Creating Worst-Case Instances for Upper and Lower Bounds of the Two-Dimensional Strip Packing Problem

Abstract

We present a new approach to create instances with large performance ratio, i.e., worst-case instances, of common heuristics for the two-dimensional Strip Packing Problem. The idea of this new approach is to optimise the width and the height of all items aiming to find an instance with maximal performance ratio with respect to the considered heuristic. Therefore, we model the pattern obtained by the heuristic as a solution of an ILP problem and merge this model with a Padberg-type model of the two-dimensional Strip Packing Problem. In fact, the composed model allows to compute the absolute worst-case performance ratio of the heuristic with respect to a limited number of items. We apply the new approach for the Next-Fit Decreasing-Height, the First-Fit Decreasing-Height, and the Best-Fit Decreasing-Height heuristic. Furthermore, we provide an opportunity to use this idea to create worst-case instances for lower bounds.