A branch-and-cut-and-price algorithm for one-and two-dimensional two-staged cutting (stock) problems

I N T R O D U C T I O N In a number of industries, such as paper and film, there is an important class of problems OVER THE past 20 years, a substantial amount that falls in between the well known one and of work has been done on one and two-dimentwo-dimensional problems. These are referred sional cutting stock problems. A number of to here as two-stage cutting stock problems early authors [1, ...

We describe a new hierarchical 2D-guillotine Cutting Stock Problem. In contrast to the classic cutting stock problem, waste is not an issue. The problem relates to the removal of a defective part and assembly of the remaining parts into homogeneous size blocks. The context is the packing stages of cake manufacturing. The company’s primary objective is to minimise total processing time at the su...

In this paper, we address the combined assortment and trim loss minimization problem. In real settings, when different stock lengths are available, a common problem is to select a subset of stock lengths from which to cut the ordered items. In the cutting and packing literature, this problem is known as the assortment problem. Solving the assortment and trim loss minimization problem in a singl...

We consider the feasibility problem OPP in higher-dimensional orthogonal packing: given a set of d-dimensional (d ≥ 2) rectangular items, decide whether all of them can be orthogonally packed in the given rectangular container without rotation. The 1D ‘bar’ LP relaxation of OPP reduces the latter to a 1D cutting-stock problem where the packing of each stock bar represents a possible 1D stitch t...

We consider two-dimensional cutting stock problems where single rectangular stocks have to be cut into some smaller rectangular so that the number of stocks needed to satisfy the demands is minimum. In this paper we focus our study to the problem where the stocks have to be cut with guillotine cutting type and fixed orientation of finals. We formulate the problem as an integer programming, wher...