A PARAMETRIC PROGRAMMING SOLUTION TO THE VECTOR MAXIMUM PROBLEM, WITH APPLICATIONS TO DECISIONS UNDER UNCERTAINTY
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Abstract
Abstract : This work begins with a study of individual decision-making under uncertainty. Several methods for circumventing uncertainty in the constraints are briefly reviewed, and several decision criteria for circumventing uncertainty in the objective function are discussed. Particular attention is devoted to the demonstration of certain relationships between these criteria. It is concluded that vector maximum reformulations of the problem play a prominent role in dealing with uncertainty in such decision problems. Two methods for transforming a vector maximum problem into an equivalent parametric programming problem are discussed. Existing computational methods for the latter problems are briefly surveyed. The principal contribution of this work is presented as a class of algorithms for solving parametric concave programming problems. This problem also subsumes the standard (non-parametric) concave programming problem when a feasible solution is known. Thus the present algorithms provide a deformation method of concave programming.