Stochastic approximations for optimal buffer capacity of many-station production lines

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. We obtain 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. Two approximations are developed, each useful under different risk-acceptance assumptions. Simulation results populate the equations. A motivating case study from a discrete part manufacturing line, including an example of using regression on the simulated results, is presented.