Marginal values in mixed integer linear programming (Q1119179)

Marginal values of a given optimization problem are the directional partial derivatives of the value with respect to perturbations in the data. If \(v(c,A,b)=\min \{cx|\) Ax\(\geq b\), \(x\geq 0\}\) and if \(u=(c',A',b')\) is a vector, then the marginal value in direction u is defined by \[ \frac{\partial v}{\partial u}=\lim_{\epsilon \to 0+}\frac{v(c+\epsilon c',\quad A+\epsilon A',\quad b+\epsilon b')- v(c,A,b)}{\epsilon}. \] In this paper this concept is extended to mixed integer linear programming problems. Some applications to model formulation and post-optimal analysis are given.