Flow sumiffromnodesflow sumiftonodesflow

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Unformatted text preview: t;= 15 0 <= 12 0 <= 2 0 <= 23 0 <= 8 0 <= 6 0 <= 14 0 <= 15 0 <= 16 0 <= 6 0 <= 15 0 <= 4 6 For each node, calculate the net flow as a function of the changing cells. This can be done using the SUMIF function. In each case, the first SUMIF function calculates the flow leaving the node and the second one calculates the flow entering the node. For example, consider the A node (H5). SUMIF(From, Nodes, Flow) in I5 sums each individual entry in Flow (the changing cells in D5:D19) if that entry is in a row where the entry in From (B5:B19) is the same as in the entry in that row of Nodes (i.e., A). Since the only rows that have A in From (B5:B19) are rows 5 and 6, the sum in the ship column is only over these same rows, so this sum is D5+D6. 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 G thousands of gallons / hour Flow Capacity 0 <= 20 0 <= 20 0 <= 2 0 <= 15 0 <= 12 0 <= 2 0 <= 23 0 <= 8 0 <= 6 0 <= 14 0 <= 15 0 <= 16 0 <= 6 0 <= 15 0 <= 4 H Nodes A B C D E F G I J K thousands of gallons / hour Net Flow Supply/Demand 0 0 = 0 0 = 0 0 = 0 0 = 0 0 = 0 0 I 4 5 6 7 8 9 10 11 Net Flow =SUMIF(From,Nodes,Flow)-SUMIF(To,Nodes,Flow) =SUMIF(From,Nodes,Flow)-SUMIF(To,Nodes,Flow) =SUMIF(From,Nodes,Flow)-SUMIF(To,Nodes,Flow) =SUMIF(From,Nodes,Flow)-SUMIF(To,Nodes,Flow) =SUMIF(From,Nodes,Flow)-SUMIF(To,Nodes,Flow) =SUMIF(From,Nodes,Flow)-SUMIF(To,Nodes,Flow) =SUMIF(From,Nodes,Flow)-SUMIF(To,Nodes,Flow) 7 The goal is to maximize the amount shipped from A to G. Since nodes B through F are transshipment nodes (net flow = 0), any amount that leaves A must enter G. Thus, maximizing the flow out of A will achieve our goal. Thus, the formula entered into the objective cell MaximumFlow (D21) is =I5. B C D 3 thousands 4 From To Flow 5 A B 0 6 A C 0 7 B C 0 8 B D 0 9 B F 0 10 C B 0 11 C E 0 12 C F 0 13 D F 0 14 D G 0 15 E F 0 16 E G 0 17 F D 0 18 F E 0 19 F G 0 20 21 Maximum Flow 0 E F G of gallons / hour Capacity <= 20 <= 20 <= 2 <= 15...
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This document was uploaded on 01/31/2014.

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