Abstract
Abstract In this paper, two formulations of the group technology problem are considered: the standard formulation and the augmented formulation. The standard formulation is based on the 0–1 machine-incidence matrix and does not consider any costs. In the augmented formulation with each partj, cost c j is associated and the number of machines in each cell is limited to N. This formulation allows the creation of machine cells and part families with a low degree of interaction (or without any interaction, if required) by removing parts with low values of the corresponding costs from the incidence matrix. To solve these formulations, tow very efficient algorithms are presented. The cluster identification algorithm with the computational time complexity 0(2mn) finds optimal machine cells and part families provided that the machine-part incidence matrix has the block diagonal structure embedded. This appears to be the most efficient algorithm developed to date. The cost analysis algorithm is designed to solve the augmented group technology problem. Its computational complexity is 0(2 mn + nlogn). The two algorithms are illustrated in numerical examples.
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