decisions. Los Alamitos, CA: IEEE Computer Society Press.
Nakayama, H. (1989). Sensitivity and trade-off analysis in multiobjective programming. In A. Lewandowski & I. Stanchev (Eds.), Methodology and software for interactive decision support (Lecture notes in economics and mathematical systems, Vol. 337, pp. 86–93). Berlin: Springer-Verlag.
Sakawa, M. (1982). Interactive multiobjective decision making by the sequential proxy optimization technique: SPOT. European Journal of Operational Research, 9, 386–396.
Steuer, R. E. (1986). Multiple criteria optimization: Theory, computation, and application. New York: Wiley.
Steuer, R. E., & Choo, E.-U. (1983). An interactive weighted Tchebycheff procedure for multiple objective programming. Mathematical Programming, 26, 326–344.
White, D. J. (1990). A bibliography on the applications of mathematical programming multiple-objective methods. Journal of the Operational Research Society, 41, 669–691.
Wierzbicki, A. P. (1982). A mathematical basis for satisficing decision making. Mathematical Modelling, 3, 391–405.
Zopounidis, C., & Pardalos, P. M. (2010). Handbook of multicriteria analysis. Berlin/Heidelberg: Springer-Verlag.
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Pet-Armacost, J., Mollaghasemi, M., Armacost, R.L. (2013). Interactive Multiple Objective Mathematical Programming. In: Gass, S.I., Fu, M.C. (eds) Encyclopedia of Operations Research and Management Science. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1153-7_471
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