On some fractional programming models occurring in minimum-risk problems. (English) Zbl 0706.90056

Generalized convexity and fractional programming with economic applications, Proc. Workshop, Pisa/Italy 1988, Lect. Notes Econ. Math. Syst. 345, 295-324 (1990).
[For the entire collection see Zbl 0698.00041.]
This paper is primarily concerned with an extension to nonlinear problems of the Charnes and Cooper minimum risk criterion by means of which a stochastic programming problem is transformed into a deterministic fractional programming problem. The general problem is: Minimize f(a(t),x) subject to \(x\in S\) where the set \(S\subseteq R^ n\), the real vector-valued function a: \(A\to B\), the real-valued function f: \(B\times S\to R\), the sets \(A\subseteq R\) and \(B\subseteq R^ m\) are deterministic and known, and t(w) is a random variable on a given probability space.
An equivalent deterministic problem is given, and applications are made to the linear Tchebysheff problem, the bottleneck transportation problem, the max-min (bilinear and linear fractional) problems, and the multiobjective minimum risk problem.
Some algorithms are given.
Reviewer: M.A.Hanson


90C15 Stochastic programming
90C32 Fractional programming
90C29 Multi-objective and goal programming
90-08 Computational methods for problems pertaining to operations research and mathematical programming
90C30 Nonlinear programming


Zbl 0698.00041