A transformed two-stage method for reducing the part-usage variation and a comparison of the product-level and part-level solutions in sequencing mixed-model assembly lines

The minimization of the two-stage variation in the mixed-model sequencing problem of reducing the part-level variation is transformed to product-level terms. The development is based on an existing simplification of the one-stage part-level variation, a simplification of the two-stage part-level variation, and the usage of a relationship matrix that evaluates the relevance among the product structures of various models. Algorithms based on these simplification and transformation are presented. The transformation can be shown to be equivalent to that of Bautista et al. but results in a smaller empirical computational burden in minimizing the two-stage variation and uses a relationship matrix that is independent of product-mix changes. The computational results show that the transformed two-stage algorithm significantly outperforms the direct enumeration method in computation time for large problems, and generally outperforms the one-stage method in mean squared deviation. The transformed two-stage method can be used as a heuristic procedure or as an intermediate tool for another solution approach. A more general sufficient condition than the existing conditions for the equivalence of the problems of minimizing the product-level variation and minimizing the part-level variation is also presented. The computational experimentation demonstrates that there is a potential of obtaining significantly better solutions in part usage variation by directly considering the part-level variation when this sufficient condition is not met.