In this article we solve a nonlinear cutting stock problem which represents a cutting stock problem that considers the minimization of, both, the number of objects used and setup. We use a linearization of the nonlinear objective function to make possible the generation of good columns with the Gilmore and Gomory procedure. Each time a new column is added to the problem, we solve the original n...

A two-dimensional cutting stock problem can be defined as follows: A set of rectangular stock sheets of p different types is available. For each type of sheet Sp we know its length Lp and width Wp. From these sheets we have to cut smaller rectangular pieces of length li and width wi, i = 1, ...,m in order to satisfy a given demand for di pieces of each type. The objective is to minimize the tot...

1. The following four books are all reviewed together by William Gasarch. Fair Division: From Cake Cutting to Dispute Resolution) , by Brams and Taylor, Cake Cutting: Be Fair if You Can by Robertson and Webb, The Win-Win Solution by Brams and Taylor, and Fair Allocation (Proceedings of Symposia in Applied Mathematics, Vol 33) Edited by H. Peyton Young. These books all deal with the problem of f...

The purpose of this paper is to show that the gap is possibly smaller than 2. Some helpful results are summarized. Zusammenfassung: Es werden Ergebnisse vorgestellt und diskutiert, die bei der Untersuchung der maximalen Differenz zwischen den Optimalwerten des ganzzahligen und stetigen eindimensionalen Zuschnittproblems erhalten wurden.

This paper discusses some of the basic formulation issues and solution procedures for solving oneand twodimensional cutting stock problems. Linear programming, sequential heuristic and hybrid solution procedures are described. For two-dimensional cutting stock problems with rectangular shapes, we also propose an approach for solving large problems with limits on the number of times an ordered s...