Abstract
A method for determining an upper bound for the homogeneous case of a two-dimensional packing problem is presented in this paper. It is based on an analysis of the problem's structure and can be evaluated as the optimal solution of a non-convex minimization problem which can be transformed to a piecewise linear problem by using its special properties. Finally a comparative analysis of solution quality and time complexity is presented.
Zusammenfassung
In dieser Arbeit wird ein Verfahren zur Bestimmung oberer Schranken für ein homogenes zweidimensionales Packproblem vorgestellt. Auf der Grundlage von Analysen der Problemstruktur kann man eine obere Schranke als optimale Lösung eines nichtkonvexen Minimierungsproblems ermitteln, das unter Ausnutzung spezieller Eigenschaften in ein stückweise lineares Problem transformiert werden kann. Den Abschluß dieser Arbeit bildet eine vergleichende Analyse von Lösungsqualität und Rechenzeitbedarf.
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References
Barnes F (1979) Packing the Maximum Number of m x n Tiles in a Large P×Q Rectangle, Discrete Mathematics 26: p. 93–100
Bischoff E, Dowsland W (1982) An Application of the Micro to Product Design and Distribution, Journal of the Operational Research Society 33: p. 271–281
De Cani P (1978) A Note on the Two-Dimensional Rectangular Cutting-Stock Problem, Journal of the Operational Research Society 29: p. 703–706
Dowsland K (1985) Determining an Upper Bound for a Class of Rectangular Packing Problems, Computers and Operations Research 12: p. 201–205
Dowsland K, Dowsland W (1983) A Comparative Analysis of Heuristics for the Two-Dimensional Packing Problem, Paper for EURO VI Conference, Wien 1983
Exeler H (1987) Das homogene Packproblem in der betriebswirtschaftlichen Logistik, Dissertation an der Universität Ulm
Smith A, De Cani P (1980) An Algorithm to Optimize the Layout of Boxes in Pallets, Journal of the Operational Research Society 31: p. 573–578
Steudel H (1979) Generating Pallet Loading Patterns, Management Science 25: p. 997–1004
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Exeler, H. Upper bounds for the homogeneous case of a two-dimensional packing problem. ZOR - Methods and Models of Operations Research 35, 45–59 (1991). https://doi.org/10.1007/BF01415959
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DOI: https://doi.org/10.1007/BF01415959