A linear-approximation method for solving a special-class of the chance-constrained programming problem

This article presents a technique which seeks the optimum (or near optimum) solution of a nonlinear problem by searching through the set of nondominated solutions of the Bicriterion Linear Programming (BLP) problem. An approximation formula for constructing two linear objective functions, based on the nonlinear objective function of the equivalent deterministic form of the stochastic programming model, is presented. It is proved that a finite number of nondominated solutions need to be investigated before the algorithm converges to the optimum solution point. Each nondominated solution point is the optimum solution of a linear problem over the feasible region of the nonlinear problem along with an added ‘compromise’ constraint. This compromise constraint is a hyperplane passing through the ideal solution point of the BLP problem. The most attractive feature of this new practical technique is its ability to search for the optimal solution without examining the whole set of feasible solutions.