ABSTRACT
Network flows is a problem domain that lies in the cusp between several fields of enquiry, including applied mathematics, computer science, engineering, management, and operations research. The minimum cost flow problem is a fundamental network flow problem. The objective of this problem is to send units of a good that reside at one or more points in a network (sources or supplies) with arc capacities to one or more other points in the network (sinks or demands), incurring minimum cost. In this chapter, we consider algorithmic approaches for solving the minimum cost flow problem and discuss a few applications. These algorithms are among the most efficient algorithms known in applied mathematics, computer science, and operations research for solving large-scale optimization problems.
