Minimizing response time in a two-stage supply chain system with variable lead time and stochastic demand

We consider customer response time minimization in a two-stage system facing stochastic demand. Traditionally, the objective of representative mathematical models is to minimize costs related to production, inventory holding, and shortage. However, the highly competitive market characterized by impatient customers warrants the inclusion of costs related to customer waiting. Therefore we investigate a supply chain system in an uncertain demand setting that encompasses customer waiting costs as well as traditional plant costs (i.e. production and inventory costs). A representative expected cost function is derived and the closed form optimal solution is determined for a general demand distribution. We also provide examples to illustrate results for some common probability distributions. Our results indicate significant cost savings under certain assumptions when comparing solutions from the proposed model to the traditional newsvendor order/production quantity.