Linear programming wi̇th R
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The document discusses using the lpSolveAPI package in R to solve linear programming problems. It provides examples of how to represent a linear programming problem in R, solve it using the lp_solve library, and retrieve the optimal objective value and variable values. Specifically, it shows how to create and populate the constraint matrix, set the objective function, constraint types and bounds, and then call the solver to find the optimal solution.
![Kind Std Std
Type Real Real
Upper Inf Inf
Lower 0 0
Solve
> solve(lprec)
[1] 0
Get maximum profit
> get.objective(lprec)
[1] 6315.625
Get the solution
> get.variables(lprec)
[1] 21.875 53.125
Thus, to achieve the maximum profit ($6315.625), the farmer](https://image.slidesharecdn.com/linearprogrammingwithr-160729111009/85/Linear-programming-wi-th-R-3-320.jpg)
![Lower 0 0
> solve(my.lp)
[1] 0
>
> get.objective(my.lp)
[1] -3.5
>
> get.variables(my.lp)
[1] 1.5 0.5
>
> get.constraints(my.lp)
[1] 3 2 3
Example:
First, we create an LPMO with 3 constraints and 4 decision variables.
> lprec <- make.lp(3, 4)
Next we set the values in the
first column. > set.column(lprec, 1, c(0, 0.24, 12.68))
The lp solve library is capable of using a sparse vectors to represent the constraints matrix. In
the remaining three columns, only the nonzero entries are set.
> set.column(lprec, 2, 78.26, indices = 1)
> set.column(lprec, 3, c(11.31, 0.08), indices = 2:3)
> set.column(lprec, 4, c(2.9, 0.9), indices = c(1, 3))
Next, we set the objective function, constraint types and right-hand-side.
> set.objfn(lprec, c(1, 3, 6.24, 0.1))
> set.constr.type(lprec, c(">=", "<=", ">="))
> set.rhs(lprec, c(92.3, 14.8, 4))](https://image.slidesharecdn.com/linearprogrammingwithr-160729111009/85/Linear-programming-wi-th-R-5-320.jpg)
![By default, all decision variables are created as real with range [0,∞). Thus we must change
the type of the decision variables x2 and x3.
> set.type(lprec, 2, "integer")
> set.type(lprec, 3, "binary")
We still need to set the range constraints on x1 and x4.
> set.bounds(lprec, lower = c(28.6, 18), columns = c(1, 4))
> set.bounds(lprec, upper = 48.98, columns = 4) Finally, we name the decision variables and
the constraints.
> RowNames <- c("THISROW", "THATROW", "LASTROW")
> ColNames <- c("COLONE", "COLTWO", "COLTHREE", "COLFOUR")
> dimnames(lprec) <- list(RowNames, ColNames)
Lets take a look at what we have done so far.
[1] 92.3000 6.8640 391.2928
Prepared by Volkan OBAN](https://image.slidesharecdn.com/linearprogrammingwithr-160729111009/85/Linear-programming-wi-th-R-6-320.jpg)
Linear programming wi̇th R
- 1. LINEAR PROGRAMMING WİTH R— lpsolve and IpSolveAPI Package: The lpSolveAPI package provides an R API for the lp solve library, a mixed integer linear pro gramming (MILP) solver with support for pure linear, (mixed) integer/binary, semi-continuou s and special ordered sets (SOS) models. The lp solve library uses the revised simplex method to solve pure linear programs and uses the branch-and-bound algorithm to handle integer varia bles, semi-continuous variables and special ordered sets. Example: maximize P = (110)(1.30)x + (30)(2.00)y = 143x + 60y subject to 120x + 210y <= 15000 110x + 30y <= 4000 x + y <= 75 x >= 0 y >= 0 Using R to solve Install lpsolve library > install.packages("lpSolveAPI")
- 2. Load lpsolve library > library("lpSolveAPI") Represent our problem > lprec <- make.lp(0, 2) > lp.control(lprec, sense="max") > set.objfn(lprec, c(143, 60)) > add.constraint(lprec, c(120, 210), "<=", 15000) > add.constraint(lprec, c(110, 30), "<=", 4000) > add.constraint(lprec, c(1, 1), "<=", 75) Display the lpsolve matrix > lprec Model name: C1 C2 Maximize 143 60 R1 120 210 <= 15000 R2 110 30 <= 4000 R3 1 1 <= 75
- 3. Kind Std Std Type Real Real Upper Inf Inf Lower 0 0 Solve > solve(lprec) [1] 0 Get maximum profit > get.objective(lprec) [1] 6315.625 Get the solution > get.variables(lprec) [1] 21.875 53.125 Thus, to achieve the maximum profit ($6315.625), the farmer
- 4. Example: Model name: C1 C2 Minimize -2 -1 R1 1 3 <= 4 R2 1 1 <= 2 R3 2 0 <= 3 >install.packages("lpSolveAPI") library(lpSolveAPI) > > my.lp <- make.lp(3, 2) > > my.lp Model name: C1 C2 Minimize 0 0 R1 0 0 free 0 R2 0 0 free 0 R3 0 0 free 0 Kind Std Std Type Real Real Upper Inf Inf Lower 0 0 > set.column(my.lp, 1, c(1, 1, 2)) > > set.column(my.lp, 2, c(3, 1, 0)) > > set.objfn(my.lp, c(-2, -1)) > > set.constr.type(my.lp, rep("<=", 3)) > > set.rhs(my.lp, c(4, 2, 3)) > my.lp Model name: C1 C2 Minimize -2 -1 R1 1 3 <= 4 R2 1 1 <= 2 R3 2 0 <= 3 Kind Std Std Type Real Real Upper Inf Inf
- 5. Lower 0 0 > solve(my.lp) [1] 0 > > get.objective(my.lp) [1] -3.5 > > get.variables(my.lp) [1] 1.5 0.5 > > get.constraints(my.lp) [1] 3 2 3 Example: First, we create an LPMO with 3 constraints and 4 decision variables. > lprec <- make.lp(3, 4) Next we set the values in the first column. > set.column(lprec, 1, c(0, 0.24, 12.68)) The lp solve library is capable of using a sparse vectors to represent the constraints matrix. In the remaining three columns, only the nonzero entries are set. > set.column(lprec, 2, 78.26, indices = 1) > set.column(lprec, 3, c(11.31, 0.08), indices = 2:3) > set.column(lprec, 4, c(2.9, 0.9), indices = c(1, 3)) Next, we set the objective function, constraint types and right-hand-side. > set.objfn(lprec, c(1, 3, 6.24, 0.1)) > set.constr.type(lprec, c(">=", "<=", ">=")) > set.rhs(lprec, c(92.3, 14.8, 4))
- 6. By default, all decision variables are created as real with range [0,∞). Thus we must change the type of the decision variables x2 and x3. > set.type(lprec, 2, "integer") > set.type(lprec, 3, "binary") We still need to set the range constraints on x1 and x4. > set.bounds(lprec, lower = c(28.6, 18), columns = c(1, 4)) > set.bounds(lprec, upper = 48.98, columns = 4) Finally, we name the decision variables and the constraints. > RowNames <- c("THISROW", "THATROW", "LASTROW") > ColNames <- c("COLONE", "COLTWO", "COLTHREE", "COLFOUR") > dimnames(lprec) <- list(RowNames, ColNames) Lets take a look at what we have done so far. [1] 92.3000 6.8640 391.2928 Prepared by Volkan OBAN
- 7. Source: 1-https://r- forge.rproject.org/scm/viewvc.php/*checkout*/pkg/inst/doc/lpSolveAPI.pdf?revision=91&ro ot=lpsolve&pathrev=91 2-http://icyrock.com/blog/2013/12/linear-programming-in-r-using-lpsolve/ 3- Modeling and Solving Linear Programming with R