Computing and Applications: The Maximum Flow and Minimum Cost – Maximum Flow Problems

Abstract

The maximum flow and minimum cost-maximum flow problems are both concerned with determining flows through a network between a source and a destination. Maximum flow applies to any problem where the objective is move as many as possible goods/objects/people between two locations via intermediate locations. Maximum flow-minimum cost applies to flow problems where both capacities and costs are involved. When given information about a network (network flow diagram, capacities, costs), computing enables one to arrive at a solution to the problem. Once the solution becomes available, it has to be applied to a real world problem. The use of the following computer software in solving these problems will be discussed: R (several packages and functions), specially written Pascal programs and Excel SOLVER. The minimum cost-maximum flow solutions to the following problems will also be discussed: maximum flow, minimum cost-maximum flow, transportation problem, assignment problem, shortest path problem, caterer problem.