The Maximum Flow and Minimum Cost–Maximum Flow Problems: Computing and Applications
Asian Journal of Probability and Statistics,
Page 2857
DOI:
10.9734/ajpas/2020/v7i330185
Abstract
The maximum flow and minimum costmaximum flow problems are both concerned with determining flows through a network between a source and a destination. Both these problems can be formulated as linear programming problems. 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 costmaximum flow solutions to the following problems will also be discussed: maximum flow, minimum costmaximum flow, transportation problem, assignment problem, shortest path problem, caterer problem.
Keywords:
 Maximum flow
 minimum costmaximum flow
 nodes
 arcs
 source
 sink
 capacities
 costs
 objective function
 flow conservation and capacity constraints
 algorithm
 optimal solution
 network optimization
 transportation problem
 assignment problem
 shortest path problem
 caterer problem.
How to Cite
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