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### workforce5.py

#!/usr/bin/python

# Copyright 2018, Gurobi Optimization, LLC

# Assign workers to shifts; each worker may or may not be available on a
# particular day. We use multi-objective optimization to solve the model.
# The highest-priority objective minimizes the sum of the slacks
# (i.e., the total number of uncovered shifts). The secondary objective
# minimizes the difference between the maximum and minimum number of
# shifts worked among all workers.  The second optimization is allowed
# to degrade the first objective by up to the smaller value of 10% and 2 */

from gurobipy import *

try:
# Sample data
# Sets of days and workers
Shifts = [ "Mon1", "Tue2", "Wed3", "Thu4", "Fri5", "Sat6",
"Sun7", "Mon8", "Tue9", "Wed10", "Thu11", "Fri12", "Sat13",
"Sun14" ]
Workers = [ "Amy", "Bob", "Cathy", "Dan", "Ed", "Fred", "Gu", "Tobi" ]

# Number of workers required for each shift
S = [ 3, 2, 4, 4, 5, 6, 5, 2, 2, 3, 4, 6, 7, 5 ]
shiftRequirements = { s : S[i] for i,s in enumerate(Shifts) }

# Worker availability: 0 if the worker is unavailable for a shift
A = [ [ 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1 ],
[ 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1 ],
[ 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1 ],
[ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ]
availability = { (w,s) : A[j][i] for i,s in enumerate(Shifts)
for j,w in enumerate(Workers) }

# Create initial model
model = Model("workforce5")

# Initialize assignment decision variables:
# x[w][s] == 1 if worker w is assigned to shift s.
# This is no longer a pure assignment model, so we must
# use binary variables.
x = model.addVars(availability.keys(), ub=availability, vtype=GRB.BINARY,
name='x')

# Slack variables for each shift constraint so that the shifts can
# be satisfied
slacks = model.addVars(Shifts, name='Slack')

# Variable to represent the total slack

# Variables to count the total shifts worked by each worker
totShifts = model.addVars(Workers, name='TotShifts')

# Constraint: assign exactly shiftRequirements[s] workers
# to each shift s, plus the slack
model.addConstrs((x.sum('*',s) + slacks[s] == shiftRequirements[s] for s in Shifts),
name='shiftRequirement')

# Constraint: set totSlack equal to the total slack
model.addConstr(totSlack == slacks.sum(), name='totSlack')

# Constraint: compute the total number of shifts for each worker
model.addConstrs((totShifts[w] == x.sum(w,'*') for w in Workers),
name='totShifts')

# Constraint: set minShift/maxShift variable to less/greater than the
# number of shifts among all workers

# Set global sense for ALL objectives
model.ModelSense = GRB.MINIMIZE

# Set up primary objective
model.setObjectiveN(totSlack, index=0, priority=2, abstol=2.0, reltol=0.1,
name='TotalSlack')

# Set up secondary objective
model.setObjectiveN(maxShift - minShift, index=1, priority=1,
name='Fairness')

# Save problem
model.write('workforce5.lp')

# Optimize
model.optimize()

status = model.Status
if status == GRB.Status.INF_OR_UNBD or \
status == GRB.Status.INFEASIBLE  or \
status == GRB.Status.UNBOUNDED:
print('The model cannot be solved because it is infeasible or unbounded')
sys.exit(0)

if status != GRB.Status.OPTIMAL:
print('Optimization was stopped with status ' + str(status))
sys.exit(0)

# Print total slack and the number of shifts worked for each worker
print('')
print('Total slack required: ' + str(totSlack.X))
for w in Workers:
print(w + ' worked ' + str(totShifts[w].X) + ' shifts')
print('')

except GurobiError as e:
print('Error code ' + str(e.errno) + ": " + str(e))

except AttributeError as e:
print('Encountered an attribute error: ' + str(e))

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