Hint: You should have 12 rows.
Note: use this numbering scheme
1 |
Pearlsburg |
2 |
Kitchen Corner |
3 |
Quarry |
4 |
Morgan Creek |
5 |
Stone House |
6 |
Cedar Creek |
7 |
Cutters Store |
8 |
Blakes Crossing |
9 |
Homer |
10 |
McKinney Farm |
11 |
Wellis Farm |
12 |
Bottom Town |
13 |
Holbrook |
Segment | From Node | To Node | Time |
Pearlsburg to Kitchen Corner | 1 | 2 | 10 |
Pearlsburg to Quarry | 1 | 3 | 15 |
Pearlsburg to Morgan Creek | 1 | 4 | 12 |
Kitchen Corner to Cutter's Store | 2 | 7 | 20 |
Kitchen Corner to Stone House | 2 | 5 | 14 |
Kitchen Corner to Quarry | 2 | 3 | 8 |
Quarry to Blake's Crossing | 3 | 8 | 18 |
Quarry to Cedar Creek | 3 | 6 | 9 |
Morgan Creek to Quarry | 4 | 3 | 16 |
Morgan Creek to Cedar Creek | 4 | 6 | 7 |
Morgan Creek to Homer | 4 | 9 | 18 |
Morgan Creek to McKinney Farm | 4 | 10 | 11 |
Stone House to Cutter's Store | 5 | 7 | 10 |
Stone House to Blake's Crossing | 5 | 8 | 6 |
Cedar Creek to Blake's Crossing | 6 | 8 | 10 |
Cedar Creek to Wellis Farm | 6 | 11 | 17 |
Cedar Creek to Homer | 6 | 9 | 5 |
Cutter's Store to Blake's Crossing | 7 | 8 | 12 |
Cutter's Store to Bottom Town | 7 | 12 | 14 |
Blake's Crossing to Bottom Town | 8 | 12 | 6 |
Blake's Crossing to Holbrook | 8 | 13 | 15 |
Blake's Crossing to Wellis Farm | 8 | 11 | 9 |
Homer to Wellis Farm | 9 | 11 | 11 |
Homer to McKinney Farm | 9 | 10 | 8 |
McKinney Farm to Wellis Farm | 10 | 11 | 21 |
Wellis Farm to Holbrook | 11 | 13 | 10 |
Bottom Town to Holbrook | 12 | 13 | 12 |
Shortest route is determined using Excel Solver as follows:
EXCEL FORMULAS:
Node | Netflow | RHS | |
1 | =SUMIF($B$2:$B$28,G2,$E$2:$E$28)-SUMIF($C$2:$C$28,G2,$E$2:$E$28) | = | 1 |
2 | =SUMIF($B$2:$B$28,G3,$E$2:$E$28)-SUMIF($C$2:$C$28,G3,$E$2:$E$28) | = | 0 |
3 | =SUMIF($B$2:$B$28,G4,$E$2:$E$28)-SUMIF($C$2:$C$28,G4,$E$2:$E$28) | = | 0 |
4 | =SUMIF($B$2:$B$28,G5,$E$2:$E$28)-SUMIF($C$2:$C$28,G5,$E$2:$E$28) | = | 0 |
5 | =SUMIF($B$2:$B$28,G6,$E$2:$E$28)-SUMIF($C$2:$C$28,G6,$E$2:$E$28) | = | 0 |
6 | =SUMIF($B$2:$B$28,G7,$E$2:$E$28)-SUMIF($C$2:$C$28,G7,$E$2:$E$28) | = | 0 |
7 | =SUMIF($B$2:$B$28,G8,$E$2:$E$28)-SUMIF($C$2:$C$28,G8,$E$2:$E$28) | = | 0 |
8 | =SUMIF($B$2:$B$28,G9,$E$2:$E$28)-SUMIF($C$2:$C$28,G9,$E$2:$E$28) | = | 0 |
9 | =SUMIF($B$2:$B$28,G10,$E$2:$E$28)-SUMIF($C$2:$C$28,G10,$E$2:$E$28) | = | 0 |
10 | =SUMIF($B$2:$B$28,G11,$E$2:$E$28)-SUMIF($C$2:$C$28,G11,$E$2:$E$28) | = | 0 |
11 | =SUMIF($B$2:$B$28,G12,$E$2:$E$28)-SUMIF($C$2:$C$28,G12,$E$2:$E$28) | = | 0 |
12 | =SUMIF($B$2:$B$28,G13,$E$2:$E$28)-SUMIF($C$2:$C$28,G13,$E$2:$E$28) | = | 0 |
13 | =SUMIF($B$2:$B$28,G14,$E$2:$E$28)-SUMIF($C$2:$C$28,G14,$E$2:$E$28) | = | -1 |
Total Time | = | =SUMPRODUCT(D2:D28,E2:E28) |
Shortest route is indicated by flow variable having value of 1
Therefore, shortest route from node 1 to 13 is: 1-4-6-8-13
Minimum time = 44
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