Contributing to solving a one-dimensional cutting stock problema with two objectives based on the generation of cutting patterns

Resumen

In the classic versions of the cutting stock problem, the aim is to find a solution to cut a main object into several parts commonly called pieces, in order to minimize the total trim loss of the raw material. Many studies have addressed this type of problem. However, in real-world applications there are usually constraints that make the problem shape different from the classic version and make it more difficult to solve. In this article we propose a technique to solve the one-dimensional cutting stock problem with two-objectives, where one seeks to minimize at the same time the total trim loss of the raw material and numbers of setups to be carried out. This technique is constituted of two stages whose first consists in generating all the feasible cutting patterns and the second allows to build cutting planes, satisfying the demands, thanks to a subset of these patterns. These different cutting plans represent all of the feasible solutions, each of which is characterized by a number of setups and total quantity of falls.