Abstract: We consider a network design problem which has
shortest routing restriction based on the values determined by the
installed facilities on each arc. In conventional multicommodity
network design problem, a commodity can be routed through any
possible path when the capacity is available. But, we consider
a problem in which the commodity between two nodes must be
routed on a path which has shortest metric value and the link
metric value is determined by the installed facilities on the link.
By this routing restriction, the problem has a distinct characteristic.
We present an integer programming formulation containing the
primal-dual optimality conditions to the shortest path routing. We
give some computational results for the model.