Discrete cost multicommodity network optimization problems and exact solution methods

We first introduce a generic model for discrete cost multicommodity network optimization, together with several variants relevant to telecommunication networks such as: the case where discrete node cost function (accounting for switching equipment) have to be included in the objective; the case where survivability constraints with respect to single-link and/or single-node failure have to be taken into account. An overview of existing exact solution methods is presented, both for special cases (such as the so-called single-facility and two-facility network loading problems) and for the general case where arbitrary step-increasing link cost-functions are considered. The basic discrete cost multicommodity flow problem as well as its variant with survivability constraints are addressed. Several possible directions for improvement or future investigations are mentioned in the concluding section.