We review the most important mathematical models and algorithms developed for the exact
solution of the one-dimensional bin packing and cutting stock problems, and experimentally …

The aim of this paper is to classify the literature related to the integration between the lot-
sizing and cutting stock problem. A deterministic mathematical model, that considers …

We give a didactic introduction to the use of the column generation technique in linear and
in particular in integer programming. We touch on both, the relevant basic theory and more …

Since the beginning of the structural optimization field, the optimal design was characterized
by the least-weight configuration. In this sense, all the researchers agreed on adopting the …

The NP-hard number-partitioning problem is to separate a multiset S of n positive integers
into k subsets such that the largest sum of the integers assigned to any subset is minimized …

The optimal solutions of the restricted master problems typically leads to an unstable
behavior of the standard column generation technique and, consequently, originates an …

Production planning on multiple parallel machines is an interesting problem, both from a
theoretical and practical point of view. The parallel machine lot-sizing problem consists of …

Rebar, the core resource of reinforced concrete structures, generates more carbon dioxide
per unit weight than any other construction resource. Therefore, reducing rebar cutting …

Column generation (CG) models have several advantages over compact formulations: they
provide better linear program bounds, may eliminate symmetry, and can hide nonlinearities …

Reinforcing bars (rebar), which have the most embodied carbon dioxide (CO2) per unit
weight in built environments, generate a significant amount of cutting waste during the …