One-dimensional cutting stock decisions for rolls with multiple quality grades

Abstract

This paper presents a procedure for solving one-dimensional cutting stock problems when both the master rolls and customer orders have multiple quality gradations. The procedure described here is a two-stage sequential heuristic. An innovative shadow price-based procedure is first used to select slitting patterns for master rolls with variable quality characteristics. Then a residual problem for the available first-quality (' perfect') master rolls is solved with a linear programming model. An important characteristic of this approach is its robustness. The procedure can deal effectively with problems of varying size and complexity and can also easily be adapted to changing circumstances with respect to production quality and demand.

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

“…Belov and Scheithauer (2003) designed a sequential heuristic to minimize material input while restricting the number of open stacks to any given limit. Also, there are a number of ways in which LPM and SHP are used together to obtain the best possible answer to a given class of Cutting and Packing problems (Sweeney and Haessler, 1990;Goulimis, 1990;Hendry et al, 1996;Gradišar et al, 1999;Richard, 1996).…”

Column generation and sequential heuristic procedure for solving an irregular shape cutting stock problem

“…A number of papers combine LP-based algorithms and heuristic techniques to obtain high quality solutions to these types of cutting and packing problems (Foerster and Wäscher (2000); Furini et al (2012); Goulimis (1990); Gradišar et al (1999); Gramani et al (2009);Hendry et al (1996); Richard (1996); Sweeney and Haessler (1990); Umetani et al (2006)). Sweeney and Haessler (1990) combined LP within a two stage sequential heuristic to develop a procedure for solving a 1DCSP with quality variations across the width of the stock rolls.…”

“…Sweeney and Haessler (1990) combined LP within a two stage sequential heuristic to develop a procedure for solving a 1DCSP with quality variations across the width of the stock rolls. Goulimis (1990) used an SHP algorithm to generate a starting solution for the LP procedure to solve a 1DCSP in a board mill.…”

Bun splitting: a practical cutting stock problem

“…Some researchers handle more complicated concepts of defects in the form of multiple grades in sheets where positioning of lower grade sections within the end-product plays a role (Ronnqvist 1995;Sweeney and Haessler 1990). In this context the objective relates to either the amount of waste or the number of cuts.…”