In this paper we present a mathematical programming approach to tighten a Big-$M$ formulation ($P_M$) of a Mixed Integer Problem with Logical Implications ($P$). If $M_0$ is a valid vector (the optimal solutions of $P$ belong to the feasible solutions set of $P_{M_0}$) our procedures find a valid vector $M$ such that $M \leq M_0$. As a consequence, the upper bounds generated by using the linear relaxations of $P_M$ are stronger when $M \neq M_0$. As a result, an standard branch and cut algorithm can be used to try to solve $P$ by using $P_M$ with a high probability of obtaining better results than using $P_{M_0}$. Computational results are presented in order to show that our procedures are very promising.
Citation
Escuela de Computación, Facultad de Ciencias, Universidad Central de Venezuela (August,2014).