Linier_program_MODEL.R

library(lpSolveAPI)
#used for result visualization
library(ggplot2)
library(reshape)
library(gridExtra)
#define the datasets
train<-data.frame(W_LIST=c('w1','w2','w3'), weightcapacity=c(1,2,3), spacecapacity=c(1,2,3))
cargo<-data.frame(type=c('c1','c2','c3','c4'), available=c(1,1,2,20), volume=c(100,300,200,500),profit=c(2000,2500,5000,3500))
#create an LP model with 10 constraints and 12 decision variables
lpmodel<-make.lp(2L*NROW(train)+NROW(cargo),12)
#I used this to keep count within the loops, I admit that this could be done a lot neater
column<-0
row<-0
#build the model column per column
for(wg in train$W_LIST){
row<-row+1
for(type in seq(1,NROW(cargo$type))){
column<-column+1
#this takes the arguments 'column','values' & 'indices' (as in where these values should be placed in the column)
set.column(lpmodel,column,c(1, cargo[type,'volume'],1), indices=c(row,NROW(train)+row, NROW(train)*2+type))
}}
#set rhs weight constraints
set.constr.value(lpmodel, rhs=train$weightcapacity, constraints=seq(1,NROW(train)))
#set rhs volume constraints
set.constr.value(lpmodel, rhs=train$spacecapacity, constraints=seq(NROW(train)+1,NROW(train)*2))
#set rhs volume constraints
set.constr.value(lpmodel, rhs=cargo$available, constraints=seq(NROW(train)*2+1,NROW(train)*2+NROW(cargo)))
#set objective coefficients
set.objfn(lpmodel, rep(cargo$profit,NROW(train)))
#set objective direction
lp.control(lpmodel,sense='max')
#I in order to be able to visually check the model, I find it useful to write the model to a text file
write.lp(lpmodel,'model.lp',type='lp')
#solve the model, if this return 0 an optimal solution is found
solve(lpmodel)
#this return the proposed solution
get.objective(lpmodel)