Determining safety stocks of large transfer lines for a preset efficiency

Transfer lines, typically assembly lines, are widely used in production systems. In synchronized transfer lines the rhythm of the output is identical from each operation; therefore, the loss of production (due to machine breakdown or producing a defective item) at any stage stops the line temporarily at all subsequent stages. Consequently, transfer lines have a low efficiency. This efficiency can be increased if a safety stock is carried for each stage. Models in the literature use Markov-chains to calculate the efficiency of a transfer line for specified saftey stock sizes at each stage. The calculation must be repeated for various combinations of safety stocks at the stages until the efficiency of the line is acceptable. One motivation for this paper was to simplify the cumbersome computation needed to obtain a required efficiency; another that Markov-chain models are infeasible for transfer lines having more than three stages and they are not applicable when the random variables representing machine breakdowns and scrap production have empirical distributions. The model presented in this paper has the following advantages: it takes into account both machine breakdowns and the production of defective items; it is applicable to large transfer lines with any number of stages; it allows a required efficiency to be set and determines the proper safety stock size with a simple analytical calculation; and it accommodates any theoretical or empirical distribution of the random variables.