Intermediate integer programming representations using value disjunctions

We introduce a general technique to create an extended formulation of a mixed-integer program. We classify the integer variables into blocks, each of which generates a finite set of vector values. The extended formulation is constructed by creating a new binary variable for each generated value. Initial experiments show that the extended formulation can have a more compact complete description than the original formulation. We prove that, using this reformulation technique, the facet description decomposes into one "linking polyhedron" per block and the "aggregated polyhedron". Each of these polyhedra can be analyzed separately. For the case of identical coefficients in a block, we provide a complete description of the linking polyhedron and a polynomial-time separation algorithm. Applied to the knapsack with a fixed number of distinct coefficients, this theorem provides a complete description in an extended space with a polynomial number of variables. Based on thi...

• Type: Journal
• Year: 2008
• Where: DISOPT
• Authors: Matthias Köppe, Quentin Louveaux, Robert Weismantel
• Keywords: Compact Complete Description, Complete Description, DISOPT 2008, Extended Formulation