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.sat.python import cp_model 22import math 23 24# Data 25 26max_quantities = [["N_Total", 1944], ["P2O5", 1166.4], ["K2O", 1822.5], 27 ["CaO", 1458], ["MgO", 486], ["Fe", 9.7], ["B", 2.4]] 28 29chemical_set = [["A", 0, 0, 510, 540, 0, 0, 0], ["B", 110, 0, 0, 0, 160, 0, 0], 30 ["C", 61, 149, 384, 0, 30, 1, 31 0.2], ["D", 148, 70, 245, 0, 15, 1, 32 0.2], ["E", 160, 158, 161, 0, 10, 1, 0.2]] 33 34num_products = len(max_quantities) 35all_products = range(num_products) 36 37num_sets = len(chemical_set) 38all_sets = range(num_sets) 39 40# Model 41 42model = cp_model.CpModel() 43 44# Scale quantities by 100. 45max_set = [ 46 int( 47 math.ceil( 48 min(max_quantities[q][1] * 1000 / chemical_set[s][q + 1] 49 for q in all_products if chemical_set[s][q + 1] != 0))) 50 for s in all_sets 51] 52 53set_vars = [model.NewIntVar(0, max_set[s], "set_%i" % s) for s in all_sets] 54 55epsilon = model.NewIntVar(0, 10000000, "epsilon") 56 57for p in all_products: 58 model.Add( 59 sum(int(chemical_set[s][p + 1] * 10) * set_vars[s] 60 for s in all_sets) <= int(max_quantities[p][1] * 10000)) 61 model.Add( 62 sum(int(chemical_set[s][p + 1] * 10) * set_vars[s] 63 for s in all_sets) >= int(max_quantities[p][1] * 10000) - epsilon) 64 65model.Minimize(epsilon) 66 67# Creates a solver and solves. 68solver = cp_model.CpSolver() 69status = solver.Solve(model) 70print("Status = %s" % solver.StatusName(status)) 71# The objective value of the solution. 72print("Optimal objective value = %f" % (solver.ObjectiveValue() / 10000.0)) 73 74for s in all_sets: 75 print( 76 " %s = %f" % (chemical_set[s][0], solver.Value(set_vars[s]) / 1000.0), 77 end=" ") 78 print() 79for p in all_products: 80 name = max_quantities[p][0] 81 max_quantity = max_quantities[p][1] 82 quantity = sum( 83 solver.Value(set_vars[s]) / 1000.0 * chemical_set[s][p + 1] 84 for s in all_sets) 85 print("%s: %f out of %f" % (name, quantity, max_quantity)) 86