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### workforce3.R

# Copyright 2019, Gurobi Optimization, LLC
#
# Assign workers to shifts; each worker may or may not be available on a
# particular day. If the problem cannot be solved, relax the model
# to determine which constraints cannot be satisfied, and how much
# they need to be relaxed.

library(Matrix)
library(gurobi)

# Function to display results
printsolution <- function(result) {
if(result$status == 'OPTIMAL') { cat('The optimal objective is',result$objval,'\n')
cat('Schedule:\n')
for (s in 1:nShifts) {
cat('\t',Shifts[s],':')
for (w in 1:nWorkers) {
if (result$x[varIdx(w,s)] > 0.9) cat(Workers[w],' ') } cat('\n') } } } # define data nShifts <- 14 nWorkers <- 7 nVars <- nShifts * nWorkers varIdx <- function(w,s) {s+(w-1)*nShifts} Shifts <- c('Mon1', 'Tue2', 'Wed3', 'Thu4', 'Fri5', 'Sat6', 'Sun7', 'Mon8', 'Tue9', 'Wed10', 'Thu11', 'Fri12', 'Sat13', 'Sun14') Workers <- c( 'Amy', 'Bob', 'Cathy', 'Dan', 'Ed', 'Fred', 'Gu' ) pay <- c(10, 12, 10, 8, 8, 9, 11 ) shiftRequirements <- c(3, 2, 4, 4, 5, 6, 5, 2, 2, 3, 4, 6, 7, 5 ) availability <- list( c( 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1 ), c( 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0 ), c( 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 ), c( 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1 ), c( 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1 ), c( 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1 ), c( 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ) ) # Set-up environment env <- list() env$logfile <- 'workforce3.log'

# Build model
model            <- list()
model$modelname <- 'workforce3' model$modelsense <- 'min'

# Initialize assignment decision variables:
#    x[w][s] == 1 if worker w is assigned
#    to shift s. Since an assignment model always produces integer
#    solutions, we use continuous variables and solve as an LP.
model$lb <- 0 model$ub       <- rep(1, nVars)
model$obj <- rep(0, nVars) model$varnames <- rep('',nVars)
for (w in 1:nWorkers) {
for (s in 1:nShifts) {
model$varnames[varIdx(w,s)] = paste0(Workers[w],'.',Shifts[s]) model$obj[varIdx(w,s)]      = pay[w]
if (availability[[w]][s] == 0) model$ub[varIdx(w,s)] = 0 } } # Set-up shift-requirements constraints model$A           <- spMatrix(nShifts,nVars,
i = c(mapply(rep,1:nShifts,nWorkers)),
j = mapply(varIdx,1:nWorkers,
mapply(rep,1:nShifts,nWorkers)),
x = rep(1,nShifts * nWorkers))
model$sense <- rep('=',nShifts) model$rhs         <- shiftRequirements
model$constrnames <- Shifts # Save model gurobi_write(model,'workforce3.lp', env) # Optimize result <- gurobi(model, env = env) # Display results if (result$status == 'OPTIMAL') {
# The code may enter here if you change some of the data... otherwise
# this will never be executed.
printsolution(result);
} else if (result$status == 'INFEASIBLE') { # Use gurobi_feasrelax to find out which copnstraints should be relaxed # and by how much to make the problem feasible. penalties <- list() penalties$lb  <- Inf
penalties$ub <- Inf penalties$rhs <- rep(1,length(model$rhs)) feasrelax <- gurobi_feasrelax(model, 0, FALSE, penalties, env = env) result <- gurobi(feasrelax$model, env = env)
if (result$status == 'OPTIMAL') { printsolution(result) cat('Slack values:\n') for (j in (nVars+1):length(result$x)) {
if(result$x[j] > 0.1) cat('\t',feasrelax$model$varnames[j],result$x[j],'\n')
}
} else {
cat('Unexpected status',result$status,'\nEnding now\n') } rm(penalties, feasrelax) } else { # Just to handle user interruptions or other problems cat('Unexpected status',result$status,'\nEnding now\n')
}

#Clear space
rm(model, env, availability, Shifts, Workers, pay, shiftRequirements, result)

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