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### workforce1.R

# Copyright 2023, 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, use IIS to find a set of
# conflicting constraints. Note that there may be additional conflicts
# besides what is reported via IIS.

library(Matrix)
library(gurobi)

# 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 parameters
params <- list()
params$logfile <- 'workforce1.log' # Build model model <- list() model$modelname  <- 'workforce1'
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,'workforce1.lp', params)

# Optimize
result <- gurobi(model, params = params)

# Display results
if (result$status == 'OPTIMAL') { # The code may enter here if you change some of the data... otherwise # this will never be executed. cat('The optimal objective is',result$objval,'\n')
cat('Schedule:\n')
for (s in 1:nShifts) {
cat('\t',Shifts[s],':')
for (w in 1:nWorkers) {
if (result$x[varIdx(w,s)] > 0.9) cat(Workers[w],' ') } cat('\n') } } else if (result$status == 'INFEASIBLE') {
# Find ONE IIS
cat('Problem is infeasible.... computing IIS\n')
iis <- gurobi_iis(model, params = params)
if (iis$minimal) cat('IIS is minimal\n') else cat('IIS is not minimal\n') cat('Rows in IIS: ', model$constrnames[iis$Arows]) cat('\nLB in IIS: ', model$varnames[iis$lb]) cat('\nUB in IIS: ', model$varnames[iis$ub]) cat('\n') rm(iis) } else { # Just to handle user interruptions or other problems cat('Unexpected status',result$status,'\nEnding now\n')
}

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


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