Improved Big-M reformulation for generalized disjunctive programs

In this work, we present a new Big-M reformulation for Generalized Disjunctive Programs. The proposed MINLP reformulation is stronger than the traditional Big-M, and it does not require additional variables or constraints. We present the new Big-M, and analyze the strength in its continuous relaxation compared to that of the traditional Big-M. The new formulation is tested by solving several instances of process networks and muli-product batch plant problems with an NLP-based branch and bound method. The results show that, in most cases, the new reformulation requires fewer nodes and less time to find the optimal solution.