Uncertainty analysis on the righthand side for MILP problems



A systematic framework is developed to solve the parametric mixed integer linear programming (pMILP) problems where uncertain parameters are present on the righthand side (RHS) of the constraints. For the case of multiple uncertain parameters, a new algorithm of multiparametric linear programming (mpLP) is proposed, which solves a number of nonlinear problems (NLP) iteratively. At each iteration, a point at which the objective value cannot be represented by the current optimal functions is found, and the new optimal function is included in the next iteration. Given the range of uncertain parameters in a MILP problem, the output of this proposed framework is a set of optimal integer solutions and their corresponding critical regions and optimal functions. A number of examples are presented to illustrate the applicabilities of the proposed approach and comparison with existing techniques. © 2006 American Institute of Chemical Engineers AIChE J, 2006