This paper considers a single-machine scheduling problem where the decision authorities and information are distributed in multiple sub-production systems. Sub-production systems share the single-machine and must cooperate with each other to achieve a global goal of minimizing a linear function of the completion times of the jobs; e.g., total weighted completion times. It is assumed that neither the sub-production systems nor the shared-machine have complete information about the entire system. The associated scheduling problems are formulated as 0/1 integer programs. The solution approach is based on Lagrangian relaxation techniques modified to require less global information. Specifically, there is no need for a global upper bound, or a single master problem that has complete view of all the coupling constraints. The proposed methodology exhibits promising performance when experimentally compared to the Lagrangian relaxation with subgradient method with the added benefit that can be applied to situations with more restrictive information sharing.