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workforce5.py
#!/usr/bin/env python3.7
# Copyright 2023, 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 */
import gurobipy as gp
from gurobipy import GRB
import sys
# 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)}
try:
# Create model with a context manager. Upon exit from this block,
# model.dispose is called automatically, and memory consumed by the model
# is released.
#
# The model is created in the default environment, which will be created
# automatically upon model construction. For safe release of resources
# tied to the default environment, disposeDefaultEnv is called below.
with gp.Model("workforce5") as model:
# 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
totSlack = model.addVar(name='totSlack')
# 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
minShift = model.addVar(name='minShift')
maxShift = model.addVar(name='maxShift')
model.addGenConstrMin(minShift, totShifts, name='minShift')
model.addGenConstrMax(maxShift, totShifts, name='maxShift')
# 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 in (GRB.INF_OR_UNBD, GRB.INFEASIBLE, GRB.UNBOUNDED):
print('Model cannot be solved because it is infeasible or unbounded')
sys.exit(0)
if status != GRB.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 gp.GurobiError as e:
print('Error code ' + str(e.errno) + ": " + str(e))
except AttributeError as e:
print('Encountered an attribute error: ' + str(e))
finally:
# Safely release memory and/or server side resources consumed by
# the default environment.
gp.disposeDefaultEnv()
