Planning repair effort in transfer lines

In this paper, we propose a methodology to optimally allocate the repair rates in transfer lines, which requires estimating the gradient vector of the output rate with respect to repair rates. Partial derivatives can be obtained exactly in the case of two-machine lines. The gradient estimation method for longer lines uses this result together with an algorithm developed to approximate the performance measures of the line. The method developed is used in an optimization context to find the optimal repair rate vector to maximize the throughput given a constraint on the sum of the individual repair rates. The results obtained by this method are compared to those obtained using the finite difference method in gradient estimation.