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### workforce3.py

#!/usr/bin/python

# Copyright 2016, Gurobi Optimization, Inc.

# 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.

from gurobipy import *

# Number of workers required for each shift
shifts, shiftRequirements = 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 = multidict({
"Amy":   10,
"Bob":   12,
"Cathy": 10,
"Dan":   8,
"Ed":    8,
"Fred":  9,
"Gu":    11 })

# Worker availability
availability = 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 = 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 = {}
for w,s in availability:
x[w,s] = m.addVar(ub=1, obj=pay[w], name=w+"."+s)

# The objective is to minimize the total pay costs
m.modelSense = GRB.MINIMIZE

# Update model to integrate new variables
m.update()

# Constraint: assign exactly shiftRequirements[s] workers to each shift s
reqCts = {}
for s in shifts:
quicksum(x[w,s] for w,s in availability.select('*', s)) ==
shiftRequirements[s], s)

# Optimize
m.optimize()
status = m.status
if status == GRB.Status.UNBOUNDED:
print('The model cannot be solved because it is unbounded')
exit(0)
if status == GRB.Status.OPTIMAL:
print('The optimal objective is %g' % m.objVal)
exit(0)
if status != GRB.Status.INF_OR_UNBD and status != GRB.Status.INFEASIBLE:
print('Optimization was stopped with status %d' % status)
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.Status.INF_OR_UNBD, GRB.Status.INFEASIBLE, GRB.Status.UNBOUNDED):
print('The relaxed model cannot be solved \
because it is infeasible or unbounded')
exit(1)

if status != GRB.Status.OPTIMAL:
print('Optimization was stopped with status %d' % status)
exit(1)

print('\nSlack values:')
slacks = m.getVars()[orignumvars:]
for sv in slacks:
if sv.X > 1e-6:
print('%s = %g' % (sv.VarName, sv.X))


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