An Exact Algorithm for the Two-Dimensional Strip-Packing Problem

Marco Antonio Boschetti, Lorenza Montaletti
2010 Operations Research  
The Two-Dimensional Strip Packing Problem (2SP) appears in many industries (like steel and paper industries) and consists of cutting a rectangular master surface, called strip, with a given width and infinite height, into a number of rectangular items, each with a given size. The items must be cut with their edges always parallel or orthogonal to the edges of the master surface (orthogonal cuts) and we assume that items have a fixed orientation. The objective is to cut all the given items
more » ... e given items minimizing the total height of the used strip. In this paper we propose reduction procedures, lower and upper bounds and an exact algorithm for the 2SP. The new lower bounds are both combinatorial bounds and derived from different relaxations of a mathematical formulation of the 2SP. While, the new upper bounds are constructive heuristics based on different strategies to place the items into the strip. The new exact method is based on a branch and bound approach. Computational results on different sets of test problems derived from the literature show the effectiveness of the new lower and upper bounds and of the new exact algorithm.
doi:10.1287/opre.1100.0833 fatcat:zxiu6qzu4begfam6cp5fro76by