Resource Allocation Case 1.ipynb

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      "Welcome to the CBC MILP Solver \n",
      "Version: 2.10.3 \n",
      "Build Date: Dec 15 2019 \n",
      "\n",
      "command line - /Users/matiasgroblunecke/opt/anaconda3/lib/python3.9/site-packages/pulp/solverdir/cbc/osx/64/cbc /var/folders/y5/7v3j89sd4ps24p3x50lkvwf80000gn/T/ee65981cf18840bc942660302b38c843-pulp.mps timeMode elapsed branch printingOptions all solution /var/folders/y5/7v3j89sd4ps24p3x50lkvwf80000gn/T/ee65981cf18840bc942660302b38c843-pulp.sol (default strategy 1)\n",
      "At line 2 NAME          MODEL\n",
      "At line 3 ROWS\n",
      "At line 12 COLUMNS\n",
      "At line 73 RHS\n",
      "At line 81 BOUNDS\n",
      "At line 94 ENDATA\n",
      "Problem MODEL has 7 rows, 12 columns and 24 elements\n",
      "Coin0008I MODEL read with 0 errors\n",
      "Option for timeMode changed from cpu to elapsed\n",
      "Continuous objective value is 146500 - 0.00 seconds\n",
      "Cgl0004I processed model has 7 rows, 12 columns (12 integer (0 of which binary)) and 24 elements\n",
      "Cutoff increment increased from 1e-05 to 4.9999\n",
      "Cbc0012I Integer solution of 146500 found by DiveCoefficient after 0 iterations and 0 nodes (0.02 seconds)\n",
      "Cbc0001I Search completed - best objective 146500, took 0 iterations and 0 nodes (0.02 seconds)\n",
      "Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost\n",
      "Cuts at root node changed objective from 146500 to 146500\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:                146500.00000000\n",
      "Enumerated nodes:               0\n",
      "Total iterations:               0\n",
      "Time (CPU seconds):             0.00\n",
      "Time (Wallclock seconds):       0.02\n",
      "\n",
      "Option for printingOptions changed from normal to all\n",
      "Total time (CPU seconds):       0.00   (Wallclock seconds):       0.03\n",
      "\n",
      "Result - Optimal\n",
      "Objective value: 146500.0\n",
      "Ship 400.0 motors from Antwerp to Cologne\n",
      "Ship 100.0 motors from Antwerp to Liège\n",
      "Ship 100.0 motors from Antwerp to Nancy\n",
      "Ship 800.0 motors from Le Havre to Nancy\n",
      "Ship 100.0 motors from Rotterdam to Liège\n",
      "Ship 500.0 motors from Rotterdam to Tilburg\n",
      "Lowest unit shipping cost: 73.25\n"
     ]
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   "source": [
    "import pulp\n",
    "\n",
    "# Define the assembly plants, harbors, and their demands and supplies\n",
    "assembly_plants = [\"Cologne\", \"Liège\", \"Nancy\", \"Tilburg\"]\n",
    "harbors = [\"Antwerp\", \"Le Havre\", \"Rotterdam\"]\n",
    "\n",
    "demands = {\n",
    "    \"Cologne\": 400,\n",
    "    \"Liège\": 200,\n",
    "    \"Nancy\": 900,\n",
    "    \"Tilburg\": 500\n",
    "}\n",
    "\n",
    "supplies = {\n",
    "    \"Antwerp\": 600,\n",
    "    \"Le Havre\": 800,\n",
    "    \"Rotterdam\": 600\n",
    "}\n",
    "\n",
    "# Define the transportation costs as a nested dictionary\n",
    "transportation_costs = {\n",
    "    \"Antwerp\": {\"Cologne\": 100, \"Liège\": 60, \"Nancy\": 90, \"Tilburg\": 40},\n",
    "    \"Le Havre\": {\"Cologne\": 165, \"Liège\": 100, \"Nancy\": 80, \"Tilburg\": 110},\n",
    "    \"Rotterdam\": {\"Cologne\": 120, \"Liège\": 75, \"Nancy\": 130, \"Tilburg\": 40}\n",
    "}\n",
    "\n",
    "# Create a linear programming problem\n",
    "prob = pulp.LpProblem(\"Shipping_Cost_Minimization\", pulp.LpMinimize)\n",
    "\n",
    "# Create a variable for each route from a harbor to an assembly plant\n",
    "routes = [(harbor, plant) for harbor in harbors for plant in assembly_plants]\n",
    "route_vars = pulp.LpVariable.dicts(\"Route\", (harbors, assembly_plants), lowBound=0, cat=pulp.LpInteger)\n",
    "\n",
    "# Define the objective function (total shipping cost)\n",
    "prob += pulp.lpSum(route_vars[harbor][plant] * transportation_costs[harbor][plant] for harbor, plant in routes)\n",
    "\n",
    "# Define supply constraints (motors available at each harbor)\n",
    "for harbor in harbors:\n",
    "    prob += pulp.lpSum(route_vars[harbor][plant] for plant in assembly_plants) <= supplies[harbor]\n",
    "\n",
    "# Define demand constraints (motors required at each assembly plant)\n",
    "for plant in assembly_plants:\n",
    "    prob += pulp.lpSum(route_vars[harbor][plant] for harbor in harbors) >= demands[plant]\n",
    "\n",
    "# Solve the problem\n",
    "prob.solve()\n",
    "\n",
    "# Print the results\n",
    "print(\"Result -\", pulp.LpStatus[prob.status])\n",
    "print(\"Objective value:\", pulp.value(prob.objective))\n",
    "for harbor, plant in routes:\n",
    "    if route_vars[harbor][plant].varValue > 0:\n",
    "        print(f\"Ship {route_vars[harbor][plant].varValue} motors from {harbor} to {plant}\")\n",
    "\n",
    "# Calculate and print the lowest unit shipping cost\n",
    "lowest_cost = pulp.value(prob.objective) / sum(demands.values())\n",
    "print(f\"Lowest unit shipping cost: {lowest_cost}\")\n"
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    "The optimal solution for Autopower's motor transportation problem is as follows:\n",
    "\n",
    "Objective value: 146500.0\n",
    "\n",
    "Here are the transportation quantities from each harbor to each assembly plant:\n",
    "\n",
    "Ship 400.0 motors from Antwerp to Cologne\n",
    "Ship 100.0 motors from Antwerp to Liège\n",
    "Ship 100.0 motors from Antwerp to Nancy\n",
    "Ship 800.0 motors from Le Havre to Nancy\n",
    "Ship 100.0 motors from Rotterdam to Liège\n",
    "Ship 500.0 motors from Rotterdam to Tilburg\n",
    "The lowest unit shipping cost is 73.25.\n",
    "\n",
    "This solution minimizes the total cost of transporting motors from the harbors to the assembly plants, resulting in a total cost of 146500.0 units."
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