1. Why network models? Visualize a mathematical model
Simpler solution algorithms
exploit special structure

2. Example from Winston, Operations Research: Applications and Algorithms, p. 338
Powerco has three electric power plants that supply the needs of four cities. The amounts each power plant can supply and the peak demands for each city are shown in the table. The cost of sending 1 million kwh of electricity from plant to city depends on the distance. How can Powerco minimize the total cost of meeting each city’s peak power demand?

3. Mathematical (Linear) Programming Model
12 decision variables, 7 constraints

4. Solve by Simplex Algorithm?
Add 3 slack variables, 4 surplus variables for standard form (equality constraints)
Add 4 artificial variables to get an initial basic feasible solution
Simplex tableau has 23 columns and 8 rows
(but a lot of its entries are 0’s)
(and the nonzero entries are 1’s)

5. Graphical (Network) Representation
Cost per unit flow
Demand
Supply
Graphical (Network) Representation C1 45 8 35 P1 6 10 C2 6 20 50 P2 C3 30 40 P3 5 C4 30
Decision Variables ~ Flows on Arcs
Constraints ~ Conservation of Flow at Nodes

6. Advantages?