Aggregation of Network Flow Problems.

Abstract : Aggregation is a fundamental and widely used method of model simplification in management science, operations management, economics, database systems and related fields. It has also been used as a technical device in algorithm and software design for large scale optimization problems, particularly network flow problems. This class of problems is particularly amenable to aggregation owing to the special structural properties of networks. This research investigates aggregation of the capacitated transshipment problem. The author establishes a new framework for aggregation of this class of problems and provide an important characterization of arc types as a necessary preliminary to implementation. An aggregation procedure and a partition refinement process which generates a sequence of successively restricted aggregate problems are developed within this framework. A disaggregation methodology is defined that maps a feasible basic solution of the current aggregate problem to a basic solution of the next aggregate problem in the sequence. This map is incorporated into a complete algorithm which employs the aggregation-disaggregation concepts developed here. Finally, the results of this research are verified and tested in a computer implementation. (Author)