A classification scheme for bin packing theory. (English) Zbl 1120.90046

Summary: Classifications of published research place new results in a historical context and in so doing identify open problems. An example in wide use classifies results in scheduling theory according to a scheme originated by R. L. Graham, E. L. Lawler, J. K. Lenstra and A. H. G. Rinnooy Kan [Ann. Disc. Math. 5, 287–326 (1979; Zbl 0411.90044)]. A similar effort was made by H. Dyckhoff [Eur. J. Oper. Res. 44, 145–159 (1990; Zbl 0684.90076)] for cutting and packing problems. Such classification schemes can be combined with comprehensive bibliographies, e.g., the one provided for scheduling theory by Bruckner (available at http://www.mathematik.uni-osnabrueck.de/research/OR/class/). This paper describes a novel classification scheme for bin packing which is being applied by the authors to an extensive (and growing) bibliography of the theory. Problem classifications are supplemented by compact descriptions of the main results and of the corresponding algorithms. The usefulness of the scheme is extended by an online search engine. With the help of this software, one is easily able to determine whether results already exist for applications that appear to be new, and to assist in locating the cutting edge of the general theory.


90C27 Combinatorial optimization