Try our new documentation site (beta).


workforce5.py


#!/usr/bin/env python3.7

# Copyright 2020, 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()

Try Gurobi for Free

Choose the evaluation license that fits you best, and start working with our Expert Team for technical guidance and support.

Evaluation License
Get a free, full-featured license of the Gurobi Optimizer to experience the performance, support, benchmarking and tuning services we provide as part of our product offering.
Academic License
Gurobi supports the teaching and use of optimization within academic institutions. We offer free, full-featured copies of Gurobi for use in class, and for research.
Cloud Trial

Request free trial hours, so you can see how quickly and easily a model can be solved on the cloud.

Search

Gurobi Optimization