To set up a spreadsheet model first list all of the

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Unformatted text preview: product so as to achieve the minimum Total Cost (D13) of $58,500. 4 6.S2 Assessing the Capacity of a Pipeline Network Exxo 76 is an oil company that operates the pipeline network shown below, where each pipeline is labeled with its maximum flow rate in million cubic feet (MMcf) per day. A new oil well has been constructed near A. They would like to transport oil from the well near A to their refinery at G. Formulate and solve a network optimization model to determine the maximum flow rate from A to G. D 15 B 12 20 A 14 6 4 2 20 G F 8 16 15 C 23 E This is a minimum- cost flow problem. Associated with each pipe in the network will be an arc (or, for pipes which might flow in either direction, two arcs, one in each direction). To set up a spreadsheet model, first list all of the arcs as shown in B5:C19, along with their capacity (F5:F19). Then list all of the nodes as shown in H5:H11. All the transshipment nodes (every node except the start node A and the end node G) will be constrained to have net flow = 0 (Supply/Demand = 0). The start node (A) and end node (G) are left unconstrained. We want to maximize the net flow out of node A. B 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 C From A A B B B C C C D D E E F F F To B C C D F B E F F G F G D E G D E F G Capacity 20 20 2 15 12 2 23 8 6 14 15 16 6 15 4 H Nodes A B C D E F G I J K Supply/Demand = = = = = 0 0 0 0 0 5 The changing cells are the amount of flow to send through each pipe (arc). These are shown in Flow (D5:D19) below, with an arbitrary value of 0 entered for each. The flow through each arc is capacitated as indicated by the <= in E5:E19. B 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 From A A B B B C C C D D E E F F F C To B C C D F B E F F G F G D E G D E F thousands of gallons / hour Flow Capacity 0 <= 20 0 <= 20 0 <= 2 0 &l...
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This document was uploaded on 01/31/2014.

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