The cutting stock problem revisited

• Main Author: Goulimis, Constantine Nicholas
• Published: Imperial College London 2011
• Subjects: 519.7
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.505669

The subject of this thesis is the well-known problem in the theory of mathematical programming, the cutting stock problem. Its applications are numerous, occurring whenever material must be cut from "master" items, but this thesis is primarily concerned with the paper industry, where the cutting and slitting of big sheets of paper into smaller ones is an important and cost-sensitive part of the manufacturing process. Algorithms described in Chapters 2 and 3 solve certain classes of such problems to optimality (in the sense of having the least possible waste) in reasonable time. These classes include the one-dimensional problem, the one-and-a-half dimensional problem and certain two-stage problems. For each of these classes we report on industrial case studies in the paper and board industry. This is, apparently, the first time in the published literature that such optimal solutions for these problems have been routinely generated. This work has resulted in the development of two commercial packages - used on a daily basis in six paper and board mills, the first of which was installed in February 1985. In these sites, savings in the range of 1%-5% in utilisation have been achieved as compared against other programs or human practice. in Chapter 4 a heuristic algorithm is developed for rearranging a previously generated solution to reduce the number of knife settings required. Another heuristic takes existing solutions and reduces the number of patterns present in the solution. We describe a general framework for solving assortment problems and examine its application in the paper industry. Finally, statistical techniques are used to answer such "green-field site" questions as what are good geometric characteristics for a paper machine, and what is the relationship between waste and run length.