A Multicommodity Network Flow with Inverse Linear Constraints

In many application areas engineering, communications, logistics, manufacturing, transportation, different non-homogeneous commodities are distributed over the same underlying network. Usually the separate commodities share common arc capacities that restrict the integrated flow of the gross commodities on the arc. Furthermore, there exists a mutual interaction between the commodities. The generic multicommodity flow is a comparatively complex generalization of the standard single-commodity flow [1, 2, 4]. Another more general class of single-commodity flow is introduced and investigated in [3] a network flow with inverse linear constraints (ILC-flow). The values of this flow are bounded down by linear inequalities with real non-zero coefficients. Both generalizations do not have the specific properties as the standard singlecommodity flow. The respective problems do not necessary provide integer flows notwithstanding the input data the supply/demand and the capacity, is integer valued . Still they are linear programs with special structures that allow the use of the decomposition approach. The present paper discusses a multicommodity network flow with inverse linear constraints. The results obtained for the ILC-flow are extended to this flow. The network properties of the investigated flow, although reduced, are exploited considerably.