Generalized cross-decomposition method : algorithm and implementation

Abstract : We present an algorithm which considers a set of product types and a set of machine types. The algorithm works out a partition of p subsets of product types, called product families, and a partition of q subsets of machine types, called production subsystems such that : either p = q and there exists a one-to-one relationship between and product families production subsystems, or p = q + 1 (or q = p + 1) and there exists a one-to-one relationship between r product families and production subsystems where r is the minimum value of p and q. The supplementary subset of product (or machine) types has non corresponding subset of machine (or product) types. In both cases the partitions obtained maximize a criterion which is the weighted sum of normalized processing times of each product family in its related production subsystem and the complements of normalized processing times of each product family outside its related production subsystem. In the latter case the supplementary subset of product (or machine) types contains only products which have insignificant processing times (or machines which are only rarely or briefly involved by product transformation). We prove the convergence of our algorithm and give some numerical results. The presentation is closed with the description of an implementation of the algorithm for large data sets.
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Rapport
[Research Report] RR-1055, INRIA. 1989, pp.19
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Dernière modification le : samedi 17 septembre 2016 - 01:06:49
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Jean Hilger, George Harhalakis, Jean-Marie Proth. Generalized cross-decomposition method : algorithm and implementation. [Research Report] RR-1055, INRIA. 1989, pp.19. 〈inria-00075504〉

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