{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "963d23cf-65a6-4ca4-ba2d-d604ec9be655",
   "metadata": {
    "id": "x1bd_c_mjCvJ"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Tue Dec 14 2021\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.9.9\n",
      "IPython version      : 7.27.0\n",
      "\n",
      "gurobipy: 9.5.0\n",
      "\n",
      "Watermark: 2.2.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import gurobipy as gp\n",
    "from gurobipy import GRB\n",
    "\n",
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "565f58ec-659d-4b6a-8e4b-e38a9196536e",
   "metadata": {},
   "source": [
    "# Data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b0b42e2-2ed9-48ee-8c6a-0c771c32160b",
   "metadata": {},
   "source": [
    "## Product and cluster sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "92f05341-f63b-441e-b1c7-24f7718e310d",
   "metadata": {},
   "outputs": [],
   "source": [
    "products = ['p1', 'p2']\n",
    "clusters = ['k1', 'k2']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "317ec642-8fdf-4846-8ced-ce23dfb9cc02",
   "metadata": {},
   "source": [
    "## Expected profit per cluster and product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0fca665c-08b2-4d1b-807a-f8a6f08a6038",
   "metadata": {
    "id": "9Kx_owENjCvK"
   },
   "outputs": [],
   "source": [
    "cp, expected_profit = gp.multidict({\n",
    "    ('k1', 'p1'): 2000,\n",
    "    ('k1', 'p2'): 1000,\n",
    "    ('k2', 'p1'): 3000,\n",
    "    ('k2', 'p2'): 2000\n",
    "})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64aa442d-f8b3-4614-a06b-8a2d916f6a93",
   "metadata": {},
   "source": [
    "## Expected cost per cluster and product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "dec6550d-a7f7-4ea1-a01a-72b65866ec3d",
   "metadata": {
    "id": "3NejHPuKjCvL"
   },
   "outputs": [],
   "source": [
    "cp, expected_cost = gp.multidict({\n",
    "    ('k1', 'p1'): 200,\n",
    "    ('k1', 'p2'): 100,\n",
    "    ('k2', 'p1'): 300,\n",
    "    ('k2', 'p2'): 200\n",
    "})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21317d67-1ddc-4b65-bd49-af77331c0bd8",
   "metadata": {},
   "source": [
    "## Number of customers in each cluster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "dee8eec0-5a35-4357-8c05-d0a7093034c0",
   "metadata": {
    "id": "wuFfsCCmjCvM"
   },
   "outputs": [],
   "source": [
    "clusters, number_customers = gp.multidict({\n",
    "    ('k1'): 5,\n",
    "    ('k2'): 5\n",
    "})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d933758-7d04-469f-95ca-ef6c63b60d44",
   "metadata": {},
   "source": [
    "## Minimum number offers for each product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "dd4face1-baf8-4bae-a6c5-9773b4389bc1",
   "metadata": {
    "id": "IJa_hZumjCvM"
   },
   "outputs": [],
   "source": [
    "products, min_offers = gp.multidict({\n",
    "    ('p1'): 2,\n",
    "    ('p2'): 2\n",
    "})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a33ead68-48e4-4fe1-a555-042739cdff45",
   "metadata": {
    "id": "AygTRhcVjCvN"
   },
   "source": [
    "## Hurdle-rate is twenty percent and budget available for the marketing campaign\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e978b251-6f20-4fa9-a6da-7d944ab7906a",
   "metadata": {
    "id": "5KpWIPUcjCvN"
   },
   "outputs": [],
   "source": [
    "# Define the corporate hurdle-rate\n",
    "R = 0.20\n",
    "\n",
    "# Define the value of budget available for campaign\n",
    "budget = 200 "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce4bf59f-8960-4591-bcad-f55d6bc5db3a",
   "metadata": {
    "id": "st89srb0jCvN"
   },
   "source": [
    "# Model Formulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "fd522d41-e405-477a-8be0-b537c3f7bc96",
   "metadata": {
    "id": "mcy9dcrrjCvN",
    "outputId": "85228153-dacb-4187-fab2-2b366ec17c6d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Restricted license - for non-production use only - expires 2023-10-25\n"
     ]
    }
   ],
   "source": [
    "# Declare and initialize model\n",
    "mt = gp.Model('Tactical')\n",
    "\n",
    "# Define the decisions variables\n",
    "\n",
    "# Allocation of product offers to customers in clusters.\n",
    "y = mt.addVars(cp, name=\"allocate\")\n",
    "\n",
    "# Budget correction\n",
    "z = mt.addVar(name=\"budget_correction\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25581dda-bda2-4e32-9ed0-55c016ebf50b",
   "metadata": {},
   "source": [
    "## Constraints"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5dcfef8-70c6-4117-90a3-6075fa8d37e8",
   "metadata": {
    "id": "1jwAnJ9ujCvO",
    "tags": []
   },
   "source": [
    "### Max number of offers for each cluster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1af996f6-5dc7-44fe-a828-535bc30afc5e",
   "metadata": {
    "id": "nPmOsmDjjCvP"
   },
   "outputs": [],
   "source": [
    "max_offers_c = mt.addConstrs((y.sum(k,'*') <= number_customers[k]  for k in clusters), name='max_offers')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5b2d7a4-6e14-4f5f-b892-0b05ee894cdd",
   "metadata": {
    "id": "gAR2Kx9HjCvP"
   },
   "source": [
    "### Max Budget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "cdcb1a6e-910c-4dba-aa9a-646969170b30",
   "metadata": {
    "id": "qcqhHVdCjCvP"
   },
   "outputs": [],
   "source": [
    "budget_c = mt.addConstr((y.prod(expected_cost) - z <= budget), name='budget')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5785873-b951-4519-8c56-d716217dbd5d",
   "metadata": {
    "id": "Jw_8f7BHjCvP"
   },
   "source": [
    "### Minimum number of offers of each product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ea614b40-1028-4621-b957-0bb50d623a0d",
   "metadata": {
    "id": "Rsv_JEakjCvQ"
   },
   "outputs": [],
   "source": [
    "min_offers_c = mt.addConstrs( (y.sum('*',j) >= min_offers[j] for j in products), name='min_offers')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b020a6a-82d4-4dfa-b27e-d6427af66742",
   "metadata": {
    "id": "Nyb8VkuRjCvQ"
   },
   "source": [
    "### Minimum ROI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ebada7d8-fa54-47be-b41a-b2c25067cb55",
   "metadata": {
    "id": "CWKyiLfOjCvQ"
   },
   "outputs": [],
   "source": [
    "roi_c = mt.addConstr((y.prod(expected_profit) - (1 + R)*y.prod(expected_cost) >= 0), name='roi')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc2b49b7-f526-4ed1-a354-e3102f6bfc05",
   "metadata": {
    "id": "7ZyNh-qRjCvR"
   },
   "source": [
    "## Objective Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ef41e858-464e-4a05-b12c-f29b299c7e38",
   "metadata": {
    "id": "WLsgMEHajCvR"
   },
   "outputs": [],
   "source": [
    "# Maximize total expected profit\n",
    "\n",
    "# The value of 𝑀 should be higher than any of the expected profits to ensure \n",
    "# that the budget is increased only when the model is infeasible if this parameter \n",
    "# is not increased.\n",
    "M = 10000\n",
    "\n",
    "mt.setObjective(y.prod(expected_profit) -M*z, GRB.MAXIMIZE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a85c6838-5a53-4776-b7e4-cb6d7bfdc2fa",
   "metadata": {
    "id": "5dY26d5XjCvR"
   },
   "outputs": [],
   "source": [
    "# Verify model formulation\n",
    "\n",
    "mt.write('tactical.lp')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13b4f5de-0c0d-47e1-967f-499cb6c37509",
   "metadata": {},
   "source": [
    "# Optimize the Campaign"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e2a92f7d-7958-4d96-9a39-8f78fc05768b",
   "metadata": {
    "id": "d59476ZvjCvS",
    "outputId": "3300291b-e8cd-4596-c859-fcd4ae583110"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "Optimize a model with 6 rows, 5 columns and 17 nonzeros\n",
      "Model fingerprint: 0x168ba328\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 3e+03]\n",
      "  Objective range  [1e+03, 1e+04]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [2e+00, 2e+02]\n",
      "Presolve removed 1 rows and 0 columns\n",
      "Presolve time: 0.09s\n",
      "Presolved: 5 rows, 5 columns, 13 nonzeros\n",
      "\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    2.5000000e+04   8.787500e+01   0.000000e+00      0s\n",
      "       4   -3.9940000e+06   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 4 iterations and 0.24 seconds (0.00 work units)\n",
      "Optimal objective -3.994000000e+06\n"
     ]
    }
   ],
   "source": [
    "mt.optimize()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "893bd50c-bf2e-4a9e-bb9c-f5d4ed66ba09",
   "metadata": {},
   "source": [
    "## Allocation of Product Offers to Clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "8e4aad53-11e0-4697-aaf7-37a74dfc09d3",
   "metadata": {
    "id": "thxKOnz-jCvT",
    "outputId": "c45bc8f2-1036-4137-825e-88b610fc6551"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The number of customers in cluster k1 that gets an offer of product p1 is: 2.0\n",
      "The number of customers in cluster k1 that gets an offer of product p2 is: 2.0\n",
      "The number of customers in cluster k2 that gets an offer of product p1 is: 0.0\n",
      "The number of customers in cluster k2 that gets an offer of product p2 is: 0.0\n"
     ]
    }
   ],
   "source": [
    "total_expected_profit = 0\n",
    "total_expected_cost = 0\n",
    "\n",
    "for k,p in cp:\n",
    "#     if y[k,p].x > 1e-6:\n",
    "    print(f\"The number of customers in cluster {k} that gets an offer of product {p} is: {y[k,p].x}\")\n",
    "    total_expected_profit += expected_profit[k,p]*y[k,p].x\n",
    "    total_expected_cost += expected_cost[k,p]*y[k,p].x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "515e3be9-9a38-4491-94da-bf6428222ebd",
   "metadata": {},
   "source": [
    "## Financial Reports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "bc09d04c-ca6a-4c80-b323-9bc0328397e4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The increase correction in the campaign budget is $400.00.\n",
      "Optimal total expected profit is $6,000.00.\n",
      "Optimal total expected cost is $600.00 with a budget of $200.00 and an extra amount of $400.00.\n",
      "Optimal ROI is 1000.0% with a minimum ROI of  120.0%.\n"
     ]
    }
   ],
   "source": [
    "increased_budget = '${:,.2f}'.format(z.x)\n",
    "optimal_ROI = round(100*total_expected_profit/total_expected_cost,2)\n",
    "min_ROI = round(100*(1+R),2)\n",
    "\n",
    "money_expected_profit = '${:,.2f}'.format(total_expected_profit)\n",
    "money_expected_cost = '${:,.2f}'.format(total_expected_cost)\n",
    "money_budget = '${:,.2f}'.format(budget)\n",
    "\n",
    "print(f\"The increase correction in the campaign budget is {increased_budget}.\")\n",
    "print(f\"Optimal total expected profit is {money_expected_profit}.\")\n",
    "print(f\"Optimal total expected cost is {money_expected_cost} with a budget of {money_budget} and an extra amount of {increased_budget}.\")\n",
    "print(f\"Optimal ROI is {optimal_ROI}% with a minimum ROI of  {min_ROI}%.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "480d8ce9-cfd5-44e2-aa74-a2edbeae5356",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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