Setting planned lead-times in a stochastic production environment

In this paper, a serial production system operating on a make-to-order basis is considered, where the actual procurement and processing times are stochastic. The problem is to find the optimal lead-time planning for such a system. We formulate the problem model by trading off expected holding cost at all stages and expected penalty cost for exceeding the total planned lead-time. A stochastic optimization algorithm for a two-stage stochastic production system is proposed to optimize stage lead-times. In the optimization algorithm, perturbation analysis is used to derive the gradient estimate of the cost function with respect to stage lead-times. It is shown that the gradient estimate is unbiased, which ensures that the estimate is accurate when it is used to solve the problem. Finally, a numerical example is given to investigate the performance of the proposed algorithm.