LP model (python - Pulp).ipynb

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      "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"
   ]
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