On optimal expediting policy for supply systems with uncertain lead-times

We examine the role of expediting in dealing with lead-time uncertainties associated with global supply chains of "functional products" (high volume, low demand uncertainty goods). In our developed stylized model, a retailer sources from a supplier with uncertain lead-time to meet his stable and known demand, and the supply lead-time is composed of two random duration stages. At the completion time of the first stage, the retailer has the option to expedite a portion of the replenishment order via an alternative faster supply mode. We characterize the optimal expediting policy in terms of if and how much of the order to expedite and explore comparative statics on the optimal policy to better understand the effects of changes in the cost parameters and lead-time properties. We also study how the expediting option affects the retailer's decisions on the replenishment order (time and size of order placement). We observe that with the expediting option the retailer places larger orders closer to the start of the selling season, thus having this option serve as a substitute for the safety lead-time and allowing him to take increased advantages of economies of scale. Finally we extend the basic model by looking at correlated lead-time stages and more than two random lead-time stages.