1# Copyright 2010-2021 Google LLC 2# Licensed under the Apache License, Version 2.0 (the "License"); 3# you may not use this file except in compliance with the License. 4# You may obtain a copy of the License at 5# 6# http://www.apache.org/licenses/LICENSE-2.0 7# 8# Unless required by applicable law or agreed to in writing, software 9# distributed under the License is distributed on an "AS IS" BASIS, 10# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 11# See the License for the specific language governing permissions and 12# limitations under the License. 13 14# We are trying to group items in equal sized groups. 15# Each item has a color and a value. We want the sum of values of each group to 16# be as close to the average as possible. 17# Furthermore, if one color is an a group, at least k items with this color must 18# be in that group. 19 20 21from ortools.linear_solver import pywraplp 22 23import math 24 25# Data 26 27max_quantities = [["N_Total", 1944], ["P2O5", 1166.4], ["K2O", 1822.5], 28 ["CaO", 1458], ["MgO", 486], ["Fe", 9.7], ["B", 2.4]] 29 30chemical_set = [["A", 0, 0, 510, 540, 0, 0, 0], ["B", 110, 0, 0, 0, 160, 0, 0], 31 ["C", 61, 149, 384, 0, 30, 1, 32 0.2], ["D", 148, 70, 245, 0, 15, 1, 33 0.2], ["E", 160, 158, 161, 0, 10, 1, 0.2]] 34 35num_products = len(max_quantities) 36all_products = range(num_products) 37 38num_sets = len(chemical_set) 39all_sets = range(num_sets) 40 41# Model 42 43max_set = [ 44 min(max_quantities[q][1] / chemical_set[s][q + 1] for q in all_products 45 if chemical_set[s][q + 1] != 0.0) for s in all_sets 46] 47 48solver = pywraplp.Solver("chemical_set_lp", 49 pywraplp.Solver.GLOP_LINEAR_PROGRAMMING) 50 51set_vars = [solver.NumVar(0, max_set[s], "set_%i" % s) for s in all_sets] 52 53epsilon = solver.NumVar(0, 1000, "epsilon") 54 55for p in all_products: 56 solver.Add( 57 sum(chemical_set[s][p + 1] * set_vars[s] 58 for s in all_sets) <= max_quantities[p][1]) 59 solver.Add( 60 sum(chemical_set[s][p + 1] * set_vars[s] 61 for s in all_sets) >= max_quantities[p][1] - epsilon) 62 63solver.Minimize(epsilon) 64 65print(("Number of variables = %d" % solver.NumVariables())) 66print(("Number of constraints = %d" % solver.NumConstraints())) 67 68result_status = solver.Solve() 69 70# The problem has an optimal solution. 71assert result_status == pywraplp.Solver.OPTIMAL 72 73assert solver.VerifySolution(1e-7, True) 74 75print(("Problem solved in %f milliseconds" % solver.wall_time())) 76 77# The objective value of the solution. 78print(("Optimal objective value = %f" % solver.Objective().Value())) 79 80for s in all_sets: 81 print( 82 " %s = %f" % (chemical_set[s][0], set_vars[s].solution_value()), 83 end=" ") 84 print() 85for p in all_products: 86 name = max_quantities[p][0] 87 max_quantity = max_quantities[p][1] 88 quantity = sum( 89 set_vars[s].solution_value() * chemical_set[s][p + 1] for s in all_sets) 90 print("%s: %f out of %f" % (name, quantity, max_quantity)) 91