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

  • Authors:

  • F. Chauny;R. Loulou;S. Sadones;F. Soumis

  • Affiliations:

  • GERAD, Ecole des Hautes Etudes Commerciales, Montreal, Que., Canada H3T 1V6;GERAD, McGill University, Montreal, Que., Canada H3A 1G5;GERAD, McGill University, Montreal, Que., Canada H3A 1G5;GERAD, Ecole Polytechnique, 2500 Ch de Polytechnique, Montreal, Que., Canada

  • Venue:
  • Operations Research Letters
  • Year:
  • 1987

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Abstract

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.