On Some Fractional Programming Models Occurring in Minimum-Risk Problems

This paper deals with an extension of the minimum-risk criterion considered by B. Bereanu [5, 6, 7] and A. Charnes and W. W. Cooper [11] in the linear case to the nonlinear mathematical programming case. In what follows the minimum-risk criterion is applied to some special classes of nonlinear problems as are, for instance, linear Tchebysheff problems, bottlenech transportation problems, max-min (linear or linear fractional) problems with linked constraints, max-min bilinear programming problems. It is shown that, under certain hypotheses, these stochastic problems are equivalent to deterministic fractional problems. The last section examines the vectorial minimum-risk problem. The ideas discussed in this paper string together the developments given by the authors in [33–38, 43–45].