A genetic algorithm for the one-dimensional cutting stock problem with setups

This paper investigates the one-dimensional cutting stock problem considering two conflicting objective functions: minimization of both the number of objects and the number of different cutting patterns used. A new heuristic method based on the concepts of genetic algorithms is proposed to solve the problem. This heuristic is empirically analyzed by solving randomly generated instances and also practical instances from a chemical-fiber company. The computational results show that the method is efficient and obtains positive results when compared to other methods from the literature. © 2014 Brazilian Operations Research Society

Bin Packing Problems with Variable Pattern Processing Times: A Proof-of-concept

In several real-world applications the time required to accomplish a job generally depends on the number of tasks that compose it. Although the same also holds for packing (or cutting) problems when the processing time of a bin depends by the number of its items, the approaches proposed in the literature usually do not consider variable bin processing times and therefore become inaccurate when time costs are worth more than raw material costs. In this paper we discuss this issue by considering a variant of the one-dimensional bin packing problem in which items are due by given dates and a convex combination of number of used bins and maximum lateness has to be minimized. An integer linear program that takes into account variable pattern processing times is proposed and used as proof-of-concept