Lead Time Options in Supply Chain

We study lead time options in a manufacturer and a retailer supply chain where the retailer uses the (R, Q) inventory policy: the retailer places an order to the manufacturer who initially promises to deliver the order a lead time later. The manufacturer also promises to expedite or postpone the delivery of the order by a certain amount of time if the retailer makes such a request. Consequently, the retailer has an opportunity to modify the lead time by using most up-to-date demand information before the order is delivered. However, the retailer does not have the option to modify the order quantity, unlike well-studied flexible order quantity models. We establish the optimal lead time policy and provide an approximation for the critical levels associated with the lead time policy. We discuss that R is much more sensitive to lead times than Q, and primarily focus on finding optimal R. Towards that, we provide a cost approximation which yields unimodular costs in R. We also discuss the application of lead time options. Finally, we numerically illustrate the benefit of lead time options in improving supply chain performance.