The solution of multiperiod network models with bundle constraints by aggregation

The authors present a new network aggregtion/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, the authors 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. The authors describe the determination of theoretical a priori and a posteriori bounds. They 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.