Generalization and Implementation of the GP Method to Generate Manufacturing Cell and Part Families.

Abstract

We present an algorithm that 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 no corresponding subset of machine (or product) types. In both cases the partitions obtained maximize a criterion that 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 that 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 paper is concluded with the description of an implementation of the algorithm for large data sets.