[Help-glpk] Solving shortest path problem and getting wrong answer

[Merike]

  Hi,

I'm trying to solve shortest path problem using glpsol and mps format. I 
have it working correct with one example but I'm getting wrong results 
with another one and I can't understand if there's something wrong with 
my input or if it's glpsol that gives wrong output.

My directed graph is the following, first number being edge tail id, the 
second one head id and last one respective weight.
3 5 19
5 1 26
1 4 28
4 9 11
9 7 29
7 8 21
8 6 18
6 2 30
2 1 23
10 3 27
9 5 20
1 7 26
6 4 21
9 8 11
9 8 29
9 3 13
10 1 19
2 4 29
5 2 18
2 5 28
8 7 14
5 7 29
2 6 20
8 4 18
8 2 14
1 7 17
2 4 19
4 5 29
10 6 26
10 7 17

Based on that I generate the following mps file to find shortest path 
from 5 to 3:
NAME shortest-path
ROWS
  N PATH
  L EQ14
  L EQ17
  L EQ21
  L EQ24
  L EQ25
  L EQ26
  L EQ35
  L EQ45
  L EQ49
  L EQ51
  L EQ52
  L EQ57
  L EQ62
  L EQ64
  L EQ78
  L EQ82
  L EQ84
  L EQ86
  L EQ87
  L EQ93
  L EQ95
  L EQ97
  L EQ98
  L EQ101
  L EQ103
  L EQ106
  L EQ107
  E START
COLUMNS
  X1 EQ14 -1
  X1 EQ17 -1
  X1 EQ21  1
  X1 EQ51  1
  X1 EQ101  1
  X2 EQ21 -1
  X2 EQ24 -1
  X2 EQ25 -1
  X2 EQ26 -1
  X2 EQ52  1
  X2 EQ62  1
  X2 EQ82  1
  X3 EQ35 -1
  X3 EQ93  1
  X3 EQ103  1
  X3 PATH -1
  X4 EQ45 -1
  X4 EQ49 -1
  X4 EQ14  1
  X4 EQ24  1
  X4 EQ64  1
  X4 EQ84  1
  X5 EQ51 -1
  X5 EQ52 -1
  X5 EQ57 -1
  X5 EQ25  1
  X5 EQ35  1
  X5 EQ45  1
  X5 EQ95  1
  X5 START 1
  X6 EQ62 -1
  X6 EQ64 -1
  X6 EQ26  1
  X6 EQ86  1
  X6 EQ106  1
  X7 EQ78 -1
  X7 EQ17  1
  X7 EQ57  1
  X7 EQ87  1
  X7 EQ97  1
  X7 EQ107  1
  X8 EQ82 -1
  X8 EQ84 -1
  X8 EQ86 -1
  X8 EQ87 -1
  X8 EQ78  1
  X8 EQ98  1
  X9 EQ93 -1
  X9 EQ95 -1
  X9 EQ97 -1
  X9 EQ98 -1
  X9 EQ49  1
  X10 EQ101 -1
  X10 EQ103 -1
  X10 EQ106 -1
  X10 EQ107 -1
RHS
  RHS1 START 0
  RHS1 EQ14 28
  RHS1 EQ17 17
  RHS1 EQ21 23
  RHS1 EQ24 19
  RHS1 EQ25 28
  RHS1 EQ26 20
  RHS1 EQ35 19
  RHS1 EQ45 29
  RHS1 EQ49 11
  RHS1 EQ51 26
  RHS1 EQ52 18
  RHS1 EQ57 29
  RHS1 EQ62 30
  RHS1 EQ64 21
  RHS1 EQ78 21
  RHS1 EQ82 14
  RHS1 EQ84 18
  RHS1 EQ86 18
  RHS1 EQ87 14
  RHS1 EQ93 13
  RHS1 EQ95 20
  RHS1 EQ97 29
  RHS1 EQ98 11
  RHS1 EQ101 19
  RHS1 EQ103 27
  RHS1 EQ106 26
  RHS1 EQ107 17
ENDATA

Which gives me:
X1     9
X2   18
X3   61
X4   37
X5     0
X6   16
X7     0
X8   19
X9   48
X10 34

I haven't verified all of these but X1 being 9 cannot be correct looking 
at graph data. There's no way to get from 5 to 1 with total weight of 9. 
I can't see anything wrong with my input though.
All help and pointers appreciated.

Merike