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The NETFLOW Procedure

Mathematical Description of NPSC

If a network programming problem with side constraints has nodes, arcs, nonarc variables, and side constraints, then the formal statement of the problem solved by PROC NETFLOW is

     

where

  • is the arc variable objective function coefficient vector (the cost vector)

  • is the arc variable value vector (the flow vector)

  • is the nonarc variable objective function coefficient vector

  • is the nonarc variable value vector

  • is the node-arc incidence matrix of the network, where

    if arc is directed from node

  • if arc is directed toward node

  • otherwise

  • is the node supply/demand vector, where

    if node has supply capability of units of flow

  • if node has demand of units of flow

  • if node is a trans-shipment node

  • is the side constraint coefficient matrix for arc variables, where is the coefficient of arc in the th side constraint

  • is the side constraint coefficient matrix for nonarc variables, where is the coefficient of nonarc in the th side constraint

  • is the side constraint right-hand-side vector

  • is the arc lower flow bound vector

  • is the arc capacity vector

  • is the nonarc variable lower bound vector

  • is the nonarc variable upper bound vector

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