The Solution of Multiperiod Network Models with Bundle Constraints by Aggregation

Management Science · 1993 · Volume 39 · Issue 1

Abstract

We present a new network aggregation/disaggregation approach for solving a multiperiod, network model with bundle (Generalized Upper Bounding) side constraints. The model describes production planning and distribution problems. Instead of solving the original multicommodity problem, we transform it so that a pair of single-commodity network flow problems can be solved. The original network is aggregated and the resulting problem is solved. Its solution determines a disaggregated problem that yields a feasible, near optimal solution to the original problem. We describe the determination of theoretical a priori and a posteriori bounds. We also introduce a very tight “computational” error bound. The implementation of the algorithm was tested against MPSX/370, and the specialized code for solving networks with side constraints NETSIDE. The proposed solution method was found to be much more efficient with negligible error.

Keywords

networks/graphs: flow algorithms, multicommodity, applications, aggregation, production scheduling, inventory production: production smoothing

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