Nodal decomposition–coordination for stochastic programs with private information restrictions

ABSTRACT We present a nodal decomposition–coordination method for stochastic programs with private data (information) restrictions. We consider coordinated systems where a single optimal or close-to-optimal solution is desired. However, because of competitive issues, confidentiality requirements, incompatible database issues, or other complicating factors, no global view of the system is possible. In our iterative methodology, each entity in the cooperation forms its own nodal deterministic or stochastic program. We use Lagrangian relaxation and subgradient optimization techniques to facilitate negotiation between the nodal decisions in the system without any one entity gaining access to the private information from other nodes. We perform a computational study on supply chain inventory coordination problem instances. The results demonstrate that the new methodology can obtain solution values that are close to the optimal within a stipulated time without violating private information restrictions. The results also show that the stochastic solutions outperform the corresponding expected value solutions.