with A ∈ IRm×n, b ∈ IR, and x, c ∈ IR. We will assume that the number of columns n of matrix A is so large that it is impossible to generate and store the matrix A in memory. The revised simplex method in Chapter 7 of Chvátal can be appropriately modified to solve linear programs of the form (1); the resulting method is known as the column generation method where columns of A are generated as n...

This paper describes the design and implementation of a solution to the constrained 2-D cutting stock problem on a cluster of workstations. The constrained 2-D cutting stock problem is an irregular problem with a dynamically modified global data set and irregular amounts and patterns of communication. A replicated data structure is used for the parallel solutionsince the ratio of reads to write...

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...

We present an exact method, based on an arc-flow formulation with side constraints, for solving bin packing and cutting stock problems — including multi-constraint variants — by simply representing all the patterns in a very compact graph. Our method includes a graph compression algorithm that usually reduces the size of the underlying graph substantially without weakening the model. Our formul...

This paper studies the following problem in stock cutting: when it is required to cut out complicated designs from parent material, it is cumbersome to cut out the exact design or shape, especially if the cutting process involves optimization. In such cases, it is desired that, as a first step, the machine cut out a relatively simpler approximation of the original design, in order to facilitate...

A generalized approach is introduced for getting minimal trim in onedimensional cutting stock problem (1D-CSP) which occurs extensively while manufacturing of different engineering objects. Our study is especially focused on transmission tower manufacturing industry. The concept of computing total trim by using the idea of pre-defined sustainable trim has been explored in previous work of autho...

In this paper, the authors present a hybrid genetic approach for the two-dimensional rectangular guillotine oriented cutting-stock problem. In this method, the genetic algorithm is used to select a set of cutting patterns while the linear programming model permits one to create the lengths to produce with each cutting pattern to fulfil the customer orders with minimal production cost. The effec...