Linear Integer Optimization Model for Two-Stage Guillotine Cutting Stock Problem Using Branch and Bound Method in the Garment Industry

A branch-and-price algorithm for the two-stage guillotine cutting stock problem

We investigate the two-stage guillotine two-dimensional cutting stock problem. This problem commonly arises in the industry when small rectangular items need to be cut out of large stock sheets. We propose an integer programming formulation that extends the well-known Gilmore and Gomory model by explicitly considering solutions that are obtained by both slitting some stock sheets down their wid...

Solving the Two-Stage Cutting Stock Problem

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, ...

A simple approach to the two-dimensional guillotine cutting stock problem

Cutting stock problems are within knapsack optimization problems and are considered as a non-deterministic polynomial-time (NP)-hard problem. In this paper, two-dimensional cutting stock problems were presented in which items and stocks were rectangular and cuttings were guillotine. First, a new, practical, rapid, and heuristic method was proposed for such problems. Then, the ...

An integer programming model for two- and three-stage two-dimensional cutting stock problems

In this paper, an integer programming model for two-dimensional cutting stock problems is proposed. In the problems addressed, it is intended to cut a set of small rectangular items of given sizes from a set of larger rectangular plates in such a way that the total number of used plates is minimized. The two-stage and three-stage, exact and non-exact, problems are considered. Other issues are a...

Two Stage Flow Shop Scheduling Problem Including Transportation Time and Weightage of Jobs with Branch and Bound Method