As new areas develop around major cities, entire networks of collector sewers and treatment plants must be
Question:
As new areas develop around major cities, entire networks of collector sewers and treatment plants must be constructed to service growing population. Figure 1, displays wastewater network structure.
Nodes 1 to 8 of the network represent population centers, where smaller sewer feed into the main regional network, and locations where treatment plants might be built. Wastewater loads are roughly proportional to the population, so inflows indicated at nodes represent population units (in thousands). Arcs joining nodes 1 to 8 show possible routes for main collector sewers. Most follow the topology in gravity flow, but one pumped line (4,3) is included. A large part of construction cost for either type of line is fixed: right -of-way acquisition, trenching, and so on. Still the cost of a line also grows with the number of population units carried, because greater flows imply larger diameter pipes. Table 1, shows the fixed and variable cost for each arc in thousands of dollars. Treatment plant costs actually occur at nodes –here nodes 3,7, and 8. Figure 1, illustrates, however, that such costs can modeled on arcs by introducing an artificial “super sink” node 9. Costs shown for arcs (3,9), (7,9), and (8,9) capture the fixed and variable expenses of plant construction as flows depart the network. Required: Formulate integer linear programming model to determine which arcs (with its capacity)that should be included within wastewater network.