[R] lpSolve: how to allow variables to become negative

[Rob Helpert]

Sorry. Of course, I meant the DIFFERENCE of two non-negative
variables.  So, for example, write b1 = b1p - b1n, where both b1p and
b1n are non-negative.

On Thu, Jul 2, 2009 at 4:18 PM, Rob Helpert<rhelpert at gmail.com> wrote:
> Hi Alicia,
>
> I think the trick may be to split b1 into the sum of two non-negative
> variables.  You will then also have to alter your constraints and
> objective to include the two new variables with negative values in
> appropriate places, but I believe that this will solve the problem.
>
>
> On Thu, Jul 2, 2009 at 12:37 PM, Alicia
> Perez-alonso<alicia.perez-alonso at eui.eu> wrote:
>> Dear all,
>>
>> I am interested in solving a MIP problem with binary outcomes and continuous
>> variables, which ARE NOT RESTRICTED TO BE NEGATIVE. In particular,
>>
>> Max {z1,z2,z3,b1}  z1 +  z2 + z3 (s.t.)
>> #   7 z1 + 0 z2 + 0 z3 + b1 <= 5
>> #   0 z1 + 8 z2 + 0 z3 - b1 <= 5
>> #   0 z1 + 0 z2 + 6 z3 + b1 <= 7
>> #   z1, z2, z3   BINARY {0,1}
>> #  -5<= b1 <=5 (i.e.  b1 <= 5; -b1 <= 5 )
>>
>> Using the lpSolve package of R, I wrote:
>>
>> library (lpSolve)
>> f.obj <- c(1, 1, 1, 0)
>> f.con <- matrix (c(7, 0, 0, -1, 0, 8, 0, 1, 0, 0, 6, -1, 0, 0, 0, 1 ),
>> nrow=4, byrow=TRUE)
>> f.dir <- c("<=", "<=", "<=", "<=")
>> f.rhs <- c(5, 5, 7, 5)
>>
>> lp ("max", f.obj, f.con, f.dir, f.rhs, binary.vec=1:3)
>> lp ("max", f.obj, f.con, f.dir, f.rhs, binary.vec=1:3)$solution
>>
>> The problem is that BY DEFAULT,  "b1" is constrained to be ">=0",  thus, the
>> constraint "-b1 <= 5" does not apply.
>>
>> Given that there is not any global variable in the lp() command such that I
>> can change the default value of 0 (to -5 or -inf), I do not get the correct
>> solution to the problem, which is indeed b1= -2.
>>
>> Thank you very much in advance for your help,
>> Alicia
>>
>> --
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>> _________________________________________________________
>> Alicia Pérez-Alonso
>> Departament of Economics
>> European University Institute
>> via della Piazzuola 43
>> 50133 Firenze (FI)
>> ITALY
>>
>> Room: 40 (Second Floor)
>> Phone: (+39) 0554685955
>> Fax: (+39) 0554685902
>> E-mail: alicia.perez-alonso at eui.eu
>> URL: http://www.eui.eu/Personal/Fellows/Perez-Alonso/
>>
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>