Decompositions of Multiattribute Utility Functions Based on Convex Dependence

Article Abstract:

A method of assessing Von Neumann-Morgenstern utility functions on a two-attribute space and its extension to n-attribute spaces is described. The concept of convex dependence between two attributes is introduced first. Then the change of shapes of conditional utility functions is considered. Finally theorems which show how to decompose a two-attribute utility function using the concept of convex dependence are considered. This concept covers a wide range of situations involving trade-offs. The convex decomposition included as special case Keeney's additive-multiplicative decompositions, Fishburn's bilateral decomposition, and Bell's decomposition under the interpolation independence. Moreover, the convex decomposition is an exact grid model which was axiomatized by Fishburn and Forquhar. Finally, the convex decomposition theorem from two attributes to an arbitrary number of attributes is extended.

Decision theory, Simulation, Decision Making, Function Analysis, Theorem Proving

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A Class of Linear Programs Convertible to Network Problems

Article Abstract:

A class of two commodity network flow problems with additional structured linear constraints in place of the usual capacity constraints is considered. The class of linear programs arose as subproblems in a mixed integer programming formulation of a location model, and was solved by Ramakrishnan using a special purpose primal simplex algorithm. Although the constraint matrices of these problems are not transformable to constraint matrices of pure network problems. The transformation depends on the existence of a set of variables whose non-negativity restrictions are redundant to the definition of the feasible region. Other situations in which such structure occurs are included.

Linear programming, Algorithms, Integer programming, Algorithm, Matrix Computations

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Model Building Techniques for the Correction of End Effects in Multistage Convex Programs

Article Abstract:

Model building procedures that can be used to reduce end effects in multistage planning models are discussed. Problems that are peculiar to energy planning applications are emphasized. The paper presents and compares four methods for mitigating end effects. It concludes that one of these four methods, the dual equilibrium, is best. The major drawback of the dual equilibrium procedure is its lack of simplicity. If it is to be widely used, then it must be widely understood.

Business planning, Forecasting, Modeling, Data modeling software, Applications, Energy Management, Approximation

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