The Two-Dimensional Guillotine Cutting Stock Problem with Stack Constraints

Abstract

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 constructive heuristics extended from the literature for the problem, in addition to a dynamic programming based heuristic that uses as a subroutine an exact pseudo-polynomial time algorithm developed for the Rectangular Knapsack Problem with Batch Constraints. Computational experiments, performed on three sets of realistic instances, showed that the dynamic programming based heuristic found solutions with smaller optimally gaps in all instances evaluated.