(R,Q) Policy with Lead Time Options — Offered by a manufacturer / transporter to a retailer

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 uses a transporter to deliver the order a lead time later. The manufacturer promises to expedite or postpone the delivery (using its own means or different transportation options) by a certain amount of time if the retailer makes such a request. Consequently, the retailer has an option to modify the lead time by using most up-to-date demand information. However, the retailer does not modify the order quantity. We establish the optimal lead time policy and provide approximations for the critical levels associated with it. We also discuss that R is much more sensitive to lead times than Q, and primarily focus on finding optimal R. Towards that, a cost approximation which yields unimodular costs in R is provided. Finally, the effect of lead time options on supply chain performance is illustrated with a numerical study.