Exam 6: Network Optimization Problems

Which of the following problems are special types of minimum cost flow problems? I. Transportation problems. II. Assignment problems. III. Transshipment problems. IV. Shortest path problems.

A network representation is a very specific conceptual aid and is only used in special cases.

A manufacturing firm has four plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: \text{Customer (requirement)}\\ \begin{array} { l c c c c } &&Customer ~2 &Customer ~3& Customer ~4\\ \text { Factory (capacity)}&\text{ Customer } 1 ( 125 ) & ( 150 ) & ( 175 ) & ( 75 ) \\ A ( 100 ) & \$ 15 & \$ 10 & \$ 20 & \$ 17 \\ \mathrm {~B} ( 75 ) & \$ 20 & \$ 12 & \$ 19 & \$ 20 \\ \mathrm { C } ( 100 ) & \$ 22 & \$ 20 & \$ 25 & \$ 14 \\ \mathrm { D } ( 250 ) & \$ 21 & \$ 15 & \$ 28 & \$ 12 \end{array} Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. What is the optimal quantity to ship from Factory B to Customer 3?

The source and sink of a maximum flow problem are analogous to the supply nodes and demand nodes of a minimum cost flow problem.