Optimal Two-staged Cutting Patterns For Rectangular Blanks Based On The Block

The research on the cutting stock problems is to study how to generate cutting patterns to maximize material usage. Cutting stock problems appear in many industries, such as the industries of mechanical manufacturing, furniture, leather, and so on. Improving material usage may reduce the costs of production and thus it is an efficient way to increase the profits of the enterprises. Improving material usage is a system project. Many factors should be considered to get a good solution, such as production management, cutting stock process, and decision support. For the cutting stock process, the key problem is to construct an efficient algorithm. The rectangular cutting problem is a branch of the two-dimensional cutting problems.Although a lot of papers have focused on the two-dimensional cutting problems of rectangular items, there are many factors that affect the cutting stock process. These factors are changing continuously with the advances of the production. As a consequence, cutting problems with new features also come continuously. New algorithms must be developed for these cutting problems to meet the demand of the production.In practice, the shearing and punching process is often used to cut the metal plate into finished items in two stages. The first stage is referred to as the shearing stage, at which a guillotine shear cuts the plate into strips. The second stage is referred to as the punching stage, at which a stamping press cuts the strips into finished items. The algorithms are used in the shearing stage to arrange the strips on the plate optimally, so as to maximize the material utilization. Algorithms that are appropriate for the shearing and punching process have been rarely reported in the literature.Considering the features of the strip cutting at the shearing stage, this paper proposes the homogenous block two-staged patterns (HBTSP). A homogenous block consists of homogenous strips. Each homogenous strip contains items of the same type. Each cut on a homogenous block cuts down either a horizontal or vertical strip. A plate is divided into homogenous blocks within two stages. At the first stage, a group of parallel cuts divide the plate into complex strips. Each complex strip contains a row of homogenous blocks. At the second stage, each complex strip is divided into homogenous blocks with cuts perpendicular to the strip. The HBTSP patterns have the following good features: the patterns are appropriate for the shearing and punching process because they are strip based; Applying patterns consisting of one homogenous block may...