GOALI: Large Scale Dynamic Programming for Optimizing the Design and Operation of Complex Systems with Applications to Production Line Design

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Dynamic programming is an extremely general framework for the formulation and solution of nonlinear discrete optimization problems. It allows for the explicit incorporation of either-or decisions as well as the effects of underlying uncertainty that may be present in the system being modeled. Its principal drawback is the tendency for the underlying state space of the formulation to grow explosively with respect to the size of the system. This grant provides funding for the development of procedures to limit to manageable proportions the growth of the state space that needs to be considered. This will be accomplished in two ways: (1) Model Simplification though hierarchical state aggregation; and (2) Solution Acceleration through state pruning. The former approach can introduce errors which will be controlled through the ability to compute bounds on the resulting error of the approximation. The models and algorithms developed will be implemented and validated on a large scale problem in production line design in cooperation with research staff at the General Motors R&D Center at Warren, Michigan. If this research effort is successful, the resulting ability to approximately model and optimize large scale complex systems with easily implemented dynamic programming techniques will greatly expand the class of design and operational problems in manufacturing and service sectors that are amenable to analysis.