The implications of a fractile approach to linear programming under risk through maximizing a given fractile of the distribution of profits under linear programming restrictions are examined here both theoretically, computationally and empirically.

A linear programming problem is said to be stochastic if one or more of the coefficients in the objective function or the system of constraints or resource availabilities is known only by its probability distribution. Various approaches are available in this case, which may be classified into...

An ordinary linear programming problem is formulated as <disp-formula><tex-math><![CDATA[$$\mbox{Maximize} z = cz$$]]></tex-math></disp-formula> under the constraints <disp-formula><tex-math><![CDATA[\begin{eqnarray*} Ax \leqq b,\\ x \geqq 0, \end{eqnarray*}]]></tex-math></disp-formula> where A is a matrix with m rows and n columns, x and c are column vectors with n elements, and b is a column vector with n elements. The theory of stochastic linear programming first suggested by Tintner [Tintner, G....