This paper considers game-theoretic models of lead-time reduction in a two-level supply chain involving a manufacturer and a retailer. The retailer manages her inventory system using the order quantity, reorder point, continuous-review (q,r) policy. To satisfy the retailer's order, the manufacturer sets up his facility, implements a pre-determined production schedule and delivers finished products to the retailer. In our paper, the lead-time consists of three components: setup time, production time and shipping time, each being in a range between minimum and "normal" durations. The first two lead-time components are naturally determined by the manufacturer, whereas the shipping lead time may be chosen by the manufacturer or the retailer. We thus consider two problems according to who decides the shipping lead time, and for each problems in the non-cooperative setting, we obtain Pareto-optimal Nash and Stackelberg equilibria. We find that, for all games, the manufacturer should be responsible for the setup time and production time at their normal durations. Next, we develop a simple profit-sharing contract to achieve supply chain coordination. We show that, under our properly designed contract, the two supply chain members are better off, and thus, they would have no incentive to deviate from the global solution that maximizes the system-wide profit.
