Competitive pressures and technological improvements are leading many firms to consider centralized information systems to manage inventories and schedule production. We propose a simple model to explore the potential benefits of such coordination. The model represents two products competing for a single production facility. Simple Markovian behavior is assumed throughout. The key step in the analysis is the explicit solution of a queueing model with a novel priority discipline. Serve a customer from the class having the largest number of customers in the system.