Approximate Answer to MP-MILP Problems Using McCormic Release of Modified Components

Multi-parametric programming theory is a valuable tool for decision making under uncertainty and has been an active area of research. Although multi-parametric programming with uncertainty in the objective function coefficients and right-hand side of constraints has been extensively discussed and various methods have been proposed for this, uncertainty in the coefficients matrix (i.e. left-hand side uncertainty) have been less considered. In this work, a new method for solving multi-parametric mixed-integer linear problems (mp-MILP) with uncertainty in constraints is presented. This procedure consists of two steps, which in the first step, the bounds of the bilinear terms are improved by using tightening piecewise McCormick relaxations and secondly, based on these improved bounds and estimating bilinear terms, an approximate model of mp-MILP is obtained. The performance of the presented method is investigated by two examples. To do this, the approximation of the problem has been done in different partitioning factors and computational requirements to solve them have been compared.