Flow constrained minimum cost flow problem

Abstract

The paper deals with the uncapacitated minimum cost flow problems subject to additional flow constraints whether or not the sum of node capacities is zero. This is a generalization and extension of transportation problems with restrictions on total flow value. The relationship between the desired flow value and the sum of node capacities of source(s) and sink(s) gives rise to the different set of problems. Mathematical models for the various cases are formulated. For each case an equivalent standard minimum cost flow problem (MCFP) is formulated whose optimal solution provides the optimal solution to the original flow constrained problem. The paper not only extends the similar concept of transportation problem to the case of MCFP but also suggests an alternative equivalent formulation. Solving the alternative problem is computationally better in comparison to the formulation analogous to the transportation case. A broad computational comparison is carried out at the end.