A Biased Random-Key Genetic Algorithm for the 2-Dimensional Guillotine Cutting Stock Problem with Stack Constraints

This paper tackles the 2-Dimensional Guillotine Cutting Stock Problem with Stack Constraints. The problem asks for the cutting of a set of items with the minimum amount of raw material. The cutting patterns are subject to a number of constraints, including a new realistic constraint, regarding item precedence, which has just been introduced in the literature. In this case, the items are organized in stacks, where each stack represents a customer request and defines the order in which the items must be cut. That is, if item i precedes item j within a stack, then i must be cut before j. However, there is no precedence constraint between items in different stacks. This constraint comes from applications where items must be stacked and shipped in the exact order that they will be used by the customer, thus avoiding the risk of damaging fragile items (as is the case in the glass industry) or the cost of moving heavy items (as is the case in the steel industry). We propose two heuristics, one Evolutionary Algorithm (EA) adapted from a similar problem in the literature, and a novel Biased Random Key Genetic Algorithm (BRKGA). Computational results show that BRKGA outperforms the evolutionary algorithm from the literature.