Coordinating production and shipment decisions in a two-stage supply chain with time-sensitive demand

This paper investigates a supply chain system consisting of one manufacturer who receives an order from a single retailer and then coordinates a production and shipment schedule to fulfill the retailer's order as quickly and cost effectively as possible. It is assumed that the neither the manufacturer nor the retailer has inventory on hand at the time the retailer's order is received by the manufacturer, and that the demand rate at the retailer is constant. It is also assumed that shortages at the retailer result in lost sales penalties. In this setting, lost sales penalties are incurred during the time in which the retailer has no inventory on hand, which illustrates the time-sensitive nature of the demand. We derive the manufacturer's optimal production and shipping policy for the case in which the retailer controls the supply chain relationship, and also for the case in which the manufacturer controls the relationship.