Abstract
The goal programming problem is determined by a feasible set of vectors and a goal point; its aim is to select a feasible point closest to the goal point in certain sense. A particular case of the goal programming problem is the rationing problem, when a given amount of resource must be distributed among agents with unequal claims on the resource. We impose axioms on a selection rule that guarantee the solution of the rationing problem under the selection rule of the goal programming problem to be equal sacrifice with respect to a certain family of utility functions of agents. For problems with convex relatively closed feasible sets, the general selection rule minimizes the proximity measure to the goal point given by the sum of antiderivatives of differences between utility functions. The least squares solution and maximal weighted entropy solution are obtained under additional axioms.
Partial support from the European Community under Grant INTAS 96-106 is gratefully acknowledged. The authors would like to express sincere gratitude to Anna Khmelnitskaya and Victor Domanskij for fruitful discussions.
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Bregman, L.M., Naumova, N.I. (2002). Goal Programming Solutions Generated by Utility Functions. In: Tangian, A.S., Gruber, J. (eds) Constructing and Applying Objective Functions. Lecture Notes in Economics and Mathematical Systems, vol 510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56038-5_27
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DOI: https://doi.org/10.1007/978-3-642-56038-5_27
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