Lead-time planning in stochastic production system: an approach using perturbation analysis

Determining appropriate production lead-time is an important and complex issue in production planning and control for a stochastic production system. The problem of interest in this paper is to find optimal lead-time for a serial production system operating on a make-to-order basis, in which the actual procurement and processing times are stochastic. We formulate this problem as an unconstrained minimization problem by minimizing the expected sum of the work-in-process holding cost and product tardiness cost. 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. We prove that the gradient estimate is unbiased, and thus ensure that the estimate is accurate when it is used to solve the problem. Also, a numerical example is given to show the performance of the proposed algorithm.