Thanks to Peter and Mark for your replies - I am obviously not setting up
the inputs correctly.

On Thu, Oct 23, 2008 at 3:02 AM, <markleeds@verizon.net> wrote:

>  Hi Selwyn: To follow up on Peter's reply, you're either not setting up the
> problem to do what you want it to do or you're not understand
> what it is doing. I explain your first two cases  below.
>
> CASE 1)
>
> proportions = c( 0.46, 0.28, 0.26)
> constraints = c( 352, 75, 171)
>
> temp <- lp(objective.in = proportions,
> const.mat = diag(c(1,1,1)),
> const.rhs=constraints,
> const.dir=rep('<=',3),
> direction='max'
> )
>
> print(temp$solution)
>
> ## > Success: the objective function is 227.38
>
> 227.38*proportions
>
> 227.38 * proportions #[1] 104.5948  63.6664  59.1188 (OK all less than
> constraints, however...)
>
>
>
> #==================================================================================
> MY COMMENT
>
> the problem you just set up above  is
>
> max( .46*x1 + 0.28*x2 + 0.26*x3 )
> subject to
>
> x1 <= 352
> x2 <= 75
> x3 <= 171
>
> x_i >= 0 for all i ( that's an implied constraint in lpSolve becaue all
> decision variables are restericted to be positive implicitly )
>
> and if you type
>
> print(temp$solution)
>
> you will see that the answer is x1=352, x2 = 75 and x3 = 171.
>
> Now,  in below you said 267 is a better answer but there are 2 problems
> with this statement.
>
> 1) how did you achieve the objective function of 267 ? the objective
> function is 0.46*x1 + 0.28*x2 + 0.26*x3
>
> 2) multiplying the objective function VALUE by the propotions has no
> meaning. the solution, which is the INDIVIDUAL VALUES OF
> THE SOLUTUON, multiplies the proportions  and this is the optimal value of
> objective function You can't get any better objective function value
> than 227.38 in your model formulation above. It basically just sets the
> values of the x1, x32 and x3 so that the constraints are binding.
> this way the maximum objective function is achieved because all the
> coefficients of the objective function ( what you
> call proportions ) are positive.
>
>
> #=========================================================================
>
> CASE2 :  this problem set up is similar to the rpevious one just with
> different values. it's
>
> max( .47*x1 + 0.28*x2 + 0.25*x3 )
> subject to
>
> x1 <= 12
> x2 <= 7
> x3 <= 99
>
> essentially my commet here is the as the  previous comment. the budget
> constraints are not violated. if you type print(temp$solution) you will
> see that the solution is x1=12, x2 = 7 and x3 = 99.  again, 32.35*
> proprtions2 has no meaning in this problem. you
> need to multiply the coefficients , x1, x2 and x3 by their correspoding
> proportions and you will see that this
> equals the value of the objective function. and again, the constraints are
> not violated because the constraints
> are in fact binding.  x1 goes to its maximum value, x2 takes on its maximum
> value and x3 takes on its maximum value.
>
> so, maybe these are not the problems you're trying to solve but lpSolve is
> doing the correct thing, given the problems you are sending it.
> I hope this helped. Good luck.
>
> ## This example goes over the budget constraints
>
> proportions2 = c( 0.47, 0.28, 0.25)
> constraints2 = c(12, 7, 99)
>
> temp <- lp(objective.in = proportions2,
> const.mat = diag(c(1,1,1)),
> const.rhs=constraints2,
> const.dir=rep('<=',3),
> direction='max'
> )
>
> print(temp$solution)
>
> ## > Success: the objective function is 32.35
> 32.35 * proportions2 ##[1] 15.2045  9.0580  8.0875 1st and second values
> are
> higher than the constraints allow!!!
>
>
>
>
> # your original email is below.
>
>
> #====================================================================================
>
> On Wed, Oct 22, 2008 at 10:33 AM, Selwyn McCracken wrote:
>
>  Hi list,
>>
>> I want to find the total maximum resources I can spend given a set
>> allocation proportion and some simple budget constraints.
>>
>> However, I get suboptimal results via lp and friends (i.e. lpSolve and
>> simplex in the linprog and boot) .
>>
>> For example:
>>
>> library(lpSolve)
>>
>> proportions = c( 0.46, 0.28, 0.26)
>> constraints = c( 352, 75, 171)
>>
>> lp(objective.in = proportions,
>>   const.mat = diag(c(1,1,1)),
>>   const.rhs=constraints,
>>   const.dir=rep('<=',3),
>>   direction='max'
>>   )
>>
>> ## > Success: the objective function is 227.38
>> 227.38 * proportions #[1] 104.5948  63.6664  59.1188 (OK all less than
>> constraints, however...)
>>
>> 267 * proportions ## [1] 122.82  74.76  69.42 (... a better result is
>> possible)
>>
>> ## This example goes over the budget constraints
>>
>> proportions2 = c( 0.47, 0.28, 0.25)
>> constraints2 = c(12, 7, 99)
>>
>> lp(objective.in = proportions2,
>>   const.mat = diag(c(1,1,1)),
>>   const.rhs=constraints2,
>>   const.dir=rep('<=',3),
>>   direction='max'
>>   )
>>
>> ## > Success: the objective function is 32.35
>> 32.35 * proportions2 ##[1] 15.2045  9.0580  8.0875 1st and second values
>> are
>> higher than the constraints allow!!!
>>
>> Any help gratefully received.
>>
>> Best regards,
>> Selwyn
>>
>>        [[alternative HTML version deleted]]
>>
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>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>

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