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Probabilistic processing times, times between breakdowns and repair times make the amount of stock in buffers between stations in production lines behave as a stochastic process. Too much or too little buffer stock reduces system economy and efficiency, respectively. Optimum buffer capacities and initial stock levels for production lines employing a mathematical random walk approach based on the maximum and minimum values of a stochastic process in a time window can be obtained. Approximations can be provide for the purpose.
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