Flexibility and Rigidity in Multicriterion Linear Programming
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Morse J.N., Lieb E.B. (1980) Flexibility and Rigidity in Multicriterion Linear Programming. In: Fandel G., Gal T. (eds) Multiple Criteria Decision Making Theory and Application. Lecture Notes in Economics and Mathematical Systems, vol 177. Springer, Berlin, Heidelberg.
One justification for modeling with multiobjective linear programming (MOLP) is its ability to generate unique managerial information. One drawback of MOLP is the unwieldy nondominated set which it presents to the decision maker. Two new concepts for picking one element of this set are examined in this paper. Flexibility is a universal evaluative criterion which can yield a (partial) ordering of the points in the nondominated set. It is based on the natural desire of planners to choose strategies that are reversible. Rigidity is an inverse concept. It reflects the situation in which planners specifically do not want flexibility in the chosen alternatives. Rigidity has the potential of ordering the nondominated set. Flexibility fits naturally into a financial context. Portfolio selection, for example, is a problem where the frictional costs of changing a decision are readily seen to be brokerage fees. Therefore this data base was used for an empirical study of flexibility. Rigidity, however, does not lend itself so easily to a mathematical approach. It is expressed here in a loose geometrical way. Further research may lead to an algebraic index of rigidity.