Constrained network models can be used to describe a wide variety of real-world applications ranging from production, inventory, and distribution problems to financial applications. These problems can be solved with the legacy NETFLOW procedure.
The Node data set specifies the nodal supplies and demands.
The Arc data set specifies arc costs, capacities, and lower flow bounds.
The Side constraints data set gives additional linear constraints in either a dense or sparse format that is more flexible than, but consistent with, the MPS format. Nonarc variables, which do not correspond directly to any flows in the network, can appear in side constraints.
The Arc solution data set includes arc flows and nonarc activities, reduced costs, and the basis structure.
The Node solution data set includes dual variables associated with the nodal constraints and the linear side constraints.
The macro status variable, which describes the outcome of the optimization process and any solution found, is saved for easier system integration.
A given model can be specified in many alternative but equivalent ways, simplifying programming for model generation. The input data is designed to minimize the work necessary to change from a linear programming specification to a side-constrained network specification.
The primal simplex network algorithm and primal partitioning algorithm (also know as the GUB-based or factorization algorithm) exploit the network structure by representing the network component of the basis with a spanning tree, thus maximizing list processing and minimizing arithmetic computation.
The interior-point algorithm (primal-dual predictor-corrector) is used for pure linear programs automatically and for network flow problems optionally.
Problem sparsity in both the side constraint component and the LU factorization of the network component of the basis is exploited.
Crash routines identify an advanced starting basis.
Numerous optimizer tuning parameters, especially affecting pricing, are available.
include interactive and programmed interruption of iterations by
resetting optimizer tuning parameters
providing single-step or multiple-step processing
print subsets of the current activities of arc and nonarc variables
save intermediate solutions that can be used for warm starts in subsequent optimizations
switch from optimization of the relaxed network model (side constraints ignored) to the fully constrained model