├── LICENSE ├── README.md ├── VRP (MTZ Formulation).ipynb ├── VRP Flow-Based Formulation.ipynb ├── VRP Multi-Commodity Flow Formulation.ipynb └── VRP Set Partitioning Formulation.ipynb /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2025 Renato Maynard Etchepare 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Vehicle Routing Problem (VRP) Formulations 2 | 3 | This repository contains four classical formulations for the Vehicle Routing Problem, along with Gurobi + Python (NetworkX) examples. Each formulation includes: 4 | 5 | 1. **Mathematical Models** in LaTeX (ready to copy-paste). 6 | 2. **Python Code** to demonstrate how to: 7 | - Build and solve the MIP model in Gurobi. 8 | - Plot resulting routes using NetworkX and Matplotlib. 9 | 10 | ## 1. Classical VRP (MTZ Formulation) 11 | - **File**: `VRP (MTZ Formulation).ipynb` 12 | - **Description**: Uses the Miller–Tucker–Zemlin (MTZ) constraints to eliminate subtours. 13 | - **Key Variables**: 14 | - `x[i,j]` (binary) indicating route arcs. 15 | - `u[i]` (continuous) for subtour elimination. 16 | - **Pros**: Simpler to implement. 17 | - **Cons**: Weaker LP bounds for large instances. 18 | 19 | ## 2. Flow-Based VRP 20 | - **File**: `VRP Flow-Based Formulation.ipynb` 21 | - **Description**: Uses a single flow variable `f[i,j]` to ensure connectivity and capacity constraints. 22 | - **Key Variables**: 23 | - `x[i,j]` (binary) for arcs, 24 | - `f[i,j]` (continuous) representing the flow on each arc. 25 | - **Pros**: Stronger LP relaxation. 26 | - **Cons**: Larger model (more variables). 27 | 28 | ## 3. Set Partitioning Formulation (Branch-and-Price Perspective) 29 | - **File**: `VRP Set Partitioning Formulation.ipynb` 30 | - **Description**: Each variable `y_r` represents an entire feasible route. The model partitions the set of customers among a chosen subset of routes. 31 | - **Key Variables**: 32 | - `y_r` (binary) indicates whether route `r` is used. 33 | - **Usage**: Often used with branch-and-price or column generation, especially for large-scale VRPs. 34 | 35 | ## 4. Multi-Commodity Flow Formulation 36 | - **File**: `VRP Multi-Commodity Flow Formulation.ipynb` 37 | - **Description**: One flow variable per commodity (often one commodity per customer) to model capacity in more granular detail. 38 | - **Key Variables**: 39 | - `x[i,j]` (binary), 40 | - `f[i,j,k]` (continuous) for commodity k on edge (i,j). 41 | - **Pros**: Very flexible, can handle multiple demand types. 42 | - **Cons**: Potentially huge model. 43 | 44 | ## How to Run 45 | 1. Make sure you have [Gurobi](https://www.gurobi.com/) installed and licensed. 46 | 2. Install [networkx](https://networkx.org/) and [matplotlib](https://matplotlib.org/). 47 | ```bash 48 | pip install networkx matplotlib 49 | 50 | ## References 51 | 1. G. B. Dantzig and J. H. Ramser. The truck dispatching problem. Management Science, 6(1): 80–91, 1959. 52 | 2. P. Toth and D. Vigo. Vehicle Routing: Problems, Methods, and Applications, 2nd ed. SIAM, 2014. 53 | 3. G. Laporte. Fifty Years of Vehicle Routing. Transportation Science, 43(4): 408–416, 2009. 54 | 4. R. Baldacci, A. Mingozzi, and R. Roberti. Recent exact algorithms for solving the vehicle routing problem under capacity and time window constraints. EJOR, 218(1): 1–6, 2012. 55 | -------------------------------------------------------------------------------- /VRP (MTZ Formulation).ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "id": "8a62d49f", 6 | "metadata": {}, 7 | "source": [ 8 | "# VRP Miller-Tucker-Zemlin (MTZ) formulation" 9 | ] 10 | }, 11 | { 12 | "cell_type": "markdown", 13 | "id": "0a91e0f0", 14 | "metadata": {}, 15 | "source": [ 16 | "#### Keywords: VRP, MTZ, Miller-Tucker-Zemlin formulation, IP, Gurobi, Python, Networkx" 17 | ] 18 | }, 19 | { 20 | "cell_type": "markdown", 21 | "id": "edfff52b", 22 | "metadata": {}, 23 | "source": [ 24 | "$ \\text{Variables} $\n", 25 | "\n", 26 | "$x_{ij} = \\begin{cases}\n", 27 | "1 & \\text{if the vehicle travels from node } i \\text{ to node } j \\\\\n", 28 | "0 & \\text{otherwise}\n", 29 | "\\end{cases} \\quad \\forall i,j \\in \\{0,1,\\ldots,n\\},\\ i \\ne j$\n", 30 | "\n", 31 | "$u_i \\in \\mathbb{R} \\quad \\forall i \\in \\{1, \\ldots, n\\}$\n", 32 | "\n", 33 | "\\begin{equation*}\n", 34 | "\\begin{aligned}\n", 35 | "& \\underset{}{\\text{Minimize}} \n", 36 | "& & \\sum_{i=0}^{n} \\sum_{\\substack{j=0 \\\\ j \\ne i}}^{n} c_{ij} \\, x_{ij} \\\\\n", 37 | "& \\text{Subject to}\n", 38 | "& & \\sum_{\\substack{j=0 \\\\ j \\ne i}}^{n} x_{ij} = 1, \\quad i = 1,\\ldots,n, \\\\\n", 39 | "&\n", 40 | "& & \\sum_{\\substack{i=0 \\\\ i \\ne j}}^{n} x_{ij} = 1, \\quad j = 1,\\ldots,n, \\\\\n", 41 | "&\n", 42 | "& & \\sum_{j=1}^{n} x_{0j} = K, \\quad \\sum_{i=1}^{n} x_{i0} = K, \\\\\n", 43 | "&\n", 44 | "& & u_i - u_j + n \\cdot x_{ij} \\le n - 1, \\quad \\forall i \\ne j,\\ i,j = 1,\\ldots,n, \\\\\n", 45 | "&\n", 46 | "& & 1 \\le u_i \\le n - 1, \\quad i = 1,\\ldots,n, \\\\\n", 47 | "&\n", 48 | "& & x_{ij} \\in \\{0,1\\}, \\quad \\forall i \\ne j,\\ i,j = 0,\\ldots,n, \\\\\n", 49 | "&\n", 50 | "& & u_i \\in \\mathbb{R}, \\quad i = 1,\\ldots,n. \\\\\n", 51 | "\\end{aligned}\n", 52 | "\\end{equation*}\n" 53 | ] 54 | }, 55 | { 56 | "cell_type": "markdown", 57 | "id": "7dcfe256", 58 | "metadata": {}, 59 | "source": [ 60 | "## Import Library and Model Enviroment" 61 | ] 62 | }, 63 | { 64 | "cell_type": "code", 65 | "execution_count": 1, 66 | "id": "4c6470ab", 67 | "metadata": {}, 68 | "outputs": [ 69 | { 70 | "name": "stdout", 71 | "output_type": "stream", 72 | "text": [ 73 | "Set parameter Username\n", 74 | "Academic license - for non-commercial use only - expires 2026-03-13\n" 75 | ] 76 | } 77 | ], 78 | "source": [ 79 | "import gurobipy as gp\n", 80 | "from gurobipy import GRB\n", 81 | "import networkx as nx\n", 82 | "import numpy as np\n", 83 | "import matplotlib.pyplot as plt\n", 84 | "m = gp.Model(\"VRP_MTZ\")" 85 | ] 86 | }, 87 | { 88 | "cell_type": "markdown", 89 | "id": "73722f92", 90 | "metadata": {}, 91 | "source": [ 92 | "### Create Data and Matrix of Distances" 93 | ] 94 | }, 95 | { 96 | "cell_type": "code", 97 | "execution_count": 18, 98 | "id": "52c965c8", 99 | "metadata": {}, 100 | "outputs": [], 101 | "source": [ 102 | "n = 24 # number of customers\n", 103 | "K = 4 # number of vehicles\n", 104 | "#Create a Random Matrix\n", 105 | "c = np.random.randint(1, 100, size=(n+1, n+1))\n", 106 | "# A_i,i = 0\n", 107 | "np.fill_diagonal(c, 0)" 108 | ] 109 | }, 110 | { 111 | "cell_type": "markdown", 112 | "id": "895d41c9", 113 | "metadata": {}, 114 | "source": [ 115 | "### Variables" 116 | ] 117 | }, 118 | { 119 | "cell_type": "code", 120 | "execution_count": 19, 121 | "id": "a192a3b0", 122 | "metadata": {}, 123 | "outputs": [], 124 | "source": [ 125 | "x = m.addVars(n+1, n+1, vtype=GRB.BINARY, name=\"x\")\n", 126 | "u = m.addVars(n+1, vtype=GRB.CONTINUOUS, lb=0, ub=n-1, name=\"u\")" 127 | ] 128 | }, 129 | { 130 | "cell_type": "markdown", 131 | "id": "ecab36cb", 132 | "metadata": {}, 133 | "source": [ 134 | "## Mathematical Model of VRP (MTZ Formulation)" 135 | ] 136 | }, 137 | { 138 | "cell_type": "markdown", 139 | "id": "2c866d6d", 140 | "metadata": {}, 141 | "source": [ 142 | "### Objective Function" 143 | ] 144 | }, 145 | { 146 | "cell_type": "code", 147 | "execution_count": 20, 148 | "id": "efdfc866", 149 | "metadata": {}, 150 | "outputs": [], 151 | "source": [ 152 | "m.setObjective(\n", 153 | " gp.quicksum(c[i][j] * x[i,j] for i in range(n+1) for j in range(n+1) if i != j),\n", 154 | " GRB.MINIMIZE\n", 155 | ")" 156 | ] 157 | }, 158 | { 159 | "cell_type": "markdown", 160 | "id": "73217077", 161 | "metadata": {}, 162 | "source": [ 163 | "### Subject to:" 164 | ] 165 | }, 166 | { 167 | "cell_type": "code", 168 | "execution_count": 21, 169 | "id": "200de506", 170 | "metadata": {}, 171 | "outputs": [], 172 | "source": [ 173 | "# 1) Each customer i has exactly one outgoing edge\n", 174 | "for i in range(1, n+1):\n", 175 | " m.addConstr(gp.quicksum(x[i,j] for j in range(n+1) if j != i) == 1)" 176 | ] 177 | }, 178 | { 179 | "cell_type": "code", 180 | "execution_count": 22, 181 | "id": "cda0ca56", 182 | "metadata": {}, 183 | "outputs": [], 184 | "source": [ 185 | "# 2) Each customer i has exactly one incoming edge\n", 186 | "for j in range(1, n+1):\n", 187 | " m.addConstr(gp.quicksum(x[i,j] for i in range(n+1) if i != j) == 1)\n" 188 | ] 189 | }, 190 | { 191 | "cell_type": "code", 192 | "execution_count": 23, 193 | "id": "bbd552f6", 194 | "metadata": {}, 195 | "outputs": [ 196 | { 197 | "data": { 198 | "text/plain": [ 199 | "" 200 | ] 201 | }, 202 | "execution_count": 23, 203 | "metadata": {}, 204 | "output_type": "execute_result" 205 | } 206 | ], 207 | "source": [ 208 | "# 3) Exactly K vehicles leaving/entering depot\n", 209 | "m.addConstr(gp.quicksum(x[0,j] for j in range(1, n+1)) == K)\n", 210 | "m.addConstr(gp.quicksum(x[i,0] for i in range(1, n+1)) == K)" 211 | ] 212 | }, 213 | { 214 | "cell_type": "code", 215 | "execution_count": 24, 216 | "id": "d21c6b20", 217 | "metadata": {}, 218 | "outputs": [], 219 | "source": [ 220 | "# 4) MTZ constraints\n", 221 | "for i in range(1, n+1):\n", 222 | " for j in range(1, n+1):\n", 223 | " if i != j:\n", 224 | " m.addConstr(u[i] - u[j] + (n+1)*x[i,j] <= n - 1)" 225 | ] 226 | }, 227 | { 228 | "cell_type": "markdown", 229 | "id": "4e7eca7d", 230 | "metadata": {}, 231 | "source": [ 232 | "### Solve the VRP (MTZ Formulation)" 233 | ] 234 | }, 235 | { 236 | "cell_type": "code", 237 | "execution_count": 25, 238 | "id": "7f809cd8", 239 | "metadata": {}, 240 | "outputs": [ 241 | { 242 | "name": "stdout", 243 | "output_type": "stream", 244 | "text": [ 245 | "Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (win64 - Windows 11+.0 (26100.2))\n", 246 | "\n", 247 | "CPU model: AMD Ryzen 7 4800H with Radeon Graphics, instruction set [SSE2|AVX|AVX2]\n", 248 | "Thread count: 8 physical cores, 16 logical processors, using up to 16 threads\n", 249 | "\n", 250 | "Optimize a model with 5706 rows, 5954 columns and 27756 nonzeros\n", 251 | "Model fingerprint: 0xd0f3f93a\n", 252 | "Variable types: 127 continuous, 5827 integer (5827 binary)\n", 253 | "Coefficient statistics:\n", 254 | " Matrix range [1e+00, 5e+01]\n", 255 | " Objective range [1e+00, 1e+02]\n", 256 | " Bounds range [1e+00, 5e+01]\n", 257 | " RHS range [1e+00, 5e+01]\n", 258 | "\n", 259 | "MIP start from previous solve produced solution with objective 267 (0.02s)\n", 260 | "MIP start from previous solve produced solution with objective 220 (0.04s)\n", 261 | "Loaded MIP start from previous solve with objective 220\n", 262 | "\n", 263 | "Presolve removed 3154 rows and 3354 columns\n", 264 | "Presolve time: 0.08s\n", 265 | "Presolved: 2552 rows, 2600 columns, 12450 nonzeros\n", 266 | "Variable types: 50 continuous, 2550 integer (2550 binary)\n", 267 | "\n", 268 | "Explored 0 nodes (0 simplex iterations) in 0.14 seconds (0.15 work units)\n", 269 | "Thread count was 16 (of 16 available processors)\n", 270 | "\n", 271 | "Solution count 2: 220 267 \n", 272 | "\n", 273 | "Optimal solution found (tolerance 1.00e-04)\n", 274 | "Best objective 2.200000000000e+02, best bound 2.200000000000e+02, gap 0.0000%\n" 275 | ] 276 | }, 277 | { 278 | "data": { 279 | "image/png": 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", 280 | "text/plain": [ 281 | "
" 282 | ] 283 | }, 284 | "metadata": {}, 285 | "output_type": "display_data" 286 | }, 287 | { 288 | "name": "stdout", 289 | "output_type": "stream", 290 | "text": [ 291 | "Optimal cost: 220.0\n", 292 | "Route from 0 to 4\n", 293 | "Route from 0 to 13\n", 294 | "Route from 0 to 15\n", 295 | "Route from 0 to 21\n", 296 | "Route from 1 to 6\n", 297 | "Route from 2 to 20\n", 298 | "Route from 3 to 1\n", 299 | "Route from 4 to 11\n", 300 | "Route from 5 to 22\n", 301 | "Route from 6 to 12\n", 302 | "Route from 7 to 0\n", 303 | "Route from 8 to 23\n", 304 | "Route from 9 to 3\n", 305 | "Route from 10 to 0\n", 306 | "Route from 11 to 5\n", 307 | "Route from 12 to 14\n", 308 | "Route from 13 to 19\n", 309 | "Route from 14 to 2\n", 310 | "Route from 15 to 9\n", 311 | "Route from 16 to 7\n", 312 | "Route from 17 to 16\n", 313 | "Route from 18 to 10\n", 314 | "Route from 19 to 24\n", 315 | "Route from 20 to 0\n", 316 | "Route from 21 to 18\n", 317 | "Route from 22 to 0\n", 318 | "Route from 23 to 17\n", 319 | "Route from 24 to 8\n" 320 | ] 321 | } 322 | ], 323 | "source": [ 324 | "m.optimize()\n", 325 | "\n", 326 | "# -------------\n", 327 | "# NetworkX Plot\n", 328 | "# -------------\n", 329 | "if m.status == GRB.OPTIMAL:\n", 330 | " sol_x = m.getAttr('x', x)\n", 331 | " \n", 332 | " # Create directed graph\n", 333 | " G = nx.DiGraph()\n", 334 | " \n", 335 | " # Add nodes\n", 336 | " for i in range(n+1):\n", 337 | " G.add_node(i)\n", 338 | " \n", 339 | " # Add edges used in the solution\n", 340 | " for i in range(n+1):\n", 341 | " for j in range(n+1):\n", 342 | " if i != j and sol_x[i,j] > 0.5:\n", 343 | " G.add_edge(i, j)\n", 344 | " \n", 345 | " # Layout and draw\n", 346 | " pos = nx.spring_layout(G, seed=42) # positions for all nodes\n", 347 | " nx.draw(G, pos, with_labels=True, node_size=500)\n", 348 | " edge_labels = {(i, j): c[i][j] for (i, j) in G.edges()}\n", 349 | " nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels)\n", 350 | " plt.title(\"MTZ VRP Solution\")\n", 351 | " plt.show()\n", 352 | "\n", 353 | " print(\"Optimal cost:\", m.objVal)\n", 354 | " # Print route\n", 355 | " for i in range(n+1):\n", 356 | " for j in range(n+1):\n", 357 | " if i != j and sol_x[i,j] > 0.5:\n", 358 | " print(f\"Route from {i} to {j}\")\n" 359 | ] 360 | }, 361 | { 362 | "cell_type": "markdown", 363 | "id": "488ac9d5", 364 | "metadata": {}, 365 | "source": [ 366 | "### Literature" 367 | ] 368 | }, 369 | { 370 | "cell_type": "markdown", 371 | "id": "01425ee3", 372 | "metadata": {}, 373 | "source": [ 374 | "Dantzig, G. and Ramser, J. (1959) The Truck Dispatching Problem. Management Science, 6, 80-91.\n", 375 | "http://dx.doi.org/10.1287/mnsc.6.1.80" 376 | ] 377 | }, 378 | { 379 | "cell_type": "code", 380 | "execution_count": null, 381 | "id": "c30335a2", 382 | "metadata": {}, 383 | "outputs": [], 384 | "source": [] 385 | } 386 | ], 387 | "metadata": { 388 | "kernelspec": { 389 | "display_name": "Python 3 (ipykernel)", 390 | "language": "python", 391 | "name": "python3" 392 | }, 393 | "language_info": { 394 | "codemirror_mode": { 395 | "name": "ipython", 396 | "version": 3 397 | }, 398 | "file_extension": ".py", 399 | "mimetype": "text/x-python", 400 | "name": "python", 401 | "nbconvert_exporter": "python", 402 | "pygments_lexer": "ipython3", 403 | "version": "3.11.5" 404 | } 405 | }, 406 | "nbformat": 4, 407 | "nbformat_minor": 5 408 | } 409 | -------------------------------------------------------------------------------- /VRP Flow-Based Formulation.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "id": "bf61292a", 6 | "metadata": {}, 7 | "source": [ 8 | "# VRP Flow-Based Formulation" 9 | ] 10 | }, 11 | { 12 | "cell_type": "markdown", 13 | "id": "ffe96b7d", 14 | "metadata": {}, 15 | "source": [ 16 | "#### Keywords: VRP, Flow-Based, IP, Gurobi, Python, Networkx" 17 | ] 18 | }, 19 | { 20 | "cell_type": "markdown", 21 | "id": "193db7fc", 22 | "metadata": {}, 23 | "source": [ 24 | "$ \\text{Variables} $\n", 25 | "\n", 26 | "$x_{ij} =\n", 27 | "\\begin{cases}\n", 28 | "1 & \\text{if the vehicle travels from node } i \\text{ to node } j \\\\\n", 29 | "0 & \\text{otherwise}\n", 30 | "\\end{cases}\n", 31 | "$\n", 32 | "\n", 33 | "$f_{ij}$ is the amount of flow (demand) carried on arc $(i,j)$\n", 34 | "\n", 35 | "$K$ is the number of vehicles, $Q$ is vehicle capacity, and $d_i$ is demand at node $i$\n", 36 | "\n", 37 | "\\begin{equation*}\n", 38 | "\\begin{aligned}\n", 39 | "& \\underset{}{\\text{Minimize}} \n", 40 | "& & \\sum_{i=0}^{n} \\sum_{\\substack{j=0 \\\\ j \\ne i}}^{n} c_{ij} \\cdot x_{ij} \\\\\n", 41 | "& \\text{Subject to} \\\\\n", 42 | "& & \\sum_{\\substack{j=0 \\\\ j \\ne i}}^{n} x_{ij} = 1, \\quad i = 1,\\ldots,n, \\\\\n", 43 | "& & \\sum_{\\substack{i=0 \\\\ i \\ne j}}^{n} x_{ij} = 1, \\quad j = 1,\\ldots,n, \\\\\n", 44 | "& & \\sum_{j=1}^{n} x_{0j} = K, \\quad \\sum_{i=1}^{n} x_{i0} = K, \\\\\n", 45 | "& & \\sum_{j=0}^{n} f_{ij} - \\sum_{j=0}^{n} f_{ji} = d_i, \\quad i = 1,\\ldots,n, \\\\\n", 46 | "& & f_{ij} \\le Q \\cdot x_{ij}, \\quad \\forall i,j = 0,\\ldots,n, \\\\\n", 47 | "& & x_{ij} \\in \\{0,1\\}, \\quad \\forall i \\ne j,\\ i,j = 0,\\ldots,n, \\\\\n", 48 | "& & f_{ij} \\in \\mathbb{R}_+, \\quad \\forall i,j = 0,\\ldots,n.\n", 49 | "\\end{aligned}\n", 50 | "\\end{equation*}\n", 51 | "\n" 52 | ] 53 | }, 54 | { 55 | "cell_type": "markdown", 56 | "id": "b3d32032", 57 | "metadata": {}, 58 | "source": [ 59 | "## Import Library and Model Enviroment" 60 | ] 61 | }, 62 | { 63 | "cell_type": "code", 64 | "execution_count": 1, 65 | "id": "e8dea264", 66 | "metadata": {}, 67 | "outputs": [ 68 | { 69 | "name": "stdout", 70 | "output_type": "stream", 71 | "text": [ 72 | "Set parameter Username\n", 73 | "Academic license - for non-commercial use only - expires 2026-03-13\n" 74 | ] 75 | } 76 | ], 77 | "source": [ 78 | "import gurobipy as gp\n", 79 | "from gurobipy import GRB\n", 80 | "import networkx as nx\n", 81 | "import numpy as np\n", 82 | "import matplotlib.pyplot as plt\n", 83 | "m = gp.Model(\"VRP_Flow\")" 84 | ] 85 | }, 86 | { 87 | "cell_type": "markdown", 88 | "id": "3db5d754", 89 | "metadata": {}, 90 | "source": [ 91 | "### Create Data and Matrix of Distances" 92 | ] 93 | }, 94 | { 95 | "cell_type": "code", 96 | "execution_count": 2, 97 | "id": "2666f553", 98 | "metadata": {}, 99 | "outputs": [], 100 | "source": [ 101 | "n = 24 # number of customers\n", 102 | "K = 4 # number of vehicles\n", 103 | "Q = 15 # Capacity of vehicle\n", 104 | "d = [0] + list(np.random.randint(1, Q // 4 + 1, size=n)) # demands (0 for depot)\n", 105 | "\n", 106 | "#Create a Random Matrix\n", 107 | "c = np.random.randint(1, 100, size=(n+1, n+1))\n", 108 | "# A_i,i = 0\n", 109 | "np.fill_diagonal(c, 0)" 110 | ] 111 | }, 112 | { 113 | "cell_type": "markdown", 114 | "id": "badaf9ce", 115 | "metadata": {}, 116 | "source": [ 117 | "### Variables" 118 | ] 119 | }, 120 | { 121 | "cell_type": "code", 122 | "execution_count": 3, 123 | "id": "70172026", 124 | "metadata": {}, 125 | "outputs": [], 126 | "source": [ 127 | "x = m.addVars(n+1, n+1, vtype=GRB.BINARY, name=\"x\")\n", 128 | "f = m.addVars(n+1, n+1, vtype=GRB.CONTINUOUS, lb=0, name=\"f\")" 129 | ] 130 | }, 131 | { 132 | "cell_type": "markdown", 133 | "id": "b5fc3519", 134 | "metadata": {}, 135 | "source": [ 136 | "## Mathematical Model of VRP (MTZ Formulation)" 137 | ] 138 | }, 139 | { 140 | "cell_type": "markdown", 141 | "id": "674ab712", 142 | "metadata": {}, 143 | "source": [ 144 | "### Objective Function" 145 | ] 146 | }, 147 | { 148 | "cell_type": "code", 149 | "execution_count": 4, 150 | "id": "eaea589e", 151 | "metadata": {}, 152 | "outputs": [], 153 | "source": [ 154 | "m.setObjective(\n", 155 | " gp.quicksum(c[i][j] * x[i,j] for i in range(n+1) for j in range(n+1) if i != j),\n", 156 | " GRB.MINIMIZE\n", 157 | ")" 158 | ] 159 | }, 160 | { 161 | "cell_type": "markdown", 162 | "id": "af88d973", 163 | "metadata": {}, 164 | "source": [ 165 | "### Subject to:" 166 | ] 167 | }, 168 | { 169 | "cell_type": "code", 170 | "execution_count": 5, 171 | "id": "b24aeeb6", 172 | "metadata": {}, 173 | "outputs": [], 174 | "source": [ 175 | "# 1) Each customer visited exactly once\n", 176 | "for i in range(1, n+1):\n", 177 | " m.addConstr(gp.quicksum(x[i,j] for j in range(n+1) if j != i) == 1)\n", 178 | " m.addConstr(gp.quicksum(x[j,i] for j in range(n+1) if j != i) == 1)" 179 | ] 180 | }, 181 | { 182 | "cell_type": "code", 183 | "execution_count": 6, 184 | "id": "36d7b5d1", 185 | "metadata": {}, 186 | "outputs": [ 187 | { 188 | "data": { 189 | "text/plain": [ 190 | "" 191 | ] 192 | }, 193 | "execution_count": 6, 194 | "metadata": {}, 195 | "output_type": "execute_result" 196 | } 197 | ], 198 | "source": [ 199 | "# 2) Depot constraints\n", 200 | "m.addConstr(gp.quicksum(x[0,j] for j in range(1, n+1)) == K)\n", 201 | "m.addConstr(gp.quicksum(x[i,0] for i in range(1, n+1)) == K)" 202 | ] 203 | }, 204 | { 205 | "cell_type": "code", 206 | "execution_count": 7, 207 | "id": "84852953", 208 | "metadata": {}, 209 | "outputs": [], 210 | "source": [ 211 | "# 3) Flow conservation\n", 212 | "for i in range(1, n+1):\n", 213 | " m.addConstr(\n", 214 | " gp.quicksum(f[i,j] for j in range(n+1)) \n", 215 | " - gp.quicksum(f[j,i] for j in range(n+1)) \n", 216 | " == d[i])" 217 | ] 218 | }, 219 | { 220 | "cell_type": "code", 221 | "execution_count": 8, 222 | "id": "84d1d183", 223 | "metadata": {}, 224 | "outputs": [], 225 | "source": [ 226 | "# 4) Flow capacity on edges\n", 227 | "for i in range(n+1):\n", 228 | " for j in range(n+1):\n", 229 | " if i != j:\n", 230 | " m.addConstr(f[i,j] <= Q * x[i,j])" 231 | ] 232 | }, 233 | { 234 | "cell_type": "markdown", 235 | "id": "59dc0bc1", 236 | "metadata": {}, 237 | "source": [ 238 | "### Solve the VRP (Flow-Based Formulation)" 239 | ] 240 | }, 241 | { 242 | "cell_type": "code", 243 | "execution_count": 9, 244 | "id": "105924c1", 245 | "metadata": {}, 246 | "outputs": [ 247 | { 248 | "name": "stdout", 249 | "output_type": "stream", 250 | "text": [ 251 | "Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (win64 - Windows 11+.0 (26100.2))\n", 252 | "\n", 253 | "CPU model: AMD Ryzen 7 4800H with Radeon Graphics, instruction set [SSE2|AVX|AVX2]\n", 254 | "Thread count: 8 physical cores, 16 logical processors, using up to 16 threads\n", 255 | "\n", 256 | "Optimize a model with 674 rows, 1250 columns and 3552 nonzeros\n", 257 | "Model fingerprint: 0x8f83061a\n", 258 | "Variable types: 625 continuous, 625 integer (625 binary)\n", 259 | "Coefficient statistics:\n", 260 | " Matrix range [1e+00, 2e+01]\n", 261 | " Objective range [1e+00, 1e+02]\n", 262 | " Bounds range [1e+00, 1e+00]\n", 263 | " RHS range [1e+00, 4e+00]\n", 264 | "Presolve removed 0 rows and 50 columns\n", 265 | "Presolve time: 0.01s\n", 266 | "Presolved: 674 rows, 1200 columns, 3552 nonzeros\n", 267 | "Variable types: 600 continuous, 600 integer (600 binary)\n", 268 | "Found heuristic solution: objective 2099.0000000\n", 269 | "\n", 270 | "Root relaxation: objective 1.881000e+02, 785 iterations, 0.01 seconds (0.01 work units)\n", 271 | "\n", 272 | " Nodes | Current Node | Objective Bounds | Work\n", 273 | " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", 274 | "\n", 275 | " 0 0 188.10000 0 29 2099.00000 188.10000 91.0% - 0s\n", 276 | "H 0 0 218.0000000 188.10000 13.7% - 0s\n", 277 | "H 0 0 214.0000000 188.10000 12.1% - 0s\n", 278 | " 0 0 189.71154 0 20 214.00000 189.71154 11.3% - 0s\n", 279 | " 0 0 189.71154 0 28 214.00000 189.71154 11.3% - 0s\n", 280 | " 0 0 189.71154 0 23 214.00000 189.71154 11.3% - 0s\n", 281 | "H 0 0 207.0000000 189.82353 8.30% - 0s\n", 282 | "H 0 0 201.0000000 189.82353 5.56% - 0s\n", 283 | "H 0 0 195.0000000 189.82353 2.65% - 0s\n", 284 | " 0 0 190.09775 0 42 195.00000 190.09775 2.51% - 0s\n", 285 | " 0 0 190.09775 0 13 195.00000 190.09775 2.51% - 0s\n", 286 | " 0 0 190.09775 0 10 195.00000 190.09775 2.51% - 0s\n", 287 | "H 0 0 194.0000000 190.14810 1.99% - 0s\n", 288 | " 0 0 190.20000 0 17 194.00000 190.20000 1.96% - 0s\n", 289 | " 0 0 190.53333 0 24 194.00000 190.53333 1.79% - 0s\n", 290 | " 0 0 190.53333 0 24 194.00000 190.53333 1.79% - 0s\n", 291 | " 0 0 191.74568 0 25 194.00000 191.74568 1.16% - 0s\n", 292 | " 0 0 194.00000 0 23 194.00000 194.00000 0.00% - 0s\n", 293 | "\n", 294 | "Cutting planes:\n", 295 | " Gomory: 1\n", 296 | " Implied bound: 4\n", 297 | " MIR: 7\n", 298 | " Flow cover: 11\n", 299 | " Flow path: 3\n", 300 | " Network: 1\n", 301 | " Relax-and-lift: 2\n", 302 | "\n", 303 | "Explored 1 nodes (1659 simplex iterations) in 0.16 seconds (0.09 work units)\n", 304 | "Thread count was 16 (of 16 available processors)\n", 305 | "\n", 306 | "Solution count 8: 194 195 201 ... 2099\n", 307 | "\n", 308 | "Optimal solution found (tolerance 1.00e-04)\n", 309 | "Best objective 1.940000000000e+02, best bound 1.940000000000e+02, gap 0.0000%\n" 310 | ] 311 | }, 312 | { 313 | "data": { 314 | "image/png": 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", 315 | "text/plain": [ 316 | "
" 317 | ] 318 | }, 319 | "metadata": {}, 320 | "output_type": "display_data" 321 | }, 322 | { 323 | "name": "stdout", 324 | "output_type": "stream", 325 | "text": [ 326 | "Optimal cost: 194.0\n", 327 | "Route from 0 to 9\n", 328 | "Route from 0 to 11\n", 329 | "Route from 0 to 14\n", 330 | "Route from 0 to 16\n", 331 | "Route from 1 to 19\n", 332 | "Route from 2 to 0\n", 333 | "Route from 3 to 23\n", 334 | "Route from 4 to 6\n", 335 | "Route from 5 to 10\n", 336 | "Route from 6 to 15\n", 337 | "Route from 7 to 0\n", 338 | "Route from 8 to 0\n", 339 | "Route from 9 to 4\n", 340 | "Route from 10 to 8\n", 341 | "Route from 11 to 18\n", 342 | "Route from 12 to 1\n", 343 | "Route from 13 to 7\n", 344 | "Route from 14 to 3\n", 345 | "Route from 15 to 12\n", 346 | "Route from 16 to 21\n", 347 | "Route from 17 to 13\n", 348 | "Route from 18 to 24\n", 349 | "Route from 19 to 0\n", 350 | "Route from 20 to 22\n", 351 | "Route from 21 to 20\n", 352 | "Route from 22 to 5\n", 353 | "Route from 23 to 17\n", 354 | "Route from 24 to 2\n" 355 | ] 356 | } 357 | ], 358 | "source": [ 359 | "m.optimize()\n", 360 | "\n", 361 | "# -------------\n", 362 | "# NetworkX Plot\n", 363 | "# -------------\n", 364 | "if m.status == GRB.OPTIMAL:\n", 365 | " sol_x = m.getAttr('x', x)\n", 366 | " \n", 367 | " G = nx.DiGraph()\n", 368 | " for i in range(n+1):\n", 369 | " G.add_node(i)\n", 370 | " for i in range(n+1):\n", 371 | " for j in range(n+1):\n", 372 | " if i != j and sol_x[i,j] > 0.5:\n", 373 | " G.add_edge(i, j)\n", 374 | "\n", 375 | " pos = nx.spring_layout(G, seed=42)\n", 376 | " nx.draw(G, pos, with_labels=True, node_size=500)\n", 377 | " edge_labels = {(i, j): c[i][j] for (i, j) in G.edges()}\n", 378 | " nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels)\n", 379 | " plt.title(\"Flow-Based VRP Solution\")\n", 380 | " plt.show()\n", 381 | "\n", 382 | " print(\"Optimal cost:\", m.objVal)\n", 383 | " for i in range(n+1):\n", 384 | " for j in range(n+1):\n", 385 | " if i != j and sol_x[i,j] > 0.5:\n", 386 | " print(f\"Route from {i} to {j}\")" 387 | ] 388 | }, 389 | { 390 | "cell_type": "markdown", 391 | "id": "b49ec976", 392 | "metadata": {}, 393 | "source": [ 394 | "### Literature" 395 | ] 396 | }, 397 | { 398 | "cell_type": "markdown", 399 | "id": "98e0d554", 400 | "metadata": {}, 401 | "source": [ 402 | "Toth, P. and Vigo, D. (2014). Vehicle Routing: Problems, Methods, and Applications, 2nd ed. SIAM. A comprehensive book on VRP formulations, algorithms, and variants." 403 | ] 404 | } 405 | ], 406 | "metadata": { 407 | "kernelspec": { 408 | "display_name": "Python 3 (ipykernel)", 409 | "language": "python", 410 | "name": "python3" 411 | }, 412 | "language_info": { 413 | "codemirror_mode": { 414 | "name": "ipython", 415 | "version": 3 416 | }, 417 | "file_extension": ".py", 418 | "mimetype": "text/x-python", 419 | "name": "python", 420 | "nbconvert_exporter": "python", 421 | "pygments_lexer": "ipython3", 422 | "version": "3.11.5" 423 | } 424 | }, 425 | "nbformat": 4, 426 | "nbformat_minor": 5 427 | } 428 | -------------------------------------------------------------------------------- /VRP Set Partitioning Formulation.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "id": "bf61292a", 6 | "metadata": {}, 7 | "source": [ 8 | "# VRP Set Partitioning Formulation" 9 | ] 10 | }, 11 | { 12 | "cell_type": "markdown", 13 | "id": "ffe96b7d", 14 | "metadata": {}, 15 | "source": [ 16 | "#### Keywords: VRP, Set Partitioning Formulation, IP, Gurobi, Python, Networkx" 17 | ] 18 | }, 19 | { 20 | "cell_type": "markdown", 21 | "id": "193db7fc", 22 | "metadata": {}, 23 | "source": [ 24 | "$ \\text{Variables} $\n", 25 | "\n", 26 | "$y_r =\n", 27 | "\\begin{cases}\n", 28 | "1 & \\text{if route } r \\text{ is used} \\\\\n", 29 | "0 & \\text{otherwise}\n", 30 | "\\end{cases}\n", 31 | "\\quad \\forall r \\in \\Omega$\n", 32 | "\n", 33 | "$a_{ir} =\n", 34 | "\\begin{cases}\n", 35 | "1 & \\text{if route } r \\text{ visits customer } i \\\\\n", 36 | "0 & \\text{otherwise}\n", 37 | "\\end{cases}\n", 38 | "$\n", 39 | "\n", 40 | "$cost_r$ is the total cost of route $r$, \n", 41 | "$\\Omega$ is the set of all feasible routes, \n", 42 | "$K$ is the number of available vehicles.\n", 43 | "\n", 44 | "---\n", 45 | "\n", 46 | "\\begin{equation*}\n", 47 | "\\begin{aligned}\n", 48 | "& \\underset{}{\\text{Minimize}} \n", 49 | "& & \\sum_{r \\in \\Omega} cost_r \\cdot y_r \\\\\n", 50 | "& \\text{Subject to} \\\\\n", 51 | "& & \\sum_{r \\in \\Omega} a_{ir} \\cdot y_r = 1, \\quad \\forall i = 1,\\ldots,n, \\\\\n", 52 | "& & \\sum_{r \\in \\Omega} y_r \\le K, \\\\\n", 53 | "& & y_r \\in \\{0,1\\}, \\quad \\forall r \\in \\Omega.\n", 54 | "\\end{aligned}\n", 55 | "\\end{equation*}\n" 56 | ] 57 | }, 58 | { 59 | "cell_type": "markdown", 60 | "id": "b3d32032", 61 | "metadata": {}, 62 | "source": [ 63 | "## Import Library and Model Enviroment" 64 | ] 65 | }, 66 | { 67 | "cell_type": "code", 68 | "execution_count": 1, 69 | "id": "e8dea264", 70 | "metadata": {}, 71 | "outputs": [ 72 | { 73 | "name": "stdout", 74 | "output_type": "stream", 75 | "text": [ 76 | "Set parameter Username\n", 77 | "Academic license - for non-commercial use only - expires 2026-03-13\n" 78 | ] 79 | } 80 | ], 81 | "source": [ 82 | "import gurobipy as gp\n", 83 | "from gurobipy import GRB\n", 84 | "import networkx as nx\n", 85 | "import numpy as np\n", 86 | "import matplotlib.pyplot as plt\n", 87 | "m = gp.Model(\"VRP_SetPartitioning\")" 88 | ] 89 | }, 90 | { 91 | "cell_type": "markdown", 92 | "id": "3db5d754", 93 | "metadata": {}, 94 | "source": [ 95 | "### Create Data and Matrix of Distances" 96 | ] 97 | }, 98 | { 99 | "cell_type": "code", 100 | "execution_count": 3, 101 | "id": "2666f553", 102 | "metadata": {}, 103 | "outputs": [], 104 | "source": [ 105 | "# -------------\n", 106 | "# Data\n", 107 | "# -------------\n", 108 | "\n", 109 | "n_customers = 6\n", 110 | "K = 4 # Number of vehicles (so up to 4 routes can be selected)\n", 111 | "\n", 112 | "# Suppose we have enumerated or generated feasible routes:\n", 113 | "# Each route r starts at 0 (depot), visits some subset of customers, and returns to 0.\n", 114 | "# We'll define \"routes_dict\" mapping route r -> list of nodes in the route.\n", 115 | "routes_dict = {\n", 116 | " 0: [0, 1, 2, 0], # covers customers 1,2\n", 117 | " 1: [0, 3, 4, 0], # covers customers 3,4\n", 118 | " 2: [0, 5, 6, 0], # covers customers 5,6\n", 119 | " 3: [0, 1, 4, 6, 0], # covers customers 1,4,6\n", 120 | " 4: [0, 2, 3, 5, 0], # covers customers 2,3,5\n", 121 | " 5: [0, 6, 4, 3, 0], # covers customers 6,4,3\n", 122 | " 6: [0, 2, 5, 4, 0], # covers customers 2,5,4\n", 123 | " 7: [0, 3, 6, 5, 0], # covers customers 3,6,5\n", 124 | " 8: [0, 1, 5, 0], # covers customers 1,5\n", 125 | " 9: [0, 2, 4, 0] # covers customers 2,4\n", 126 | "}\n", 127 | "\n", 128 | "# Define a cost for each route (dummy data for demonstration).\n", 129 | "# In real applications, cost would be sum of traveling arcs. \n", 130 | "cost = {\n", 131 | " 0: 25, # route [0,1,2,0]\n", 132 | " 1: 20, # route [0,3,4,0]\n", 133 | " 2: 23, # route [0,5,6,0]\n", 134 | " 3: 30, # route [0,1,4,6,0]\n", 135 | " 4: 28, # route [0,2,3,5,0]\n", 136 | " 5: 33, # route [0,6,4,3,0]\n", 137 | " 6: 18, # route [0,2,5,4,0]\n", 138 | " 7: 27, # route [0,3,6,5,0]\n", 139 | " 8: 15, # route [0,1,5,0]\n", 140 | " 9: 22 # route [0,2,4,0]\n", 141 | "}\n", 142 | "\n", 143 | "Omega = list(routes_dict.keys()) # route indices\n", 144 | "\n", 145 | "# Build 'a[i,r]' = 1 if route r visits customer i, else 0\n", 146 | "a = {}\n", 147 | "for r in Omega:\n", 148 | " visited_customers = [node for node in routes_dict[r] if node != 0] # strip out depot\n", 149 | " for i in range(1, n_customers + 1):\n", 150 | " a[(i, r)] = 1 if i in visited_customers else 0" 151 | ] 152 | }, 153 | { 154 | "cell_type": "markdown", 155 | "id": "badaf9ce", 156 | "metadata": {}, 157 | "source": [ 158 | "### Variables" 159 | ] 160 | }, 161 | { 162 | "cell_type": "code", 163 | "execution_count": 4, 164 | "id": "70172026", 165 | "metadata": {}, 166 | "outputs": [], 167 | "source": [ 168 | "y = m.addVars(Omega, vtype=GRB.BINARY, name=\"y\")" 169 | ] 170 | }, 171 | { 172 | "cell_type": "markdown", 173 | "id": "b5fc3519", 174 | "metadata": {}, 175 | "source": [ 176 | "## Mathematical Model of VRP (MTZ Formulation)" 177 | ] 178 | }, 179 | { 180 | "cell_type": "markdown", 181 | "id": "674ab712", 182 | "metadata": {}, 183 | "source": [ 184 | "### Objective Function" 185 | ] 186 | }, 187 | { 188 | "cell_type": "code", 189 | "execution_count": 5, 190 | "id": "eaea589e", 191 | "metadata": {}, 192 | "outputs": [], 193 | "source": [ 194 | "m.setObjective(gp.quicksum(cost[r] * y[r] for r in Omega), GRB.MINIMIZE)" 195 | ] 196 | }, 197 | { 198 | "cell_type": "markdown", 199 | "id": "af88d973", 200 | "metadata": {}, 201 | "source": [ 202 | "### Subject to:" 203 | ] 204 | }, 205 | { 206 | "cell_type": "code", 207 | "execution_count": 6, 208 | "id": "b24aeeb6", 209 | "metadata": {}, 210 | "outputs": [], 211 | "source": [ 212 | "# 1) Each customer visited exactly once\n", 213 | "for i in range(1, n_customers+1):\n", 214 | " if i!=0:\n", 215 | " m.addConstr(gp.quicksum(a[(i,r)] * y[r] for r in Omega) == 1)" 216 | ] 217 | }, 218 | { 219 | "cell_type": "code", 220 | "execution_count": 7, 221 | "id": "36d7b5d1", 222 | "metadata": {}, 223 | "outputs": [ 224 | { 225 | "data": { 226 | "text/plain": [ 227 | "" 228 | ] 229 | }, 230 | "execution_count": 7, 231 | "metadata": {}, 232 | "output_type": "execute_result" 233 | } 234 | ], 235 | "source": [ 236 | "# 2) At most K routes\n", 237 | "m.addConstr(gp.quicksum(y[r] for r in Omega) <= K)" 238 | ] 239 | }, 240 | { 241 | "cell_type": "markdown", 242 | "id": "59dc0bc1", 243 | "metadata": {}, 244 | "source": [ 245 | "### Solve the VRP (Flow-Based Formulation)" 246 | ] 247 | }, 248 | { 249 | "cell_type": "code", 250 | "execution_count": 8, 251 | "id": "105924c1", 252 | "metadata": {}, 253 | "outputs": [ 254 | { 255 | "name": "stdout", 256 | "output_type": "stream", 257 | "text": [ 258 | "Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (win64 - Windows 11+.0 (26100.2))\n", 259 | "\n", 260 | "CPU model: AMD Ryzen 7 4800H with Radeon Graphics, instruction set [SSE2|AVX|AVX2]\n", 261 | "Thread count: 8 physical cores, 16 logical processors, using up to 16 threads\n", 262 | "\n", 263 | "Optimize a model with 7 rows, 10 columns and 35 nonzeros\n", 264 | "Model fingerprint: 0x1dc9bf96\n", 265 | "Variable types: 0 continuous, 10 integer (10 binary)\n", 266 | "Coefficient statistics:\n", 267 | " Matrix range [1e+00, 1e+00]\n", 268 | " Objective range [2e+01, 3e+01]\n", 269 | " Bounds range [1e+00, 1e+00]\n", 270 | " RHS range [1e+00, 4e+00]\n", 271 | "Found heuristic solution: objective 68.0000000\n", 272 | "Presolve removed 7 rows and 10 columns\n", 273 | "Presolve time: 0.00s\n", 274 | "Presolve: All rows and columns removed\n", 275 | "\n", 276 | "Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)\n", 277 | "Thread count was 1 (of 16 available processors)\n", 278 | "\n", 279 | "Solution count 2: 58 68 \n", 280 | "\n", 281 | "Optimal solution found (tolerance 1.00e-04)\n", 282 | "Best objective 5.800000000000e+01, best bound 5.800000000000e+01, gap 0.0000%\n" 283 | ] 284 | }, 285 | { 286 | "data": { 287 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", 288 | "text/plain": [ 289 | "
" 290 | ] 291 | }, 292 | "metadata": {}, 293 | "output_type": "display_data" 294 | }, 295 | { 296 | "name": "stdout", 297 | "output_type": "stream", 298 | "text": [ 299 | "Optimal cost: 58.0\n", 300 | "Using route 3: [0, 1, 4, 6, 0]\n", 301 | "Using route 4: [0, 2, 3, 5, 0]\n" 302 | ] 303 | } 304 | ], 305 | "source": [ 306 | "m.optimize()\n", 307 | "\n", 308 | "# -------------\n", 309 | "# NetworkX Plot\n", 310 | "# -------------\n", 311 | "if m.status == GRB.OPTIMAL:\n", 312 | " sol_y = m.getAttr('x', y)\n", 313 | " \n", 314 | " # For the plot, we combine all chosen routes into one graph.\n", 315 | " G = nx.DiGraph()\n", 316 | " \n", 317 | " # Add nodes\n", 318 | " for node in range(n_customers+1):\n", 319 | " G.add_node(node)\n", 320 | " \n", 321 | " # For each selected route, add edges\n", 322 | " for r in Omega:\n", 323 | " if sol_y[r] > 0.5:\n", 324 | " route_nodes = routes_dict[r]\n", 325 | " # If route_nodes = [0, 1, 2, 0], we'll draw edges (0->1), (1->2), (2->0).\n", 326 | " for i in range(len(route_nodes)-1):\n", 327 | " G.add_edge(route_nodes[i], route_nodes[i+1])\n", 328 | " \n", 329 | " pos = nx.spring_layout(G, seed=42)\n", 330 | " nx.draw(G, pos, with_labels=True, node_size=500)\n", 331 | " # For fun, label edges with \"r\" just to show which route they came from (optional)\n", 332 | " # or skip edge labels if you prefer.\n", 333 | " plt.title(\"Set Partitioning VRP Solution\")\n", 334 | " plt.show()\n", 335 | "\n", 336 | " print(\"Optimal cost:\", m.objVal)\n", 337 | " for r in Omega:\n", 338 | " if sol_y[r] > 0.5:\n", 339 | " print(f\"Using route {r}: {routes_dict[r]}\")" 340 | ] 341 | }, 342 | { 343 | "cell_type": "markdown", 344 | "id": "b49ec976", 345 | "metadata": {}, 346 | "source": [ 347 | "### Literature" 348 | ] 349 | }, 350 | { 351 | "cell_type": "markdown", 352 | "id": "98e0d554", 353 | "metadata": {}, 354 | "source": [ 355 | "Laporte, Gilbert, (2009), Fifty Years of Vehicle Routing, Transportation Science, 43, issue 4, p. 408-416, https://EconPapers.repec.org/RePEc:inm:ortrsc:v:43:y:2009:i:4:p:408-416." 356 | ] 357 | } 358 | ], 359 | "metadata": { 360 | "kernelspec": { 361 | "display_name": "Python 3 (ipykernel)", 362 | "language": "python", 363 | "name": "python3" 364 | }, 365 | "language_info": { 366 | "codemirror_mode": { 367 | "name": "ipython", 368 | "version": 3 369 | }, 370 | "file_extension": ".py", 371 | "mimetype": "text/x-python", 372 | "name": "python", 373 | "nbconvert_exporter": "python", 374 | "pygments_lexer": "ipython3", 375 | "version": "3.11.5" 376 | } 377 | }, 378 | "nbformat": 4, 379 | "nbformat_minor": 5 380 | } 381 | --------------------------------------------------------------------------------