Abstract
We consider the cutting of rectangular order pieces into stock pieces of specified width and length. The cutting process involves three stages of orthogonal guillotine cutting: Stock pieces are cut into sections that are cut into slits that are cut into order pieces. Restrictions imposed on the cutting process make the combinatorial structure of the problem more complex, but limit the scope of solution space. The objective of the problem is mainly to minimize waste, but our model also accounts for other issues such as aging stock pieces, urgent or optional orders, and fixed setup costs. Our solution approach involves a nested decomposition of the problem and the recursive use of the column-generation technique: We use a column-generation formulation of the problem (Gilmore and Gomory 1965) and the cutting-pattern—generation subproblem is itself solved using a column-generation algorithm. LP-based lower bounds on the minimum cost are computed and, by rounding the LP solution, a feasible solution and associated upper bound is obtained. This approach could in principle be used in a branch-and-bound search to solve the problem to optimality. We report computational results for industrial instances. The algorithm is being used in industry as a production-planning tool.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
