An LP-based approach to a two-stage cutting stock problem

An iterative sequential heuristic procedure to a real-life 1.5-dimensional cutting stock problem

“…Although LP is not sufficiently flexible to consistency solve problems with multi-objectives or with various additional restrictions appearing in practice, there are still quite a few papers solving this kind of problem with LP-based approach (de Carvalho and Rodrigues, 1995;Diegel et al, 1996;Dyckhoff, 1981;Gilmore and Gomory, 1965;Haessler, 1980;Washer, 1990;Zak, 2002). Gilmore and Gomory (1965) presented an LP method for solving the two-dimensional stock cutting problem with the restriction that the cutting has to be done in stages.…”

An exact algorithm for the knapsack sharing problem

“…The SK problem often arises as a subproblem in other combinatorial optimization problems. One of its famous applications is the cutting stock problem [1] where knapsack problems could account for about 60 -80% of the total computing time [5,6].…”

Models and Bounds for Two-Dimensional Level Packing Problems

“…Real world applications involving two-stage cutting problems can be found, e.g., in de Carvalho and Rodrigues [8,9] (steel industry), while an industrial three-stage cutting problem was recently considered by Vanderbeck [21].…”