notebooks/mip_models.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MIP Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pyomo.environ as pyo\n",
    "from jobshop.params import JobShopRandomParams\n",
    "from jobshop.mip import DisjModel, TimeModel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Instantiate random params of a 4x3 problem\n",
    "params = JobShopRandomParams(3, 4, seed=12)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Disjuntive model"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{align}\n",
    "    \\text{min} \\quad & C \\\\\n",
    "    \\text{s.t.} \\quad & x_{\\sigma_{h-1}^j, j} + p_{\\sigma_{h-1}^j, j} \\leq x_{\\sigma_{h}^j, j}\n",
    "        & \\forall ~ j \\in J; h \\in (2, ..., |M|)\\\\\n",
    "    & x_{m, j} + p_{m, j} \\leq x_{m, k} + V (1 - z_{m, j, k})\n",
    "        & \\forall ~ j, k \\in J, j \\neq k; m \\in M\\\\\n",
    "    & z_{m, j, k} + z_{m, k, j} = 1\n",
    "        & \\forall ~ j, k \\in J, j \\neq k; m \\in M\\\\\n",
    "    & x_{\\sigma_{|M|}^j, j} + p_{\\sigma_{|M|}^j, j} \\leq C\n",
    "        & \\forall ~ j \\in J\\\\\n",
    "    & x_{m, j} \\geq 0 & \\forall ~ j \\in J; m \\in M\\\\\n",
    "    & z_{m, j, k} \\in \\{0, 1\\} & \\forall ~ j, k \\in J; m \\in M\\\\\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "disj_model = DisjModel(params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Problem: \n",
      "- Name: unknown\n",
      "  Lower bound: 48.0\n",
      "  Upper bound: 48.0\n",
      "  Number of objectives: 1\n",
      "  Number of constraints: 48\n",
      "  Number of variables: 31\n",
      "  Number of binary variables: 48\n",
      "  Number of integer variables: 48\n",
      "  Number of nonzeros: 1\n",
      "  Sense: minimize\n",
      "Solver: \n",
      "- Status: ok\n",
      "  User time: -1.0\n",
      "  System time: 0.15\n",
      "  Wallclock time: 0.15\n",
      "  Termination condition: optimal\n",
      "  Termination message: Model was solved to optimality (subject to tolerances), and an optimal solution is available.\n",
      "  Statistics: \n",
      "    Branch and bound: \n",
      "      Number of bounded subproblems: 0\n",
      "      Number of created subproblems: 0\n",
      "    Black box: \n",
      "      Number of iterations: 0\n",
      "  Error rc: 0\n",
      "  Time: 0.25960540771484375\n",
      "Solution: \n",
      "- number of solutions: 0\n",
      "  number of solutions displayed: 0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "solver = pyo.SolverFactory(\"cbc\", options=dict(cuts=\"on\", sec=20))\n",
    "res = solver.solve(disj_model, tee=False)\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "disj_model.plot()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time-indexed model"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{align}\n",
    "    \\text{min} \\quad & C \\\\\n",
    "    \\text{s.t.} \\quad & \\sum_{t \\in T}{x_{m, j, t}} = 1\n",
    "        & \\forall ~ j \\in J; m \\in M \\\\\n",
    "    & \\sum_{j \\in J}\\sum_{t` \\in (t - p_{m, j} + 1, ..., t )}x_{m, j, t`} \\leq 1\n",
    "        & \\forall ~ m \\in M; t \\in T \\\\\n",
    "    & \\sum_{t \\in T}{(t + p_{\\sigma_{h - 1}^j, j}) x_{\\sigma_{h - 1}^j, j, t}} \\leq\n",
    "    \\sum_{t \\in T}{t x_{\\sigma_{h}^j, j, t}}\n",
    "        & \\forall ~ j \\in J; h \\in (1, 2, ..., |M|) \\\\\n",
    "    & \\sum_{t \\in T}{(t + p_{m, j}) x_{m, j, t}} \\leq C\n",
    "        & \\forall ~ j \\in J; m \\in M \\\\\n",
    "    & x_{m, j, t} \\in \\{0, 1\\} & \\forall ~ j; m \\in M; t \\in T\\\\\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "time_model = TimeModel(params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: Loading a SolverResults object with an 'aborted' status, but\n",
      "    containing a solution\n",
      "\n",
      "Problem: \n",
      "- Name: unknown\n",
      "  Lower bound: 46.0\n",
      "  Upper bound: 50.0\n",
      "  Number of objectives: 1\n",
      "  Number of constraints: 381\n",
      "  Number of variables: 1429\n",
      "  Number of binary variables: 1428\n",
      "  Number of integer variables: 1428\n",
      "  Number of nonzeros: 1\n",
      "  Sense: minimize\n",
      "Solver: \n",
      "- Status: aborted\n",
      "  User time: -1.0\n",
      "  System time: 18.58\n",
      "  Wallclock time: 18.58\n",
      "  Termination condition: maxTimeLimit\n",
      "  Termination message: Optimization terminated because the time expended exceeded the value specified in the seconds parameter.\n",
      "  Statistics: \n",
      "    Branch and bound: \n",
      "      Number of bounded subproblems: 961\n",
      "      Number of created subproblems: 961\n",
      "    Black box: \n",
      "      Number of iterations: 38219\n",
      "  Error rc: 0\n",
      "  Time: 18.761165142059326\n",
      "Solution: \n",
      "- number of solutions: 0\n",
      "  number of solutions displayed: 0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "res = solver.solve(time_model, tee=False)\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "time_model.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "venv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "c80e59d898e7c66d975776755d4e3dc6a2d556add5ce2725f479f7b2dc2ae0e0"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}