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LP model (python - Pulp).ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "b01c2277",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Status: 1\n",
+      "Total Cost: $36950.0\n",
+      "Amount of coal shipped from Mine 1 to Plant 1: 33.0 tons\n",
+      "Amount of coal shipped from Mine 1 to Plant 2: 64.0 tons\n",
+      "Amount of coal shipped from Mine 1 to Plant 3: 36.0 tons\n",
+      "Amount of coal shipped from Mine 1 to Plant 4: 72.0 tons\n",
+      "Amount of coal shipped from Mine 2 to Plant 1: 55.0 tons\n",
+      "Amount of coal shipped from Mine 2 to Plant 2: 0.0 tons\n",
+      "Amount of coal shipped from Mine 2 to Plant 3: 0.0 tons\n",
+      "Amount of coal shipped from Mine 2 to Plant 4: 0.0 tons\n",
+      "Amount of coal shipped from Mine 3 to Plant 1: 22.0 tons\n",
+      "Amount of coal shipped from Mine 3 to Plant 2: 96.0 tons\n",
+      "Amount of coal shipped from Mine 3 to Plant 3: 54.0 tons\n",
+      "Amount of coal shipped from Mine 3 to Plant 4: 108.0 tons\n"
+     ]
+    }
+   ],
+   "source": [
+    "from pulp import LpProblem, LpVariable, lpSum, LpMinimize\n",
+    "\n",
+    "# Create a linear programming problem\n",
+    "model = LpProblem(\"Coal_Shipping_Problem\", LpMinimize)\n",
+    "\n",
+    "# Decision variables\n",
+    "mines = [1, 2, 3]\n",
+    "plants = [1, 2, 3, 4]\n",
+    "\n",
+    "# Amount of coal to be shipped from each mine to each plant\n",
+    "x = LpVariable.dicts(\"coal_shipped\", ((i, j) for i in mines for j in plants), lowBound=0, cat='Integer')\n",
+    "\n",
+    "# Objective function: Minimize total cost\n",
+    "model += lpSum(62 * x[i, j] for i in mines for j in plants) + \\\n",
+    "         lpSum(7 * x[i, j] for i in mines for j in plants if j == 1) + \\\n",
+    "         lpSum(9 * x[i, j] for i in mines for j in plants if j == 2) + \\\n",
+    "         lpSum(14 * x[i, j] for i in mines for j in plants if j == 3)\n",
+    "\n",
+    "# Constraints\n",
+    "# Mine capacity constraints\n",
+    "mine_capacity = {1: 220, 2: 190, 3: 280}\n",
+    "for i in mines:\n",
+    "    model += lpSum(x[i, j] for j in plants) <= mine_capacity[i]\n",
+    "\n",
+    "# Plant demand constraints\n",
+    "plant_demand = {1: 110, 2: 160, 3: 90, 4: 180}\n",
+    "for j in plants:\n",
+    "    model += lpSum(x[i, j] for i in mines) >= plant_demand[j]\n",
+    "\n",
+    "# Ash and sulfur content constraints\n",
+    "for j in plants:\n",
+    "    model += 0.09 * x[1, j] + 0.05 * x[2, j] + 0.04 * x[3, j] <= 0.06 * lpSum(x[i, j] for i in mines)\n",
+    "    model += 0.06 * x[1, j] + 0.04 * x[2, j] + 0.03 * x[3, j] <= 0.05 * lpSum(x[i, j] for i in mines)\n",
+    "\n",
+    "# Solve the problem\n",
+    "model.solve()\n",
+    "\n",
+    "# Print the results\n",
+    "print(f\"Status: {model.status}\")\n",
+    "print(f\"Total Cost: ${model.objective.value()}\")\n",
+    "\n",
+    "for i in mines:\n",
+    "    for j in plants:\n",
+    "        print(f\"Amount of coal shipped from Mine {i} to Plant {j}: {x[i, j].value()} tons\")\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c6b0eaee",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}