OptModel2_buys.ipynb

{
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   "id": "0547bf5a-860f-4d67-9cb2-73622e1fb13e",
   "metadata": {},
   "outputs": [],
   "source": [
    "using JuMP, CSV, DataFrames, Gurobi, Interpolations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "de160448-7bf3-4d7a-9b82-cb8d54b190ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Read the test and train CSV files\n",
    "data_targeted = CSV.File(\"/Users/sanyachauhan/Downloads/Data_Targeted.csv\") |> DataFrame;\n",
    "data_email = CSV.File(\"/Users/sanyachauhan/Downloads/Data_Emails.csv\") |> DataFrame;\n",
    "data_print = CSV.File(\"/Users/sanyachauhan/Downloads/Data_Print.csv\") |> DataFrame;\n",
    "data_influencer = CSV.File(\"/Users/sanyachauhan/Downloads/Data_Influencers.csv\") |> DataFrame;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f199de45-5363-48fe-803a-97dd524778bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Budget levels\n",
    "B = [1000.0, 1500.0, 2000.0];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5e2eeb22-b7b6-4348-95b9-5e6f4cac6888",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creating linear interpolation functions for each marketing option\n",
    "interp_targeted = LinearInterpolation(data_targeted[!, :Cost], data_targeted[!, :Buys]);\n",
    "interp_email = LinearInterpolation(data_email[!, :Cost], data_email[!, :Buys]);\n",
    "interp_print = LinearInterpolation(data_print[!, :Cost], data_print[!, :Buys]);\n",
    "interp_influencers = LinearInterpolation(data_influencer[!, :Cost], data_influencer[!, :Buys]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5fba34bb-e63c-4b02-8486-d54d2fcdab67",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-08-31\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 21 rows, 16 columns and 44 nonzeros\n",
      "Model fingerprint: 0x36fcccdc\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [1e+00, 7e+00]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 1e+03]\n",
      "Presolve removed 20 rows and 9 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 1 rows, 7 columns, 7 nonzeros\n",
      "\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    7.0000000e+03   8.125000e+01   0.000000e+00      0s\n",
      "       1    5.8500000e+03   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 1 iterations and 0.00 seconds (0.00 work units)\n",
      "Optimal objective  5.850000000e+03\n",
      "\n",
      "User-callback calls 67, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = Budget : investment_targeted + investment_email + investment_print + investment_influencers ≤ 1000\n",
      "Targeted Online Advertising: $500.0\n",
      "Email Marketing: $0.0\n",
      "Print Media: $0.0\n",
      "Influencer Marketing: $500.0\n",
      "Total Buys: 5850.0\n",
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-08-31\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 21 rows, 16 columns and 44 nonzeros\n",
      "Model fingerprint: 0x76c4ace0\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [1e+00, 7e+00]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 2e+03]\n",
      "Presolve removed 20 rows and 9 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 1 rows, 7 columns, 7 nonzeros\n",
      "\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    1.0500000e+04   1.437500e+02   0.000000e+00      0s\n",
      "       1    8.1300000e+03   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 1 iterations and 0.00 seconds (0.00 work units)\n",
      "Optimal objective  8.130000000e+03\n",
      "\n",
      "User-callback calls 67, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = Budget : investment_targeted + investment_email + investment_print + investment_influencers ≤ 1500\n",
      "Targeted Online Advertising: $900.0\n",
      "Email Marketing: $0.0\n",
      "Print Media: $0.0\n",
      "Influencer Marketing: $600.0\n",
      "Total Buys: 8130.0\n",
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-08-31\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 21 rows, 16 columns and 44 nonzeros\n",
      "Model fingerprint: 0xf3e3598f\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [1e+00, 7e+00]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 2e+03]\n",
      "Presolve removed 20 rows and 9 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 1 rows, 7 columns, 7 nonzeros\n",
      "\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    1.4000000e+04   2.062500e+02   0.000000e+00      0s\n",
      "       1    9.9800000e+03   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 1 iterations and 0.00 seconds (0.00 work units)\n",
      "Optimal objective  9.980000000e+03\n",
      "\n",
      "User-callback calls 67, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = Budget : investment_targeted + investment_email + investment_print + investment_influencers ≤ 2000\n",
      "Targeted Online Advertising: $950.0\n",
      "Email Marketing: $300.0\n",
      "Print Media: $150.0\n",
      "Influencer Marketing: $600.0\n",
      "Total Buys: 9980.0\n"
     ]
    }
   ],
   "source": [
    "for Budget in B\n",
    "    # Optimization model\n",
    "    model = Model(Gurobi.Optimizer)\n",
    "    \n",
    "    # Decision variables for investments\n",
    "    @variable(model, investment_targeted >= 0)\n",
    "    @variable(model, investment_email >= 0)\n",
    "    @variable(model, investment_print >= 0)\n",
    "    @variable(model, investment_influencers >= 0)\n",
    "    \n",
    "    # Example for Targeted Online Advertising\n",
    "    @variable(model, targeted_segments[1:3] >= 0)\n",
    "    breakpoints_targeted = [0, 40, 310, 990] # Example breakpoints\n",
    "    slopes_targeted = [3, 4, 5] # Example slopes\n",
    "    @constraint(model, investment_targeted == sum(targeted_segments))\n",
    "    @constraint(model, sum(targeted_segments[i] for i in 1:3) <= breakpoints_targeted[end])\n",
    "    for i in 1:3\n",
    "        @constraint(model, targeted_segments[i] <= breakpoints_targeted[i+1] - breakpoints_targeted[i])\n",
    "    end\n",
    "    \n",
    "    # Example for Email Marketing\n",
    "    @variable(model, email_segments[1:3] >= 0)\n",
    "    breakpoints_email = [0, 50, 200, 500] # Example breakpoints\n",
    "    slopes_email = [2, 3, 4] # Example slopes\n",
    "    @constraint(model, investment_email == sum(email_segments))\n",
    "    @constraint(model, sum(email_segments[i] for i in 1:3) <= breakpoints_email[end])\n",
    "    for i in 1:3\n",
    "        @constraint(model, email_segments[i] <= breakpoints_email[i+1] - breakpoints_email[i])\n",
    "    end\n",
    "    \n",
    "    # Example for Print Media\n",
    "    @variable(model, print_segments[1:3] >= 0)\n",
    "    breakpoints_print = [0, 100, 300, 700] # Example breakpoints\n",
    "    slopes_print = [1, 2, 3] # Example slopes\n",
    "    @constraint(model, investment_print == sum(print_segments))\n",
    "    @constraint(model, sum(print_segments[i] for i in 1:3) <= breakpoints_print[end])\n",
    "    for i in 1:3\n",
    "        @constraint(model, print_segments[i] <= breakpoints_print[i+1] - breakpoints_print[i])\n",
    "    end\n",
    "    \n",
    "    # Example for Influencer Marketing\n",
    "    @variable(model, influencers_segments[1:3] >= 0)\n",
    "    breakpoints_influencers = [0, 100, 250, 600] # Example breakpoints\n",
    "    slopes_influencers = [5, 6, 7] # Example slopes\n",
    "    @constraint(model, investment_influencers == sum(influencers_segments))\n",
    "    @constraint(model, sum(influencers_segments[i] for i in 1:3) <= breakpoints_influencers[end])\n",
    "    for i in 1:3\n",
    "        @constraint(model, influencers_segments[i] <= breakpoints_influencers[i+1] - breakpoints_influencers[i])\n",
    "    end\n",
    "\n",
    "\n",
    "    # Objective: Maximize buys\n",
    "    @objective(model, Max, sum(slopes_targeted[i] * targeted_segments[i] for i in eachindex(slopes_targeted)) + \n",
    "                  sum(slopes_email[i] * email_segments[i] for i in eachindex(slopes_email)) +\n",
    "                  sum(slopes_print[i] * print_segments[i] for i in eachindex(slopes_print)) +\n",
    "                  sum(slopes_influencers[i] * influencers_segments[i] for i in eachindex(slopes_influencers)))\n",
    "\n",
    "    # Budget constraint\n",
    "    @constraint(model, Budget, investment_targeted + investment_email +\n",
    "                       investment_print + investment_influencers <= Budget)\n",
    "\n",
    "    # Solve the model\n",
    "    optimize!(model)\n",
    "\n",
    "    # Save the model in LP format with a dynamic name\n",
    "    model_filename = \"model2_\" * string(Budget) * \".lp\"\n",
    "    write_to_file(model, model_filename)\n",
    "\n",
    "    # Results\n",
    "    println(\"Optimal Investments with Budget = \", Budget)\n",
    "    println(\"Targeted Online Advertising: \\$\", value(investment_targeted))\n",
    "    println(\"Email Marketing: \\$\", value(investment_email))\n",
    "    println(\"Print Media: \\$\", value(investment_print))\n",
    "    println(\"Influencer Marketing: \\$\", value(investment_influencers))\n",
    "    println(\"Total Buys: \", objective_value(model))\n",
    "end"
   ]
  }
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