[Help-glpk] GLPK found optimal solution while XPRESS & CPLEX concluded to unbounded problem, for the same problem.

[Maurice.Djona]

Hi every body,

We basically use GLPK in our program, but we are making some tests with
XPRESS and CPLEX
because we want our program to be more flexible.
In the majority of cases the 3 software give the same results. However,
for the problem given below, GLPK (4.7) found
an optimal solution while XPRESS and CPLEX concluded to an unbounded
problem. The 3 results are:

FOR GLPK:
lpx_read_cpxlp: 53 rows, 133 columns, 212 non-zeros
lpx_read_cpxlp: 197 lines were read
*     0:   objval =   0.000000000e+00   infeas =   0.000000000e+00 (23)
*     8:   objval =  -1.000000010e-07   infeas =   0.000000000e+00 (19)
OPTIMAL SOLUTION FOUND

                                *********

FOR XPRESS:
Problem Statistics
          53 (      0 spare) rows
         133 (      0 spare) structural columns
         212 (      0 spare) non-zero elements
Global Statistics
           0 entities        0 sets        0 set members
The problem is unbounded due to column C120

                                *********
FOR CPLEX:

CPLEX also concluded to unbounded problem.

                                *********


Any suggestion is welcomed,
Maurice Djona



This is the problem, in the CPLEX LP file format submitted to the 3 LP
software.



\*Problem xxx *\  

Minimize
 obj: + C94

Subject To
R1: 0.0001 C49 - C51 <= 0 
R2: - C49 + 0.0001 C51 <= 0 
R3: C98 - C99 <= 0 
R4: C88 - C89 <= 0 
R5: C78 - C79 <= 0 
R6: C69 - C70 <= 0 
R7: C67 - C68 <= 0 
R8: C65 - C66 <= 0 
R9: 0.0001 C7 - C100 - C101 + 0.0001 C129 <= 0 
R10: - C7 + 0.0001 C101 - C129 <= 0.001 
R11: - C94 + 0.0001 C118 <= 0 
R12: 0.0001 C96 - C118 <= 0.001 
R13: 0.0001 C28 - C92 <= 0 
R14: - C28 + 0.0001 C92 <= 0.002 
R15: 0.0001 C17 - C87 <= 0 
R16: - C17 + 0.0001 C87 <= 0.002 
R17: 0.0001 C10 + 0.0001 C20 + 0.0001 C31 - C40 - C41 - C42 - C43 - C44
- C45 + 0.0001 C121 + 0.0001 C132 <= 0 
R18: - 100 C10 - 100 C20 - 100 C31 + C45 - 100 C121 - 100 C132 <= 0 
R19: - 100 C10 - 100 C20 - 100 C31 + C44 - 100 C121 - 100 C132 <= 0 
R20: - 100 C10 + C43 - 100 C132 <= 0
R21: - 100 C31 + C42 <= 0 
R22: - 100 C10 - 100 C20 - 100 C31 + C41 - 100 C121 - 100 C132 <= 0 
R23: - 100 C10 - 100 C20 - 100 C31 + C40 - 100 C121 - 100 C132 <= 0 
R24: C39 - C99 + C111 <= 0 
R25: C38 - C94 + C110 <= 0 
R26: C37 - C89 + C109 <= 0 
R27: C36 - C84 + C108 <= 0 
R28: C35 - C66 + C107 <= 0 
R29: C34 - C56 + C106 <= 0 
R30: C33 - C52 - C55 - C79 + C105 <= 0 
R31: C17 - C19 = 0 
R32: C28 - C30 = 0 
R33: C118 - C120 = 0 
R34: C129 - C131 = 0 
R35: C7 - C9 = 0 
R36: C12 + C13 + C14 + C15 + C16 - C19 + C20 = 0 
R37: C22 + C23 + C24 + C25 + C26 + C27 - C30 + C31 = 0 
R38: C112 + C113 + C114 + C115 + C116 + C117 - C120 + C121 = 0 
R39: C123 + C124 + C125 + C126 + C127 + C128 - C131 + C132 = 0 
R40: C1 + C2 + C3 + C4 + C5 + C6 - C9 + C10 = 0 
R41: - C17 + C18 + C21 = 0 
R42: - C28 + C29 + C32 = 0 
R43: - C118 + C119 + C122 = 0 
R44: - C129 + C130 + C133 = 0 
R45: - C7 + C8 + C11 = 0 
R46: - C52 + C53 + C54 = 0 
R47: - C56 + C57 + C58 + C59 + C61 + C62 + C63 + C64 = 0 
R48: - C66 + C68 + C70 + C72 + C73 + C74 + C75 + C76 + C77 = 0 
R49: - C79 + C80 + C81 + C83 = 0 
R50: - C84 + C85 + C86 + C87 = 0 
R51: - C89 + C90 + C91 + C92 = 0 
R52: - C94 + C95 + C96 + C97 = 0 
R53: C46 + C47 + C48 + C50 + C60 + C71 + C82 + C93 - C99 + C100 + C101 +
C102 + C103 + C104 = 0 

Bounds
C1 free
C2 free
C3 free
C4 free
C5 free
C6 free
C7 free
C8 free
C9 free
C10 free
C11 free
C12 free
C13 free
C14 free
C15 free
C16 free
C17 free
C18 free
C19 free
C20 free
C21 free
C22 free
C23 free
C24 free
C25 free
C26 free
C27 free
C28 free
C29 free
C30 free
C31 free
C32 free
C33 free
C34 free
C35 free
C36 free
C37 free
C38 free
C39 free
C40 free
C41 free
C42 free
C43 free
C44 free
C45 free
C46 free
C47 free
C48 free
C49 free
C50 free
C51 free
C52 free
C53 free
C54 free
C55 free
C56 free
C57 free
C58 free
C59 free
C60 free
C61 free
C62 free
C63 free
C64 free
C65 free
C66 free
C67 free
C68 free
C69 free
C70 free
C71 free
C72 free
C73 free
C74 free
C75 free
C76 free
C77 free
C78 free
C79 free
C80 free
C81 free
C82 free
C83 free
C84 free
C85 free
C86 free
C87 free
C88 free
C89 free
C90 free
C91 free
C92 free
C93 free
C94 free
C95 free
C96 free
C97 free
C98 free
C99 free
C100 free
C101 free
C102 free
C103 free
C104 free
C105 free
C106 free
C107 free
C108 free
C109 free
C110 free
C111 free
C112 free
C113 free
C114 free
C115 free
C116 free
C117 free
C118 free
C119 free
C120 free
C121 free
C122 free
C123 free
C124 free
C125 free
C126 free
C127 free
C128 free
C129 free
C130 free
C131 free
C132 free
C133 free

End