The paper examines a new problem in the irregular packing literature that has existed in industry for decades; two-dimensional irregular (convex) bin packing with guillotine constraints. Due to the cutting process of certain materials, cuts are restricted to extend from one edge of the stock-sheet to another, called guillotine cutting. This constraint is common place in glass cutting and is an ...

In this study we are concerned with the non-exact two-stage two-dimensional guillotine cutting problem considering usable leftovers, in which stock plates remainders of the cutting patterns (non-used material or trim loss) can be used in the future, if they are large enough to fulfill future demands of items (ordered smaller plates). This cutting problem can be characterized as a residual bin-p...

In this study we are concerned with the non-exact two-stage two-dimensional guillotine cutting problem considering usable leftovers, in which stock plates remainders of the cutting patterns (non-used material or trim loss) can be used in the future, if they are large enough to fulfill future demands of items (ordered smaller plates). This cutting problem can be characterized as a residual bin-p...

The two-dimensional strip packing is a special case of “Cutting and Packing” problems that arises in many applications. The problem seeks to pack a given set of rectangles into a strip of given width in order to minimize its length. Some applications in which the strip packing problem arises are: Cutting pieces from wooden boards, cutting pieces from glass or steel sheets, optimal layout of ind...

Cutting and packing (C & P) problem is to allocate a set of items to larger rectangular standardized units by minimizing the waste. Bin packing, strip packing and cutting stock problem is well-known classical C & P problem. An overview is provided of several meta-heuristics algorithms of swarm intelligence from the literature for the 2D C & P problem. The objective of this paper is to present a...

Cutting stock problems and bin packing problems are basically the same problems. They differ essentially on the variability of the input items. In the first, we have a set of items, each item with a given multiplicity; in the second, we have simply a list of items (each of which we may assume to have multiplicity 1). Many approximation algorithms have been designed for packing problems; a natur...

In this paper we describe a successful case-study where a Branch-and-Cut algorithm yields the “optimal” solution of a real-world timetabling problem for university courses (University Course Timetabling problem). The polyhedral structure of the problem is studied in conection with a polytope of the Set Packing problem. Several families of cutting planes are introduced, these being crutial to fi...

This paper presents an approach for solving a new real problem in Cutting and Packing. At its core is an innovative mixed integer programme model that places irregular pieces and defines guillotine cuts. The two-dimensional irregular shape bin packing problem with guillotine constraints arises in the glass cutting industry, for example, the cutting of glass for conservatories. Almost all cuttin...

Cutting and packing problems involving irregular shapes is an important problem variant with a wide variety of industrial applications. Despite its relevance to industry, research publications are relatively low when compared to other cutting and packing problems. One explanation offered is the perceived difficulty and substantial time investment of developing a geometric tool box to assess com...

This survey presents cutting planes that are useful or potentially useful in solving mixed integer programs. Valid inequalities for i) general integer programs, ii) problems with local structure such as knapsack constraints, and iii) problems with 0-1 coefficient matrices, such as set packing, are examined in turn. Finally the use of valid inequalities for classes of problems with structure, su...