bowman-farm-python-code

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     "text": [
      "Requirement already satisfied: pulp in /opt/anaconda3/lib/python3.12/site-packages (3.1.1)\n"
     ]
    }
   ],
   "source": [
    "!pip install pulp"
   ]
  },
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   "id": "47c0b1d9-0e52-4206-9b46-3ddc687a973d",
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   "source": [
    "import pulp\n",
    "\n",
    "# Define the LP problem\n",
    "model = pulp.LpProblem(\"Farm_Optimization\", pulp.LpMaximize)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "f48c39c7-9628-4856-9fd5-5fe13d2b90bb",
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   "source": [
    "# Decision Variable\n",
    "\n",
    "\n",
    "Xc = pulp.LpVariable(\"2025_Buy_Cows\", lowBound=0, upBound=50, cat='Integer')\n",
    "Xh = pulp.LpVariable(\"2025_Buy_Hens\", lowBound=0, upBound=1600, cat='Integer')\n",
    "\n",
    "Yc = pulp.LpVariable(\"2025_Sell_Cows\", lowBound=0, upBound=30, cat='Integer')\n",
    "Yh = pulp.LpVariable(\"2025_Sell_Hens\", lowBound=0, upBound=400, cat='Integer')\n",
    "\n",
    "Ac = pulp.LpVariable('Acres_Corn', lowBound=0, cat='Continuous')\n",
    "Aw = pulp.LpVariable('Acres_Wheat', lowBound=0, cat='Continuous')\n",
    "Ar = pulp.LpVariable('Acres_Rapeseed', lowBound=0, cat='Continuous')\n",
    "\n",
    "Zcorn = pulp.LpVariable('2025_Sell_Corn', lowBound=0, cat='Continuous')\n",
    "Zwheat = pulp.LpVariable('2025_Sell_Wheat', lowBound=0, cat='Continuous')\n",
    "\n",
    "Zrape = pulp.LpVariable('2026_Sell_Rapeseed', lowBound=0, cat='Continuous')\n",
    "\n",
    "Scorn = pulp.LpVariable('2025_Store_Corn', lowBound=0, cat='Continuous')\n",
    "Swheat = pulp.LpVariable('2025_Store_Wheat', lowBound=0, cat='Continuous')\n",
    "\n",
    "Pcorn = pulp.LpVariable('2025_Purchase_Corn', lowBound=0, cat='Continuous')\n",
    "Pwheat = pulp.LpVariable('2025_Purchase_Wheat', lowBound=0, cat='Continuous')\n",
    "\n",
    "Kinvest = pulp.LpVariable(\"Capital_Invested\", lowBound=0, cat='Continuous')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "a4783ace-16d5-4e63-8ff8-da9505ee39cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Parameters\n",
    "\n",
    "\n",
    "initial_cows = 30\n",
    "initial_hens = 400\n",
    "usable_capital = 160000 - 40000  # Net after fixed costs\n",
    "\n",
    "# A dictionary storing various costs and prices for buying, selling, planting, feeding, and residual values\n",
    "prices = {\n",
    "    'corn_selling_2025': 200,\n",
    "    'wheat_selling_2025': 195,\n",
    "\n",
    "    'corn_purchase_2025': 240,\n",
    "    'wheat_purchase_2025': 220,\n",
    "    \n",
    "    'corn_selling_2026': 210,\n",
    "    'wheat_selling_2026': 205,\n",
    "    'rape_selling_2026': 450,\n",
    "\n",
    "    'corn_plant_cost': 550,\n",
    "    'wheat_plant_cost': 400,\n",
    "    'rape_plant_cost': 244,\n",
    "    \n",
    "    'cow_income': 1300,\n",
    "    'hen_income': 155,\n",
    "    \n",
    "    'cow_buy': 1040,\n",
    "    'hen_buy': 17,\n",
    "    \n",
    "    'cow_residual': 0.9 * 1040,\n",
    "    'hen_residual': 0.85 * 17,  \n",
    "    \n",
    "    'interest_rate': 0.035,\n",
    "}\n",
    "\n",
    "# Short aliases for current livestock numbers\n",
    "Sc = initial_cows\n",
    "Sh = initial_hens\n",
    "\n",
    "# Adds up all expenses, including: Buying animals, Planting crops, Purchasing feed, Capital investment\n",
    "total_cost = (\n",
    "    prices['cow_buy'] * Xc +\n",
    "    prices['hen_buy'] * Xh +\n",
    "    \n",
    "    prices['corn_plant_cost'] * Ac +\n",
    "    prices['wheat_plant_cost'] * Aw +\n",
    "    prices['rape_plant_cost'] * Ar +\n",
    "    \n",
    "    prices['corn_purchase_2025'] * Pcorn +\n",
    "    prices['wheat_purchase_2025'] * Pwheat +\n",
    "    \n",
    "    Kinvest\n",
    ")\n",
    "\n",
    "# Calculates total revenue, from: Selling crops (current and next year), Livestock income (milk, eggs, etc.)\n",
    "revenue = (\n",
    "    prices['corn_selling_2025'] * Zcorn +\n",
    "    prices['wheat_selling_2025'] * Zwheat +\n",
    "    prices['corn_selling_2026'] * Scorn +\n",
    "    prices['wheat_selling_2026'] * Swheat +\n",
    "    prices['rape_selling_2026'] * Zrape +\n",
    "    prices['cow_income'] * (Sc + Xc - Yc) +\n",
    "    prices['hen_income'] * (Sh + Xh - Yh)\n",
    ")\n",
    "\n",
    "# Accounts for value of remaining livestock (not sold by end of cycle), adjusted by residual (salvage) rates\n",
    "residual_value = (\n",
    "    prices['cow_residual'] * (Sc + Xc - Yc) +\n",
    "    prices['hen_residual'] * (Sh + Xh - Yh)\n",
    ")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "7084e4c9-7cb1-487e-9951-a838636349da",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Objective function\n",
    "\n",
    "\n",
    "# Formula to maximize total expected wealth, combining: Revenue, Leftover livestock value, Interest on leftover cash, Subtracted by total expenses\n",
    "expected_wealth = revenue + residual_value + prices['interest_rate'] * (usable_capital + revenue - total_cost) - total_cost\n",
    "model += expected_wealth, \"Maximize_Expected_Wealth\"\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "45e18cea-4ef1-48a1-8bbc-4b2f95dbf85e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Constraints\n",
    "\n",
    "\n",
    "# Limits the number of animals the farm can hold.\n",
    "model += Sc + Xc - Yc <= 80, \"Max_Cows\"\n",
    "model += Sh + Xh - Yh <= 2000, \"Max_Hens\"\n",
    "\n",
    "# Total land constraint, also accounting for land used by cows.\n",
    "model += Ac + Aw + Ar + 2 * Xc + Sc - Yc + Sh - Yh <= 850, \"Land_Constraint\"\n",
    "\n",
    "\n",
    "# Labour constraints (simplified Frost & Dry max of 7100 hours)\n",
    "model += 3*(Sc + Xc) + 0.05*(Sh + Xh) + 2.0*Ac + 2.0*Aw + 3.0*Ar <= 7100, \"Labour_Constraint\"\n",
    "\n",
    "# Feed constraints\n",
    "# Ensures animals have enough feed, via stored or purchased crops.\n",
    "model += Scorn >= (Sc + Xc - Yc) * 1, \"Feed_Corn\"\n",
    "model += Swheat >= (Sh + Xh - Yh) * 0.04, \"Feed_Wheat\"\n",
    "\n",
    "\n",
    "# Yield constraints (in tons per acre)\n",
    "model += Zcorn + Scorn <= 3.0 * Ac, \"Corn_Yield\"\n",
    "model += Zwheat + Swheat <= 2.0 * Aw, \"Wheat_Yield\"\n",
    "model += Zrape <= 3.2 * Ar, \"Rapeseed_Yield\"\n",
    "\n",
    "# Financial feasibility\n",
    "model += total_cost <= usable_capital + revenue, \"Financial_Constraint\"\n",
    "model += usable_capital + revenue - total_cost >= 0, \"NonNegative_Cash\"\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "7e858aed-d30d-4754-b4af-dffc0ceb6576",
   "metadata": {},
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     "text": [
      "Welcome to the CBC MILP Solver \n",
      "Version: 2.10.3 \n",
      "Build Date: Dec 15 2019 \n",
      "\n",
      "command line - /opt/anaconda3/lib/python3.12/site-packages/pulp/apis/../solverdir/cbc/osx/i64/cbc /var/folders/km/kqnqtg953b76gw0hctk94d1m0000gn/T/baadbb91d5da4f9d8cd2e487394ba645-pulp.mps -max -timeMode elapsed -branch -printingOptions all -solution /var/folders/km/kqnqtg953b76gw0hctk94d1m0000gn/T/baadbb91d5da4f9d8cd2e487394ba645-pulp.sol (default strategy 1)\n",
      "At line 2 NAME          MODEL\n",
      "At line 3 ROWS\n",
      "At line 16 COLUMNS\n",
      "At line 99 RHS\n",
      "At line 111 BOUNDS\n",
      "At line 116 ENDATA\n",
      "Problem MODEL has 11 rows, 15 columns and 59 elements\n",
      "Coin0008I MODEL read with 0 errors\n",
      "Option for timeMode changed from cpu to elapsed\n",
      "Continuous objective value is 1.14591e+06 - 0.00 seconds\n",
      "Cgl0004I processed model has 4 rows, 8 columns (4 integer (0 of which binary)) and 19 elements\n",
      "Cbc0012I Integer solution of -1145912.3 found by DiveCoefficient after 0 iterations and 0 nodes (0.03 seconds)\n",
      "Cbc0038I Full problem 4 rows 8 columns, reduced to 2 rows 4 columns\n",
      "Cbc0001I Search completed - best objective -1145912.28, took 0 iterations and 0 nodes (0.03 seconds)\n",
      "Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost\n",
      "Cuts at root node changed objective from -1.14591e+06 to -1.14591e+06\n",
      "Probing was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
      "Gomory was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
      "Knapsack was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
      "Clique was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
      "MixedIntegerRounding2 was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
      "FlowCover was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
      "TwoMirCuts was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
      "ZeroHalf was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
      "\n",
      "Result - Optimal solution found\n",
      "\n",
      "Objective value:                1145912.28000000\n",
      "Enumerated nodes:               0\n",
      "Total iterations:               0\n",
      "Time (CPU seconds):             0.00\n",
      "Time (Wallclock seconds):       0.03\n",
      "\n",
      "Option for printingOptions changed from normal to all\n",
      "Total time (CPU seconds):       0.00   (Wallclock seconds):       0.04\n",
      "\n",
      "Status: Optimal\n",
      "2025_Buy_Cows: 0.00\n",
      "2025_Buy_Hens: 1600.00\n",
      "2025_Purchase_Corn: 0.00\n",
      "2025_Purchase_Wheat: 0.00\n",
      "2025_Sell_Corn: 0.00\n",
      "2025_Sell_Cows: 0.00\n",
      "2025_Sell_Hens: 400.00\n",
      "2025_Sell_Wheat: 0.00\n",
      "2025_Store_Corn: 30.00\n",
      "2025_Store_Wheat: 64.00\n",
      "2026_Sell_Rapeseed: 2489.60\n",
      "Acres_Corn: 10.00\n",
      "Acres_Rapeseed: 778.00\n",
      "Acres_Wheat: 32.00\n",
      "Capital_Invested: 0.00\n",
      "\n",
      "Max Expected Wealth: £1,288,507.28\n"
     ]
    }
   ],
   "source": [
    "# Solve the model\n",
    "model.solve()\n",
    "\n",
    "# Print results\n",
    "print(f\"Status: {pulp.LpStatus[model.status]}\")\n",
    "for variable in model.variables():\n",
    "    print(f\"{variable.name}: {variable.varValue:.2f}\")\n",
    "print(f\"\\nMax Expected Wealth: £{pulp.value(model.objective):,.2f}\")"
   ]
  }
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