Claudio Arbib We address a bilevel location problem where a leader first decides which facilities to open and their access prices; then, customers make individual decisions minimizing individual costs. In this note we prove that, when access costs do not fulfill metric properties, the problem is NP-hard even if facilities can be opened at no fixed cost. … Read more
We address a 1-dimensional cutting stock problem where, in addition to trim-loss minimization, we require that the set of cutting patterns forming the solution can be sequenced so that the number of stacks of parts maintained open throughout the process never exceeds a given $s$. For this problem, we propose a new integer linear programming … Read more
We discuss two formulations of the Pattern Minimization Problem: (1) introduced by Vanderbeck, and (2) obtained adding setup variables to the cutting stock formulation by Gilmore-Gomory. Let $z_i^{LP}(u)$ be the bound given by the linear relaxation of ($i$) under a given vector $u = (u_k)$ of parameters. We show that $z_2^{LP}(u}) \ge z_1^{LP}(u)$ and provide … Read more
One of the main issues in the glass industry is the minimization of the trim loss generated when cutting large parts (stocks) into small items. In our application stocks are produced in the plant. Many distinct stock sizes are feasible, and technical constraints limit the variety of cutting patterns to those producing a single type … Read more