Stackelberg game model of a supply chain under lead-time-dependent demand uncertainty

This paper develops a Stackelberg game theoretic model of a supply chain consisting of one manufacturer and one retailer to study pricing and production planning about lead-time and quantity. We assume that the retailer faces an uncertain demand where the uncertainty is related to lead-time. We investigate how uncertainty, capacity and salvage value influence the equilibrium outcome. We find that manufacturer's maximum output within the lead-time is always equal to the retailer's order quantity and the manufacturer can adjust the lead-time because the retailer can influence the demand by adjusting retail price. When the demand uncertainty is sufficiently small, the manufacturer shares most of the risk from demand uncertainty; otherwise, the retailer has to share part of the risk.