238 lines
8.6 KiB
Plaintext
238 lines
8.6 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"# Copyright 2010-2017 Google\n",
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"# Licensed under the Apache License, Version 2.0 (the \"License\");\n",
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"# you may not use this file except in compliance with the License.\n",
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"# You may obtain a copy of the License at\n",
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"#\n",
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"# http://www.apache.org/licenses/LICENSE-2.0\n",
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"#\n",
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"# Unless required by applicable law or agreed to in writing, software\n",
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"# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
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"# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
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"# See the License for the specific language governing permissions and\n",
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"# limitations under the License.\n",
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"\n",
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"from __future__ import print_function\n",
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"\n",
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"import collections\n",
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"\n",
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"from ortools.sat.python import cp_model\n",
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"\n",
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"\n",
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"def MinimalCpSat():\n",
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" # Creates the model.\n",
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" model = cp_model.CpModel()\n",
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"# Creates the variables.\n",
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" num_vals = 3\n",
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" x = model.NewIntVar(0, num_vals - 1, \"x\")\n",
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" y = model.NewIntVar(0, num_vals - 1, \"y\")\n",
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" z = model.NewIntVar(0, num_vals - 1, \"z\")\n",
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" # Create the constraints.\n",
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" model.Add(x != y)\n",
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"\n",
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" # Create a solver and solve.\n",
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" solver = cp_model.CpSolver()\n",
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" status = solver.Solve(model)\n",
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"\n",
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" if status == cp_model.MODEL_SAT:\n",
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" print(\"x = %i\" % solver.Value(x))\n",
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" print(\"y = %i\" % solver.Value(y))\n",
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" print(\"z = %i\" % solver.Value(z))\n",
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"\n",
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"\n",
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"class VarArraySolutionPrinter(cp_model.CpSolverSolutionCallback):\n",
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" \"\"\"Print intermediate solutions.\"\"\"\n",
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"\n",
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" def __init__(self, variables):\n",
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" self.__variables = variables\n",
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" self.__solution_count = 0\n",
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"\n",
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" def NewSolution(self):\n",
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" self.__solution_count += 1\n",
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" for v in self.__variables:\n",
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" print('%s=%i' % (v, self.Value(v)), end = ' ')\n",
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" print()\n",
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"\n",
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" def SolutionCount(self):\n",
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" return self.__solution_count\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"def MinimalCpSatAllSolutions():\n",
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" # Creates the model.\n",
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" model = cp_model.CpModel()\n",
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"# Creates the variables.\n",
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" num_vals = 3\n",
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" x = model.NewIntVar(0, num_vals - 1, \"x\")\n",
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" y = model.NewIntVar(0, num_vals - 1, \"y\")\n",
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" z = model.NewIntVar(0, num_vals - 1, \"z\")\n",
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" # Create the constraints.\n",
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" model.Add(x != y)\n",
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"\n",
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" # Create a solver and solve.\n",
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" solver = cp_model.CpSolver()\n",
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" solution_printer = VarArraySolutionPrinter([x, y, z])\n",
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" status = solver.SearchForAllSolutions(model, solution_printer)\n",
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"\n",
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" print('Number of solutions found: %i' % solution_printer.SolutionCount())\n",
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"\n",
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"\n",
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"def SolvingLinearProblem():\n",
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" # Create a model.\n",
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" model = cp_model.CpModel()\n",
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"\n",
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" # x and y are integer non-negative variables.\n",
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" x = model.NewIntVar(0, 17, 'x')\n",
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" y = model.NewIntVar(0, 17, 'y')\n",
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" model.Add(2*x + 14*y <= 35)\n",
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" model.Add(2*x <= 7)\n",
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" obj_var = model.NewIntVar(0, 1000, \"obj_var\")\n",
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" model.Add(obj_var == x + 10*y)\n",
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" objective = model.Maximize(obj_var)\n",
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"\n",
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" # Create a solver and solve.\n",
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" solver = cp_model.CpSolver()\n",
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" status = solver.Solve(model)\n",
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" if status == cp_model.OPTIMAL:\n",
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" print(\"Objective value: %i\" % solver.ObjectiveValue())\n",
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" print()\n",
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" print('x= %i' % solver.Value(x))\n",
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" print('y= %i' % solver.Value(y))\n",
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"\n",
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"\n",
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"def MinimalJobShop():\n",
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" # Create the model.\n",
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" model = cp_model.CpModel()\n",
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"\n",
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" machines_count = 3\n",
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" jobs_count = 3\n",
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" all_machines = range(0, machines_count)\n",
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" all_jobs = range(0, jobs_count)\n",
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" # Define data.\n",
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" machines = [[0, 1, 2],\n",
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" [0, 2, 1],\n",
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" [1, 2]]\n",
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"\n",
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" processing_times = [[3, 2, 2],\n",
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" [2, 1, 4],\n",
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" [4, 3]]\n",
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" # Computes horizon.\n",
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" horizon = 0\n",
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" for job in all_jobs:\n",
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" horizon += sum(processing_times[job])\n",
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"\n",
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" Task = collections.namedtuple('Task', 'start end interval')\n",
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" AssignedTask = collections.namedtuple('AssignedTask', 'start job index')\n",
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"\n",
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" # Creates jobs.\n",
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" all_tasks = {}\n",
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" for job in all_jobs:\n",
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" for index in range(0, len(machines[job])):\n",
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" start_var = model.NewIntVar(0, horizon, 'start_%i_%i' % (job, index))\n",
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" duration = processing_times[job][index]\n",
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" end_var = model.NewIntVar(0, horizon, 'end_%i_%i' % (job, index))\n",
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" interval_var = model.NewIntervalVar(start_var, duration, end_var,\n",
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" 'interval_%i_%i' % (job, index))\n",
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" all_tasks[(job, index)] = Task(start=start_var,\n",
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" end=end_var,\n",
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" interval=interval_var)\n",
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"\n",
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" # Creates sequence variables and add disjunctive constraints.\n",
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" for machine in all_machines:\n",
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" intervals = []\n",
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" for job in all_jobs:\n",
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" for index in range(0, len(machines[job])):\n",
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" if machines[job][index] == machine:\n",
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" intervals.append(all_tasks[(job, index)].interval)\n",
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" model.AddNoOverlap(intervals)\n",
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"\n",
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" # Add precedence contraints.\n",
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" for job in all_jobs:\n",
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" for index in range(0, len(machines[job]) - 1):\n",
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" model.Add(all_tasks[(job, index + 1)].start >=\n",
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" all_tasks[(job, index)].end)\n",
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"\n",
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" # Makespan objective.\n",
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" obj_var = model.NewIntVar(0, horizon, 'makespan')\n",
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" model.AddMaxEquality(\n",
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" obj_var, [all_tasks[(job, len(machines[job]) - 1)].end\n",
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" for job in all_jobs])\n",
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" model.Minimize(obj_var)\n",
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"\n",
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" # Solve model.\n",
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" solver = cp_model.CpSolver()\n",
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" status = solver.Solve(model)\n",
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"\n",
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" if status == cp_model.OPTIMAL:\n",
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" # Print out makespan.\n",
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" print('Optimal Schedule Length: %i' % solver.ObjectiveValue())\n",
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" print()\n",
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"\n",
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" # Create one list of assigned tasks per machine.\n",
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" assigned_jobs = [[] for _ in range(machines_count)]\n",
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" for job in all_jobs:\n",
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" for index in range(len(machines[job])):\n",
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" machine = machines[job][index]\n",
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" assigned_jobs[machine].append(\n",
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" AssignedTask(start = solver.Value(all_tasks[(job, index)].start),\n",
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" job = job, index = index))\n",
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"\n",
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" disp_col_width = 10\n",
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" sol_line = \"\"\n",
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" sol_line_tasks = \"\"\n",
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"\n",
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" print(\"Optimal Schedule\", \"\\n\")\n",
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"\n",
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" for machine in all_machines:\n",
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" # Sort by starting time.\n",
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" assigned_jobs[machine].sort()\n",
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" sol_line += \"Machine \" + str(machine) + \": \"\n",
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" sol_line_tasks += \"Machine \" + str(machine) + \": \"\n",
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"\n",
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" for assigned_task in assigned_jobs[machine]:\n",
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" name = 'job_%i_%i' % (assigned_task.job, assigned_task.index)\n",
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" # Add spaces to output to align columns.\n",
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" sol_line_tasks += name + \" \" * (disp_col_width - len(name))\n",
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" start = assigned_task.start\n",
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" duration = processing_times[assigned_task.job][assigned_task.index]\n",
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"\n",
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" sol_tmp = \"[%i,%i]\" % (start, start + duration)\n",
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" # Add spaces to output to align columns.\n",
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" sol_line += sol_tmp + \" \" * (disp_col_width - len(sol_tmp))\n",
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"\n",
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" sol_line += \"\\n\"\n",
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" sol_line_tasks += \"\\n\"\n",
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"\n",
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" print(sol_line_tasks)\n",
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" print(\"Time Intervals for Tasks\\n\")\n",
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" print(sol_line)\n",
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"\n",
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"\n",
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"\n",
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"def main():\n",
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" MinimalCpSat()\n",
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" MinimalCpSatAllSolutions()\n",
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" SolvingLinearProblem()\n",
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" MinimalJobShop()\n",
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"\n",
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"\n",
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"if __name__ == '__main__':\n",
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" main()"
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]
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}
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],
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"metadata": {},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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