A two-phase heuristic for strip packing: Algorithm and probabilistic analysis

The strip packing problem consists in laying out a specified list of rectangular pieces on a rectangular strip of fixed width but infinite length, in such a way as to minimized the length of strip used. We present a novel heuristic algorithm for this problem, based on a two-phase approach: the strategic and the tactical; the former has a global view of the problem and proposes a list of patterns to the latter, which in turn is in charge of actually laying out these patterns. The strategic module is based on a linear programming relaxation of the problem, whereas the tactical module is a recursive algorithm based on repeated knapsack operations. The performance of the algorithm is analyzed through a probabilitic analysis on its relative deviation from the (unknown) optimal solution; the deviation is found to converge to zero as problem size increases under some conditions on the problem data.