Sequence Dependent Machine Set-Up Times and Similarity of Parts: A Mathematical Model

This paper attempts to develop a mathematical relation between machine set-up times and similarity of parts. First, the task for setting up a machine was broken down into a distinct number of elements whose state was expressed as a binary vector called set-up task elimination vector. By introducing a corresponding rime vector, it was shown that sequence dependent set-up time is the product of the two vectors. Next, a quantitative relation between set-up tasks and the design characteristics of parts was defined as a binary interaction matrix while the similarity of parts was defined as a binary vector. It turned out that the set-up tasks elimination vector is the Boolean product of the interaction matrix and the similarity vector. Using this information, a machine set-up model was developed in terms of similarity of parts. The computation of machine set-up times and a sequencing heuristic using the model were illustrated.