Cplex给出错误的结果

Question

I created a sample test.lp file as follows:

Maximize
    y

Subject To
 +x1+100M+3M2+x4-y+A=0
 x1-M-M2-10x4>=-20
 x1 - 3 M + M2 <= 100
 M - 3.5 x4 + M2= 0
 A+x1<=140
 
Bounds
 x1<= 40
 2 <= x4 <= 3
 0<=x1
Binary
 M
Integer
 A
End

Used all default settings, and the following commands: read test.lp -> opt -> d sol v -

Result is:

Variable Name           Solution Value
y                           172.500000
x1                           40.000000
M                             1.000000
M2                            9.500000
x4                            3.000000
A                             1.000000

However, the result should be y=271.5 and A=100 , the value of other variables seems okay.

This is also tested with google OR-Tools ( SCIP solver), which gives proper results.

What did I miss?

Answer 1

If you change

Integer
 A
End

into

Generals
 A
End

you ll get the right solution

Answer 2

Integer (or Integers , or Int , or Ints ) is a keyword in LP file that's been deprecated since a very long time (probably after CPLEX V4.0, in 1995). It was kept in the code only for compatibility with old LP files, and will not be used by CPLEX when writing an LP file.

It used to work as follows. If the bound of the variable was specified, then the variable is a general integer. If the bound was not specified, then the variable is binary.

In your case, as A doesn't appear in the Bounds section, it is considered a binary variable. And indeed the value it has in the solution computed by CPLEX is coherent with this.

Using display problem all in the CPLEX Interactive will show the whole problem as it's known to CPLEX. In your case, this ends with

[...]
Bounds
 0 <= x1 <= 40
 0 <= M <= 1
 2 <= x4 <= 3
 0 <= A <= 1
 All other variables are >= 0.
Binaries
 M  A

You can see how CPLEX considers A to be a binary variable.