The paper considers a production/distribution system that involves one vendor and multiple buyers. The buyers belong to an entity that is operationally more cost ecient than the vendor. We study two settings that have been widely applied in practice: vendor-managed inventory (VMI) and retailer-managed inventory (RMI). Specically for the two-buyer problem, we characterize equilibrium under RMI and optimal solution under VMI. Our VMI solution is shown to be more cost ecient than others in literature. The general multiple-buyer problem can be non-tractibal and a heuristic is provided to approach decisions under both settings. One surprising nding is that under VMI, the production decision need not involve operational information of the buyers (e.g., inventory/logistic costs) but only their market information (e.g., demand). Numerical results suggest that VMI and just-in-time production are substitutes in improving the eciency of the distribution network. VMI can be more critical for companies with rigid capacity, seasonally low demand, or complex distribution networks.