Some thoughts on the development of integer programming during my research career – lecture delivered upon receiving the EURO Gold Medal, July 9, 2001, Rotterdam

We focus on the vertices of the master corner polyhedron (MCP), a fundamental object in the theory of integer linear programming. We introduce two combinatorial operations that transform vertices to their neighbors. This implies that each MCP can be defined by the initial vertices regarding these operations; we call them support vertices. We prove that the class of support vertices of all MCPs over a group is invariant under automorphisms of this group and describe MCP vertex bases. Among other results, we characterize its irreducible points, establish relations between a vertex and the nontrivial facets that pass through it, and prove that this polyhedron is of diameter 2.

This paper describes the development and solution of binary integer formulations for production scheduling problems in market-driven foundries. This industrial sector is comprised of small and mid-sized companies with little or no automation, working with diversified production, involving several different metal alloy specifications in small tailor-made product lots. The characteristics and constraints involved in a typical production environment at these industries challenge the formulation of mathematical programming models that can be computationally solved when considering real applications. However, despite the interest on the part of these industries in counting on effective methods for production scheduling, there are few studies available on the subject. The computational tests prove the robustness and feasibility of proposed models in situations analogous to those found in production scheduling at the analyzed industrial sector.