workforce3.py

#!/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. If the problem cannot be solved, relax the model
# to determine which constraints cannot be satisfied, and how much
# they need to be relaxed.

import gurobipy as gp
from gurobipy import GRB
import sys

# Number of workers required for each shift
shifts, shiftRequirements = gp.multidict(
    {
        "Mon1": 3,
        "Tue2": 2,
        "Wed3": 4,
        "Thu4": 4,
        "Fri5": 5,
        "Sat6": 6,
        "Sun7": 5,
        "Mon8": 2,
        "Tue9": 2,
        "Wed10": 3,
        "Thu11": 4,
        "Fri12": 6,
        "Sat13": 7,
        "Sun14": 5,
    }
)

# Amount each worker is paid to work one shift
workers, pay = gp.multidict(
    {"Amy": 10, "Bob": 12, "Cathy": 10, "Dan": 8, "Ed": 8, "Fred": 9, "Gu": 11}
)

# Worker availability
availability = gp.tuplelist(
    [
        ("Amy", "Tue2"),
        ("Amy", "Wed3"),
        ("Amy", "Fri5"),
        ("Amy", "Sun7"),
        ("Amy", "Tue9"),
        ("Amy", "Wed10"),
        ("Amy", "Thu11"),
        ("Amy", "Fri12"),
        ("Amy", "Sat13"),
        ("Amy", "Sun14"),
        ("Bob", "Mon1"),
        ("Bob", "Tue2"),
        ("Bob", "Fri5"),
        ("Bob", "Sat6"),
        ("Bob", "Mon8"),
        ("Bob", "Thu11"),
        ("Bob", "Sat13"),
        ("Cathy", "Wed3"),
        ("Cathy", "Thu4"),
        ("Cathy", "Fri5"),
        ("Cathy", "Sun7"),
        ("Cathy", "Mon8"),
        ("Cathy", "Tue9"),
        ("Cathy", "Wed10"),
        ("Cathy", "Thu11"),
        ("Cathy", "Fri12"),
        ("Cathy", "Sat13"),
        ("Cathy", "Sun14"),
        ("Dan", "Tue2"),
        ("Dan", "Wed3"),
        ("Dan", "Fri5"),
        ("Dan", "Sat6"),
        ("Dan", "Mon8"),
        ("Dan", "Tue9"),
        ("Dan", "Wed10"),
        ("Dan", "Thu11"),
        ("Dan", "Fri12"),
        ("Dan", "Sat13"),
        ("Dan", "Sun14"),
        ("Ed", "Mon1"),
        ("Ed", "Tue2"),
        ("Ed", "Wed3"),
        ("Ed", "Thu4"),
        ("Ed", "Fri5"),
        ("Ed", "Sun7"),
        ("Ed", "Mon8"),
        ("Ed", "Tue9"),
        ("Ed", "Thu11"),
        ("Ed", "Sat13"),
        ("Ed", "Sun14"),
        ("Fred", "Mon1"),
        ("Fred", "Tue2"),
        ("Fred", "Wed3"),
        ("Fred", "Sat6"),
        ("Fred", "Mon8"),
        ("Fred", "Tue9"),
        ("Fred", "Fri12"),
        ("Fred", "Sat13"),
        ("Fred", "Sun14"),
        ("Gu", "Mon1"),
        ("Gu", "Tue2"),
        ("Gu", "Wed3"),
        ("Gu", "Fri5"),
        ("Gu", "Sat6"),
        ("Gu", "Sun7"),
        ("Gu", "Mon8"),
        ("Gu", "Tue9"),
        ("Gu", "Wed10"),
        ("Gu", "Thu11"),
        ("Gu", "Fri12"),
        ("Gu", "Sat13"),
        ("Gu", "Sun14"),
    ]
)

# Model
m = gp.Model("assignment")

# Assignment variables: x[w,s] == 1 if worker w is assigned to shift s.
# Since an assignment model always produces integer solutions, we use
# continuous variables and solve as an LP.
x = m.addVars(availability, ub=1, name="x")

# The objective is to minimize the total pay costs
m.setObjective(gp.quicksum(pay[w] * x[w, s] for w, s in availability), GRB.MINIMIZE)

# Constraint: assign exactly shiftRequirements[s] workers to each shift s
reqCts = m.addConstrs((x.sum("*", s) == shiftRequirements[s] for s in shifts), "_")

# Optimize
m.optimize()
status = m.Status
if status == GRB.UNBOUNDED:
    print("The model cannot be solved because it is unbounded")
    sys.exit(0)
if status == GRB.OPTIMAL:
    print(f"The optimal objective is {m.ObjVal:g}")
    sys.exit(0)
if status != GRB.INF_OR_UNBD and status != GRB.INFEASIBLE:
    print(f"Optimization was stopped with status {status}")
    sys.exit(0)

# Relax the constraints to make the model feasible
print("The model is infeasible; relaxing the constraints")
orignumvars = m.NumVars
m.feasRelaxS(0, False, False, True)
m.optimize()
status = m.Status
if status in (GRB.INF_OR_UNBD, GRB.INFEASIBLE, GRB.UNBOUNDED):
    print(
        "The relaxed model cannot be solved \
           because it is infeasible or unbounded"
    )
    sys.exit(1)

if status != GRB.OPTIMAL:
    print(f"Optimization was stopped with status {status}")
    sys.exit(1)

print("\nSlack values:")
slacks = m.getVars()[orignumvars:]
for sv in slacks:
    if sv.X > 1e-6:
        print(f"{sv.VarName} = {sv.X:g}")