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"""
A set partitioning model of a wedding seating problem
Authors: Stuart Mitchell 2009
"""
import pulp
max_tables = 5
max_table_size = 4
guests = "A B C D E F G I J K L M N O P Q R".split()
def happiness(table):
"""
Find the happiness of the table
- by calculating the maximum distance between the letters
"""
return abs(ord(table[0]) - ord(table[-1]))
# create list of all possible tables
possible_tables = [tuple(c) for c in pulp.allcombinations(guests, max_table_size)]
# create a binary variable to state that a table setting is used
x = pulp.LpVariable.dicts(
"table", possible_tables, lowBound=0, upBound=1, cat=pulp.LpInteger
)
seating_model = pulp.LpProblem("Wedding Seating Model", pulp.LpMinimize)
seating_model += pulp.lpSum([happiness(table) * x[table] for table in possible_tables])
# specify the maximum number of tables
seating_model += (
pulp.lpSum([x[table] for table in possible_tables]) <= max_tables,
"Maximum_number_of_tables",
)
# A guest must seated at one and only one table
for guest in guests:
seating_model += (
pulp.lpSum([x[table] for table in possible_tables if guest in table]) == 1,
"Must_seat_%s" % guest,
)
seating_model.solve()
print("The choosen tables are out of a total of %s:" % len(possible_tables))
for table in possible_tables:
if x[table].value() == 1.0:
print(table)
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