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.

Keywords:

• Private information
• stochastic programming
• inventory coordination
• supply chain management

Acknowledgements

Part of this work was performed while Eric Beier was on appointment as a U.S. Department of Homeland Security (DHS) Fellow under the DHS Scholarship and Fellowship Program, a program administered by the Oak Ridge Institute for Science and Education (ORISE) for DHS through an interagency agreement with the U.S. Department of Energy (DOE). ORISE is managed by Oak Ridge Associated Universities under DOE contract number DE-AC05-00OR22750. All opinions expressed in this work are the authors’ and do not necessarily reflect the policies and views of DHS, DOE, or ORISE.

Additional information

Notes on contributors

Eric Beier

Eric Beier is a Senior Scientist for General Dynamics Information Technology supporting the Air Force Research Laboratories. He received his Ph.D. in Industrial and Systems Engineering from Texas A&M University (2011) and M.E. in Industrial Engineering (2007) and B.S. in Industrial Engineering from Lamar University (2004). His current work focuses on modeling and simulation of human effects in support of new acquisitions programs for multiple services in the United States Department of Defense.

Saravanan Venkatachalam

Saravanan Venkatachalam is a Lecturer in the Department of Engineering Technology and Industrial Distribution at Texas A&M University. He received his M.S. and Ph.D. degrees in Industrial and Systems Engineering from Texas A&M University and B.S. in Production Engineering from PSG College of Technology, India. He worked in industry for 9 years and his research interests are in stochastic integer programming, large-scale optimization, and metaheuristics. Applications of interest include supply chain management, air traffic flow management, pricing, and revenue management.

V. Jorge Leon

V. Jorge Leon is the Allen Bradley Professor in Factory Automation at Texas A&M University where he holds appointment in the Department of Engineering Technology and Industrial Distribution and the Department of Industrial and Systems Engineering. He received his Ph.D. in Industrial Engineering from Lehigh University, an M.S. in Manufacturing Engineering from the University of Massachusetts, and a B.S. in Mechanical Engineering from the Pontifical Catholic University of Peru. He is a registered engineer in Texas. His areas of interest are in operations optimization, production, inventory and capacity management, and quality, with applications relevant to manufacturing, distribution, and logistics in global value chains.

Lewis Ntaimo

Lewis Ntaimo is an Associate Professor in the Department of Industrial and Systems Engineering at Texas A&M University. He received his Ph.D. in Systems and Industrial Engineering (2004), M.S. in Mining and Geological Engineering (2000), and B.S. in Mining Engineering (1998), all from the University of Arizona. He received his Engineer-in-Training certification (07760) for the State of Arizona in June 1999. His research interests are in stochastic integer programming, systems modeling and engineering processes, and discrete-event modeling and simulation. Applications of interest include wildfire planning, air traffic flow management, wind energy, and healthcare. He is on the Editorial Board of the Journal of Global Optimization and is the Secretary for the INFORMS Minority Issues Forum.