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#----------------------------------------------------------------------------
# localsolver
# Copyright (c) 2014, WLOG Solutions
#----------------------------------------------------------------------------
#'
#' @demo
#' The problem consists in assigning 4 tasks to 4 people. Each person has certain preferences as for the tasks.
#' Each person should get only one task. Each task should be assigned to somebody. The objective is to distribute
#' the tasks so that the sum of tohe preferences of all the people is maximized.
#'
model <- "function model() {
//assignments
assignment[i in 1..4][j in 1..4] <- bool();
//columns sum
for [j in 1..4]
constraint sum[i in 1..4](assignment[i][j]) == 1;
//rows sum
for [i in 1..4]
constraint sum[j in 1..4](assignment[i][j]) == 1;
//maximize prefernces
preferencesSum <- sum[i in 1..4][j in 1..4] (preferences[i][j] * assignment[i][j]);
maximize preferencesSum;
}"
lsp <- ls.problem(model)
lsp <- set.params(lsp, lsTimeLimit=60, lsIterationLimit=250)
lsp <- add.output.expr(lsp, "preferencesSum")
lsp <- add.output.expr(lsp, "assignment", dimensions=c(4,4))
data <- list(preferences=matrix(c(1L,2L,3L,4L,2L,4L,3L,1L,4L,3L,1L,2L,2L,3L,1L,4L), byrow=T,ncol=4))
ls.solve(lsp, data)
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