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rlpsolve

Using lpsolve to define constraint for the proportion over a subset of decision variables

I am making an lp solution but am stuck at defining constraints.

Suppose I have 9 decision variables, {x1,x2...n}

Suppose also I have a constraint that involves a subset of all decision variables:

x1 / (x1+x2+x3) = 40/100

Then how can I write this for lpsolve to use this?

I have tried:

add.constraint(model, c(1,0,0,0,0,0,0,0,0), "=", c(.4,.4,.4,0,0,0,0,0,0))

and

add.constraint(model, c(0.4,0,0,0,0,0,0,0,0), "=", c(1,1,1,0,0,0,0,0,0))

Thanks in advance.

Solution

  • Assuming that you meant (x1+x2+x3) we have

    x1 / (x1+x2+x3) = 40/100

    is equivalent to

    x1 = (40/100) (x1+x2+x3)

    which is equivalent to

    (1-40/100)x1 - (40/100)x2 - (40/100)x3 = 0

    In order to get a complete problem assume that the objective is ones below and also add 9 constraints x[i] <= 1, i = 1, ..., 9 in which case we have the following for a maximization problem:

    library(lpSolve)

ones <- rep(1, 9)
a <- c(1-40/100, -40/100, -40/100, 0, 0, 0, 0, 0, 0)
A <- rbind(a, diag(9))
lp("max", ones, A, c("=", rep("<=", 9)), c(0, ones))