123 lines
3.3 KiB
Python
123 lines
3.3 KiB
Python
# Copyright 2010 Hakan Kjellerstrand hakank@gmail.com
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#
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# Licensed under the Apache License, Version 2.0 (the 'License');
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an 'AS IS' BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""
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P-median problem in Google CP Solver.
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Model and data from the OPL Manual, which describes the problem:
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'''
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The P-Median problem is a well known problem in Operations Research.
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The problem can be stated very simply, like this: given a set of customers
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with known amounts of demand, a set of candidate locations for warehouses,
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and the distance between each pair of customer-warehouse, choose P
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warehouses to open that minimize the demand-weighted distance of serving
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all customers from those P warehouses.
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'''
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Compare with the following models:
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* MiniZinc: http://hakank.org/minizinc/p_median.mzn
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* Comet: http://hakank.org/comet/p_median.co
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This model was created by Hakan Kjellerstrand (hakank@gmail.com)
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Also see my other Google CP Solver models:
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http://www.hakank.org/google_or_tools/
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"""
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from __future__ import print_function
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import sys
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from ortools.constraint_solver import pywrapcp
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def main():
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# Create the solver.
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solver = pywrapcp.Solver('P-median problem')
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#
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# data
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#
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p = 2
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num_customers = 4
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customers = list(range(num_customers))
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Albert, Bob, Chris, Daniel = customers
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num_warehouses = 3
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warehouses = list(range(num_warehouses))
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Santa_Clara, San_Jose, Berkeley = warehouses
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demand = [100, 80, 80, 70]
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distance = [[2, 10, 50], [2, 10, 52], [50, 60, 3], [40, 60, 1]]
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#
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# declare variables
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#
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open = [solver.IntVar(warehouses, 'open[%i]% % i') for w in warehouses]
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ship = {}
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for c in customers:
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for w in warehouses:
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ship[c, w] = solver.IntVar(0, 1, 'ship[%i,%i]' % (c, w))
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ship_flat = [ship[c, w] for c in customers for w in warehouses]
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z = solver.IntVar(0, 1000, 'z')
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#
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# constraints
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#
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z_sum = solver.Sum([
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demand[c] * distance[c][w] * ship[c, w]
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for c in customers
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for w in warehouses
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])
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solver.Add(z == z_sum)
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for c in customers:
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s = solver.Sum([ship[c, w] for w in warehouses])
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solver.Add(s == 1)
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solver.Add(solver.Sum(open) == p)
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for c in customers:
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for w in warehouses:
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solver.Add(ship[c, w] <= open[w])
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# objective
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objective = solver.Minimize(z, 1)
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#
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# solution and search
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#
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db = solver.Phase(open + ship_flat, solver.INT_VAR_DEFAULT,
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solver.INT_VALUE_DEFAULT)
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solver.NewSearch(db, [objective])
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num_solutions = 0
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while solver.NextSolution():
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num_solutions += 1
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print('z:', z.Value())
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print('open:', [open[w].Value() for w in warehouses])
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for c in customers:
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for w in warehouses:
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print(ship[c, w].Value(), end=' ')
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print()
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print()
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print('num_solutions:', num_solutions)
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print('failures:', solver.Failures())
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print('branches:', solver.Branches())
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print('WallTime:', solver.WallTime(), 'ms')
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if __name__ == '__main__':
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main()
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