A practical solution to a fuzzy two-dimensional cutting stock problem

Recent advances on two-dimensional bin packing problems

“…The following references are examples of industrial applications involving the above variants. A problem of trim-loss minimization in a crepe-rubber mill, studied by Schneider [44], induces subproblems of 2BP|O|G type; fuzzy two-dimensional cutting stock problems arising in the steel industry, discussed by Vasko et al [47], are related to 2BP|R|G; the problem of optimally placing articles and advertisements in newspapers and yellow pages, studied by Lagus et al [36], falls into the 2BP|O|F case; ÿnally, several applications of 2BP|R|F are considered by Bengtsson [6].…”

Simple strategies that generate bounded solutions for the multiple‐choice multi‐dimensional knapsack problem: a guide for OR practitioners

“…This approach used both a variable depth and a variable breadth tolerance strategy specified by the user. In Vasko et al (1989), the cutting of surplus steel plates is solved by defining a sequence of two-dimensional cutting stock problems, each of which is solved by a customized branch-and-bound procedure that efficiently generates cutting patterns. The problems are sequenced such that only high-priority orders and simple cutting patterns are considered initially, and then these constraints are progressively loosened in subsequent problems.…”

“…However, it is even more important that OR practitioners can guarantee the quality of the solutions that are presented to management for implementation. This is true regardless of whether the OR practitioner is called on to assist with a critical strategic planning issue (e.g., Newhart et al, 1993;Vasko et al, 2005;Vasko and Stott, 2008) or needs to implement an optimization module in a production system that is executed daily (e.g., Vasko et al, 1989Vasko et al, , 1993Vasko et al, , 1999.…”

An agent-based approach to the two-dimensional guillotine bin packing problem

“…It is denoted 2BPjRjG where R refers to the feasibility of rotation of the items by 90°and G to the requirement that the cuts be guillotine. It is applicable in the steel and shipping industries [26,15].…”