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I have a question about LpSolve in R. I have a panel with the following data: Football player ID (around 500 player), how many games each of them has already played, number of goals scored and cost of the player. I want to create a matrix from this data, but I do not know how this works with such a large amount of data (I have about 500 football players an therefore 500 rows).

The goal is to select the optimal number of players for a budget of 1,000,000. Each player can only be selected once, optimized by the number of scored goals.

In the end I want to have the optimal selection of players which scored the most goals, and the budget has to be (almost) used up.

Since I am relatively new with R I do not know how to solve this problem with LpSolve yet and I fail at the matrix production and the constraints.

I´m very grateful for your help !

My panel looks like this (example):

footballplayerID | gamesplayed | avggoals | costsperplayer

  1. 233276 | 120 | 80 | 50.000
  2. 474823 | 200 | 140 | 34.000
  3. 192834 | 150 | 90 | 14.000
  4. 192833 | 30 | 50 | 90.000
  5. 129834 | 204 | 129 | 70.000
  6. 347594 | 123 | 19 | 10.000
  7. 203845 | 129 | 57 | 43.000
  8. 128747 | 98 | 124 | 140.000

.

.

  1. 123749 | 128 | 182 | 100.000
R_Lemur
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1 Answers1

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First I create a df like this: df <- read.table(text = "footballplayerID | gamesplayed | avggoals | costsperplayer 233276 | 120 | 80 | 50000 474823 | 200 | 140 | 34000 192834 | 150 | 90 | 14000 192833 | 30 | 50 | 90000 129834 | 204 | 129 | 70000 347594 | 123 | 19 | 10000 203845 | 129 | 57 | 43000 128747 | 98 | 124 | 1400001", header = TRUE, stringsAsFactors = FALSE, sep = "|" )

library(lpSolve)

The coefficients for objective function is avggoals:

obj_fun <- df$avggoals

The constraints is the sum of costperplayer that needs to be less than or equal to 100.000.000

constraints <- matrix(df$costsperplayer, nrow = 1)
c_dir <- "<="
c_rhs <- 1000000

You can then solve that lp problem with lp(). the argument all.bin = TRUE makes sure you choose a player once or not at all. 

lp <- lp("max",
         obj_fun,
         constraints,
         c_dir,
         c_rhs, 
         all.bin = TRUE)

You can than have a look at the selected players:

df[lp$solution == 1, ]
clemens
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