#!/usr/bin/env python3.11
# Copyright 2024, 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(f"Optimization was stopped with status {status}")
sys.exit(0)
# Print total slack and the number of shifts worked for each worker
print("")
print(f"Total slack required: {totSlack.X}")
for w in Workers:
print(f"{w} worked {totShifts[w].X} shifts")
print("")
except gp.GurobiError as e:
print(f"Error code {e.errno}: {e}")
except AttributeError as e:
print(f"Encountered an attribute error: {e}")
finally:
# Safely release memory and/or server side resources consumed by
# the default environment.
gp.disposeDefaultEnv()