13 15 10 3 4 15 12 S 8 9 10 Let Ij = Min s.t. + + + + + Node 1 Node 2 Node 3 Node 4 Node 5 Node 6 Node 7 Node 8 Node 9 Node 10 1 if the are from node i to node j is on the shortest route 10 otherwise 8x12 + 15 X27 + 3X46+ 4X67 + 2X78 + 12 X95 + 1 X12 + 1 X23 + 1 X32 + 1x43 + 1 X54 + 1 x63 + 1 X69 1 X72 + 1x06+ 1x95 + 13X13+ 5x32 + 4 X54 + 2 X68 + -1 X X70 + 5 X96 + 1 x13+ 1 X27 1 X30 1 1 X59 1 X64 + Flow Out X45 + 15 X14 + 5 X36 + 12 XS9+ 5 X69 + 1 x76+ 1 X09 + 1 X96 + 2 x86 + 5 X98 + 1 X14 + 1 X46 1 X67 + 1 X78 + 1 X80 1 x90 + 10 X15 + 2X43 + 5 X63 + 15 X72 + 5x89 + 0 x x90 1 X15 1 X60 + 1 X70 1 X90 5X23 4X45 3 X64 4X76 8 X X50 + + + + + + + + -1 x12 + -1 X13 + -1 X14 + -1 X15 + -1 X36 + X96 -1 X27 + -1X60 + -1 X59 + 1 X70 + Xij 20 for all / and / Flow In -1 X32 + -1 X23 + -1 X54 + -1 X45 + -1 X4G+ -1 X67 -1 X70 + -1 X69 + 1 V XEO t -1 x72 -1X43 + -1 X64 -1 X95 X76 + -1 -1 X90 -1 X89 X90 1 -1 X63 -1 XDG + = - = = Optimal Solution: Variable Value X12 X13 X14 XXX X15 X23 X27 X32 X36 X43 X45 X46 X54 X59 X X X X63 X64 X67 X68 X69 X72 X76 X78 X70 X86 X89 X80 X95 X96 X78 X70 X86 X89 X80 X95 X96 X98 X90 Shortest Route: Total Time = minutes 1-5-4-6-7-10 1-5-9-10 1-3-4-6-7-10 1-2-7-10 1-2-3-6-7-10 1-3-6-8-7-10