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workforce5.py


#!/usr/bin/python

# Copyright 2019, 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
    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 == 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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