Market Sharing.ipynb

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    "## Problem Description\n",
    "\n",
    "- 公司----给零售商提供oil和spirit\n",
    "    - 有两个部门$D_1$和$D_2$\n",
    "    - $D_1$和$D_2$控制市场的比例为4:6(要求的)\n",
    "    \n",
    "将D划分为$D_1$(40%)和$D_2$(60%)，包括如下几个部分:\n",
    "\n",
    "    1. 交货点总数比例\n",
    "    2. 控制spirit market的比例\n",
    "    3. 每个region(1,2,3)中oil market的控制比例\n",
    "    4. 每个分组(A、B)中包含的零售商比例\n",
    "    \n",
    "划分的时候没有要求严格按4:6的比例，可以灵活点(比如有5%的偏差)，目标是划分的比例尽量接近4:6的比例.\n",
    "\n",
    "## Model Formulation\n",
    "\n",
    "### 集合\n",
    "$\\mathcal{R} := \\{retailer_1,...,retailer_n\\}$\n",
    "\n",
    "### Parameters\n",
    "1. 零售商$r$的交货点数: $\\text{deliveryPoints}_{r} \\in \\mathbb{N}^+$ \n",
    "2. 零售商$r$的Spirit market : $\\text{spiritMarket}_{r} \\in \\mathbb{R}^+$ \n",
    "3. 零售商$r$在$region_i$中的Oil market : $\\text{oilMarket}_{r,i} \\in \\mathbb{R}^+$ \n",
    "4. 零售商$r$是否在分组$j$中 : $\\text{retailer}_{j,r} \\in \\{0,1\\}$ \n",
    "5. 交货点数的百分比为p : $\\text{deliveryPoints_p} \\in \\mathbb{R}^+$ \n",
    "6. spirit Market的百分比为p : $\\text{spiritMarket_p} \\in \\mathbb{R}^+$ \n",
    "7. oil Market在$region_i$中的百分比为p : $\\text{oilMarket_{i,p}} \\in \\mathbb{R}^+$ \n",
    "8. 零售商在分组$j$中占的百分比为p : $\\text{retailer_{j,p}} \\in \\mathbb{R}^+$\n",
    "\n",
    "\n",
    "### Decision Variables\n",
    "1. $\\text{allocate}_{r} \\in \\{0,1\\}$: 零售商$r$是否属于部门$D_1$(1->属于, 0->不属于(即属于$D_2$))\n",
    "2. $\\text{deliveryPointsPos} \\in \\mathbb{R}^+$: 目标交货点数的正偏差(40%)\n",
    "3. $\\text{deliveryPointsNeg} \\in \\mathbb{R}^+$: 目标交货点数的负偏差(40%)\n",
    "4. $\\text{spiritMarketPos} \\in \\mathbb{R}^+$: 目标spirit market的正偏差(40%)\n",
    "5. $\\text{spiritMarketNeg} \\in \\mathbb{R}^+$: 目标spirit market的负偏差(40%)\n",
    "6. $\\text{oilMarket_{i}Pos} \\in \\mathbb{R}^+$ 目标$region_i$中的Oil market的正偏差(40%)\n",
    "7. $\\text{oilMarket_{i}Neg} \\in \\mathbb{R}^+$ 目标$region_i$中的Oil market的负偏差(40%)\n",
    "8. $\\text{retailer_{j}Pos} \\in \\mathbb{R}^+$: 目标分组$j$中的零售商数量正偏差(40%)\n",
    "9. $\\text{retailer_{j}Neg} \\in \\mathbb{R}^+$: 目标分组$j$中的零售商数量负偏差(40%)\n",
    "\n",
    "\n",
    "\n",
    "### Constraints\n",
    "\n",
    "**Delivery points**: The allocation of retailers at Division 1 satisfies as much as possible forty percent of the delivery points.\n",
    "\n",
    "\\begin{equation}\n",
    "\\sum_{r \\in \\text{Retailers}} \\text{deliveryPoints}_{r}*{\\text{allocate}_{r}} + \\text{deliveryPointsPos} - \\text{deliveryPointsNeg}  = \\text{deliveryPoints40}\n",
    "\\tag{1}\n",
    "\\end{equation}\n",
    "\n",
    "**Spirit Market**: The allocation of retailers at Division 1 satisfies as much as possible forty percent of the spirit market.\n",
    "\n",
    "\\begin{equation}\n",
    "\\sum_{r \\in \\text{Retailers}} \\text{spiritMarket}_{r}*{\\text{allocate}_{r}} + \\text{spiritMarketPos} - \n",
    "\\text{spiritMarketNeg}  = \\text{spiritMarket40}\n",
    "\\end{equation}\n",
    "\n",
    "**Oil market region 1**: The allocation of retailers in region 1 at Division 1 satisfies as much as possible forty percent of the oil market in that region.\n",
    "\n",
    "\\begin{equation}\n",
    "\\sum_{r \\in \\text{Retailers}} \\text{oilMarket1}_{r}*{\\text{allocate}_{r}} + \\text{oilMarket1Pos} - \n",
    "\\text{oilMarket1Neg}  = \\text{oilMarket1_40}\n",
    "\\end{equation}\n",
    "\n",
    "**Oil market region 2**: The allocation of retailers in region 2 at Division 1 satisfies as much as possible forty percent of the oil market in that region.\n",
    "\n",
    "\\begin{equation}\n",
    "\\sum_{r \\in \\text{Retailers}} \\text{oilMarket2}_{r}*{\\text{allocate}_{r}} + \\text{oilMarket2Pos} - \n",
    "\\text{oilMarket2Neg}  = \\text{oilMarket2_40}\n",
    "\\end{equation}\n",
    "\n",
    "**Oil market region 3**: The allocation of retailers in region 3 at Division 1 satisfies as much as possible forty percent of the oil market in that region.\n",
    "\n",
    "\\begin{equation}\n",
    "\\sum_{r \\in \\text{Retailers}} \\text{oilMarket3}_{r}*{\\text{allocate}_{r}} + \\text{oilMarket3Pos} - \n",
    "\\text{oilMarket3Neg}  = \\text{oilMarket3_40}\n",
    "\\end{equation}\n",
    "\n",
    "**Group A**: The allocation of retailers at Division 1 satisfies as much as possible forty percent of the retailers in group A.\n",
    "\n",
    "\\begin{equation}\n",
    "\\sum_{r \\in \\text{Retailers}} \\text{retailerA40}_{r}*{\\text{allocate}_{r}} + \\text{retailerAPos} - \n",
    "\\text{retailerANeg}  = \\text{retailerA40}\n",
    "\\end{equation}\n",
    "\n",
    "**Group B**: The allocation of retailers at Division 1 satisfies as much as possible forty percent of the retailers in group B.\n",
    "\n",
    "\\begin{equation}\n",
    "\\sum_{r \\in \\text{Retailers}} \\text{retailerB40}_{r}*{\\text{allocate}_{r}} + \\text{retailerBPos} - \n",
    "\\text{retailerBNeg}  = \\text{retailerB40}\n",
    "\\end{equation}\n",
    "\n",
    "**Flexibility**: There is flexibility in that any market share may vary by $\\pm$ 5%.\n",
    "\n",
    "$$\n",
    "\\text{deliveryPointsPos} \\leq \\text{deliveryPoints5}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\text{deliveryPointsNeg}  \\leq \\text{deliveryPoints5}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\text{spiritMarketPos} \\leq \\text{spiritMarket5}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\text{spiritMarketNeg}  \\leq \\text{spiritMarket5}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\text{oilMarket1Pos} \\leq \\text{oilMarket1_5}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\text{oilMarket1Neg} \\leq \\text{oilMarket1_5}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\text{oilMarket2Pos} \\leq \\text{oilMarket2_5}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\text{oilMarket2Neg} \\leq \\text{oilMarket2_5}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\text{oilMarket3Pos} \\leq \\text{oilMarket3_5}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\text{oilMarket3Neg} \\leq \\text{oilMarket3_5}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\text{retailerAPos} \\leq \\text{retailerA5}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\text{retailerANeg} \\leq \\text{retailerA5}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\text{retailerBPos} \\leq \\text{retailerB5}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\text{retailerBNeg} \\leq \\text{retailerB5}\n",
    "$$\n",
    "\n",
    "### Objective Function\n",
    "\n",
    "**Minimize deviations**: Minimize the sum of positive and negative deviations.\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{Minimize} \\quad  \\text{deliveryPointsPos} + \\text{deliveryPointsNeg} + \\text{spiritMarketPos} + \\text{spiritMarketNeg} +\n",
    "\\text{oilMarket1Pos} + \\text{oilMarket1Neg}\n",
    "\\end{equation}\n",
    "\n",
    "$$\n",
    "+ \\text{oilMarket2Pos} + \\text{oilMarket2Neg} + \\text{oilMarket3Pos} + \\text{oilMarket3Neg} \n",
    "$$\n",
    "\n",
    "$$\n",
    "+ \\text{retailerAPos} + \\text{retailerANeg} + \\text{retailerBPos} + \\text{retailerBNeg}\n",
    "$$"
   ]
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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from itertools import product\n",
    "import gurobipy as grb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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    "ExecuteTime": {
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    "# Create a dictionary to capture the delivery points and spirit market -in millions of gallons.\n",
    "\n",
    "retailers, deliveryPoints, spiritMarket = grb.multidict({\n",
    "    (1): [11,34],\n",
    "    (2): [47,411],\n",
    "    (3): [44,82],\n",
    "    (4): [25,157],\n",
    "    (5): [10,5],\n",
    "    (6): [26,183],\n",
    "    (7): [26,14],\n",
    "    (8): [54,215],\n",
    "    (9): [18,102],\n",
    "    (10): [51,21],\n",
    "    (11): [20,54],\n",
    "    (12): [105,0],\n",
    "    (13): [7,6],\n",
    "    (14): [16,96],\n",
    "    (15): [34,118],\n",
    "    (16): [100,112],\n",
    "    (17): [50,535],\n",
    "    (18): [21,8],\n",
    "    (19): [11,53],\n",
    "    (20): [19,28],\n",
    "    (21): [14,69],\n",
    "    (22): [10,65],\n",
    "    (23): [11,27]\n",
    "})\n",
    "\n",
    "# Create a dictionary to capture the oil market -in millions of gallons for region 1.\n",
    "\n",
    "retailers1,  oilMarket1 = grb.multidict({\n",
    "    (1): 9,\n",
    "    (2): 13,\n",
    "    (3): 14,\n",
    "    (4): 17,\n",
    "    (5): 18,\n",
    "    (6): 19,\n",
    "    (7): 23,\n",
    "    (8): 21\n",
    "})\n",
    "\n",
    "# Create a dictionary to capture the oil market -in millions of gallons for region 2.\n",
    "\n",
    "retailers2,  oilMarket2 = grb.multidict({\n",
    "    (9): 9,\n",
    "    (10): 11,\n",
    "    (11): 17,\n",
    "    (12): 18,\n",
    "    (13): 18,\n",
    "    (14): 17,\n",
    "    (15): 22,\n",
    "    (16): 24,\n",
    "    (17): 36,\n",
    "    (18): 43\n",
    "})\n",
    "\n",
    "# Create a dictionary to capture the oil market -in millions of gallons for region 3.\n",
    "\n",
    "retailers3,  oilMarket3 = grb.multidict({\n",
    "    (19): 6,\n",
    "    (20): 15,\n",
    "    (21): 15,\n",
    "    (22): 25,\n",
    "    (23): 39\n",
    "})\n",
    "\n",
    "# Create a dictionary to capture retailers in group A.\n",
    "\n",
    "groupA,  retailerA = grb.multidict({\n",
    "    (1): 1,\n",
    "    (2): 1,\n",
    "    (3): 1,\n",
    "    (5): 1,\n",
    "    (6): 1,\n",
    "    (10): 1,\n",
    "    (15): 1,\n",
    "    (20): 1\n",
    "})\n",
    "\n",
    "# Create a dictionary to capture retailers in group B.\n",
    "\n",
    "groupB,  retailerB = grb.multidict({\n",
    "    (4): 1,\n",
    "    (7): 1,\n",
    "    (8): 1,\n",
    "    (9): 1,\n",
    "    (11): 1,\n",
    "    (12): 1,\n",
    "    (13): 1,\n",
    "    (14): 1,\n",
    "    (16): 1,\n",
    "    (17): 1,\n",
    "    (18): 1,\n",
    "    (19): 1,\n",
    "    (21): 1,\n",
    "    (22): 1,\n",
    "    (23): 1\n",
    "})\n",
    "\n",
    "# Forty and five percentages of each goal\n",
    "\n",
    "deliveryPoints40 = 292\n",
    "deliveryPoints5 = 36.5\n",
    "spiritMarket40 = 958\n",
    "spiritMarket5 = 119.75\n",
    "oilMarket1_40 = 53.6\n",
    "oilMarket1_5 = 6.7\n",
    "oilMarket2_40 = 86\n",
    "oilMarket2_5 = 10.75\n",
    "oilMarket3_40 = 40\n",
    "oilMarket3_5 = 5\n",
    "retailerA40 = 3.2\n",
    "retailerA5 = 0.4\n",
    "retailerB40 = 6\n",
    "retailerB5 = 0.75"
   ]
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   "source": [
    "def MarketSharing(retailers, deliveryPoints, spiritMarket,retailers1,  oilMarket1,retailers2,  oilMarket2,\\\n",
    "                 retailers3,  oilMarket3,groupA,  retailerA,groupB,  retailerB,deliveryPoints40,deliveryPoints5,\\\n",
    "                 spiritMarket40,spiritMarket5,oilMarket1_40,oilMarket1_5,oilMarket2_40,oilMarket2_5,oilMarket3_40,\\\n",
    "                  oilMarket3_5,retailerA40,retailerA5,retailerB40,retailerB5):\n",
    "    model = grb.Model('MarketSharing')\n",
    "    # 定义变量\n",
    "    allocate = model.addVars(retailers, vtype=grb.GRB.BINARY, name=\"allocate\")\n",
    "    deliveryPointsPos = model.addVar(ub= deliveryPoints5, name='deliveryPointsPos')\n",
    "    deliveryPointsNeg = model.addVar(ub= deliveryPoints5, name='deliveryPointsNeg')\n",
    "    spiritMarketPos = model.addVar(ub=spiritMarket5, name='spiritMarketPos')\n",
    "    spiritMarketNeg = model.addVar(ub=spiritMarket5, name='spiritMarketNeg')\n",
    "    oilMarket1Pos = model.addVar(ub=oilMarket1_5, name='oilMarket1Pos')\n",
    "    oilMarket1Neg = model.addVar(ub=oilMarket1_5, name='oilMarket1Neg')\n",
    "    oilMarket2Pos = model.addVar(ub=oilMarket2_5, name='oilMarket2Pos')\n",
    "    oilMarket2Neg = model.addVar(ub=oilMarket2_5, name='oilMarket2Neg')\n",
    "    oilMarket3Pos = model.addVar(ub=oilMarket3_5, name='oilMarket3Pos')\n",
    "    oilMarket3Neg = model.addVar(ub=oilMarket3_5, name='oilMarket3Neg')\n",
    "    retailerAPos  = model.addVar(ub=retailerA5, name='retailerAPos')\n",
    "    retailerANeg  = model.addVar(ub=retailerA5, name='retailerANeg')\n",
    "    retailerBPos  = model.addVar(ub=retailerB5, name='retailerBPos')\n",
    "    retailerBNeg  = model.addVar(ub=retailerB5, name='retailerBNeg')\n",
    "    # 定义目标函数\n",
    "    obj = deliveryPointsPos + deliveryPointsNeg+ spiritMarketPos + spiritMarketNeg + oilMarket1Pos + oilMarket1Neg + oilMarket2Pos + oilMarket2Neg + oilMarket3Pos + oilMarket3Neg + retailerAPos + retailerANeg + retailerBPos + retailerBNeg \n",
    "    model.setObjective(obj)\n",
    "    # 定义约束条件\n",
    "    ## 1\n",
    "    DPConstr = model.addConstr((grb.quicksum(deliveryPoints[r]*allocate[r] for r in retailers) \n",
    "                            + deliveryPointsPos - deliveryPointsNeg == deliveryPoints40), name='DPConstrs')\n",
    "    ## 2\n",
    "    SMConstr = model.addConstr((grb.quicksum(spiritMarket[r]*allocate[r] for r in retailers) \n",
    "                            + spiritMarketPos - spiritMarketNeg == spiritMarket40), name='SMConstr')\n",
    "    ## 3\n",
    "    OM1Constr = model.addConstr((grb.quicksum(oilMarket1[r]*allocate[r] for r in retailers1) \n",
    "                            + oilMarket1Pos - oilMarket1Neg == oilMarket1_40), name='OM1Constr')\n",
    "    ## 4\n",
    "    OM2Constr = model.addConstr((grb.quicksum(oilMarket2[r]*allocate[r] for r in retailers2) \n",
    "                            + oilMarket2Pos - oilMarket2Neg == oilMarket2_40), name='OM2Constr')\n",
    "    ## 5\n",
    "    OM3Constr = model.addConstr((grb.quicksum(oilMarket3[r]*allocate[r] for r in retailers3) \n",
    "                            + oilMarket3Pos - oilMarket3Neg == oilMarket3_40), name='OM3Constr')\n",
    "    ## 6\n",
    "    AConstr = model.addConstr((grb.quicksum(retailerA[r]*allocate[r] for r in groupA) \n",
    "                            + retailerAPos - retailerANeg == retailerA40), name='AConstr')\n",
    "    ## 7\n",
    "    BConstr = model.addConstr((grb.quicksum(retailerB[r]*allocate[r] for r in groupB) \n",
    "                            + retailerBPos - retailerBNeg == retailerB40), name='BConstr')\n",
    "    # 求解\n",
    "    model.optimize()\n",
    "    # 结果分析\n",
    "    print(\"\\n\\n_________________________________________________________________________________\")\n",
    "    print(f\"The optimal allocation of retailers to Division 1 is:\")\n",
    "    print(\"_________________________________________________________________________________\")\n",
    "    for r in retailers:\n",
    "        if(allocate[r].x > 0.5):\n",
    "            print(f\"Retailer{r}\")\n",
    "    print(f\"\\nThe optimal objective function value is {model.objVal}\")\n",
    "    #######################\n",
    "    # Test that the solution is within acceptable ranges.\n",
    "\n",
    "    goal_ranges = pd.DataFrame(columns=[\"Goal\", \"Min_35\", \"Actual\", \"Max_45\"])\n",
    "\n",
    "    count = 0\n",
    "\n",
    "    DeliveryPointsGoal = 0\n",
    "    for r in retailers:\n",
    "        if (allocate[r].x > 0.5):\n",
    "            DeliveryPointsGoal += deliveryPoints[r]*allocate[r].x\n",
    "\n",
    "    goal_ranges = goal_ranges.append({\"Goal\": 'Delivery points', \"Min_35\": round(deliveryPoints40*(0.35/0.40),2), \"Actual\": round(DeliveryPointsGoal,2), \"Max_45\": round(deliveryPoints40*(0.45/0.40),2) }, ignore_index=True) \n",
    "    count += 1\n",
    "\n",
    "    spiritMarketGoal = 0\n",
    "    for r in retailers:\n",
    "        if (allocate[r].x > 0.5):\n",
    "            spiritMarketGoal += spiritMarket[r]*allocate[r].x\n",
    "\n",
    "    goal_ranges = goal_ranges.append({\"Goal\": 'Spirit market', \"Min_35\": round(spiritMarket40*(0.35/0.40),2), \n",
    "                                      \"Actual\": round(spiritMarketGoal,2), \"Max_45\": round(spiritMarket40*(0.45/0.40),2) }, \n",
    "                                     ignore_index=True) \n",
    "    count += 1\n",
    "\n",
    "    oilMarket1Goal = 0\n",
    "    for r in retailers1:\n",
    "        if (allocate[r].x > 0.5):\n",
    "            oilMarket1Goal += oilMarket1[r]*allocate[r].x\n",
    "\n",
    "    goal_ranges = goal_ranges.append({\"Goal\": 'Oil market1', \"Min_35\": round(oilMarket1_40*(0.35/0.40),2), \n",
    "                                      \"Actual\": round(oilMarket1Goal,2), \"Max_45\": round(oilMarket1_40*(0.45/0.40),2) }, \n",
    "                                     ignore_index=True) \n",
    "    count += 1\n",
    "\n",
    "    oilMarket2Goal = 0\n",
    "    for r in retailers2:\n",
    "        if (allocate[r].x > 0.5):\n",
    "            oilMarket2Goal += oilMarket2[r]*allocate[r].x\n",
    "    #\n",
    "    goal_ranges = goal_ranges.append({\"Goal\": 'Oil market2', \"Min_35\": round(oilMarket2_40*(0.35/0.40),2), \n",
    "                                      \"Actual\": round(oilMarket2Goal,2), \"Max_45\": round(oilMarket2_40*(0.45/0.40),2) }, \n",
    "                                     ignore_index=True) \n",
    "    count += 1\n",
    "\n",
    "    oilMarket3Goal = 0\n",
    "    for r in retailers3:\n",
    "        if (allocate[r].x > 0.5):\n",
    "            oilMarket3Goal += oilMarket3[r]*allocate[r].x\n",
    "    #\n",
    "    goal_ranges = goal_ranges.append({\"Goal\": 'Oil market3', \"Min_35\": round(oilMarket3_40*(0.35/0.40),2), \n",
    "                                      \"Actual\": round(oilMarket3Goal,2), \"Max_45\": round(oilMarket3_40*(0.45/0.40),2) }, \n",
    "                                     ignore_index=True) \n",
    "    count += 1\n",
    "\n",
    "    retailerAGoal = 0\n",
    "    for r in groupA:\n",
    "        if (allocate[r].x > 0.5):\n",
    "            retailerAGoal += retailerA[r]*allocate[r].x\n",
    "    #\n",
    "    goal_ranges = goal_ranges.append({\"Goal\": 'Group A', \"Min_35\": round(retailerA40*(0.35/0.40),2), \n",
    "                                      \"Actual\": round(retailerAGoal,2), \"Max_45\": round(retailerA40*(0.45/0.40),2) }, \n",
    "                                     ignore_index=True) \n",
    "    count += 1\n",
    "\n",
    "    retailerBGoal = 0\n",
    "    for r in groupB:\n",
    "        if (allocate[r].x > 0.5):\n",
    "            retailerBGoal += retailerB[r]*allocate[r].x\n",
    "    #\n",
    "    goal_ranges = goal_ranges.append({\"Goal\": 'Group B', \"Min_35\": round(retailerB40*(0.35/0.40),2), \n",
    "                                      \"Actual\": round(retailerBGoal,2), \"Max_45\": round(retailerB40*(0.45/0.40),2) }, \n",
    "                                     ignore_index=True) \n",
    "    count += 1\n",
    "    goal_ranges.index=[''] * count\n",
    "    print(goal_ranges)"
   ]
  },
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    {
     "name": "stdout",
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     "text": [
      "Gurobi Optimizer version 9.1.0 build v9.1.0rc0 (mac64)\n",
      "Thread count: 2 physical cores, 4 logical processors, using up to 4 threads\n",
      "Optimize a model with 7 rows, 37 columns and 105 nonzeros\n",
      "Model fingerprint: 0xa5aab3a9\n",
      "Variable types: 14 continuous, 23 integer (23 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 5e+02]\n",
      "  Objective range  [1e+00, 1e+00]\n",
      "  Bounds range     [4e-01, 1e+02]\n",
      "  RHS range        [3e+00, 1e+03]\n",
      "Presolve time: 0.00s\n",
      "Presolved: 7 rows, 37 columns, 105 nonzeros\n",
      "Variable types: 14 continuous, 23 integer (23 binary)\n",
      "\n",
      "Root relaxation: objective 0.000000e+00, 13 iterations, 0.00 seconds\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0    0.00000    0    7          -    0.00000      -     -    0s\n",
      "H    0     0                     131.6000000    0.00000   100%     -    0s\n",
      "H    0     0                     111.6000000    0.00000   100%     -    0s\n",
      "     0     0    0.20000    0    8  111.60000    0.20000   100%     -    0s\n",
      "H    0     0                      63.8000000    0.20000   100%     -    0s\n",
      "     0     0    0.20000    0   10   63.80000    0.20000   100%     -    0s\n",
      "     0     0    0.20000    0    8   63.80000    0.20000   100%     -    0s\n",
      "     0     0    0.20000    0    9   63.80000    0.20000   100%     -    0s\n",
      "     0     0    0.20000    0    8   63.80000    0.20000   100%     -    0s\n",
      "     0     0    0.20000    0    8   63.80000    0.20000   100%     -    0s\n",
      "     0     0    0.20000    0    8   63.80000    0.20000   100%     -    0s\n",
      "H    0     0                      60.8000000    0.20000   100%     -    0s\n",
      "H    0     0                      49.8000000    0.20000   100%     -    0s\n",
      "H    0     0                      28.8000000    0.20000  99.3%     -    0s\n",
      "     0     2    0.20000    0    8   28.80000    0.20000  99.3%     -    0s\n",
      "H   16    28                      28.6000000    0.20000  99.3%   4.8    0s\n",
      "H   47    33                      16.8000000    0.20000  98.8%   3.6    0s\n",
      "H   87    35                      12.8000000    0.20000  98.4%   3.4    0s\n",
      "H  441    48                       7.6000000    0.54528  92.8%   4.0    0s\n",
      "\n",
      "Cutting planes:\n",
      "  Gomory: 1\n",
      "  Cover: 46\n",
      "  MIR: 20\n",
      "  StrongCG: 1\n",
      "  Inf proof: 25\n",
      "  RLT: 1\n",
      "\n",
      "Explored 560 nodes (2291 simplex iterations) in 0.25 seconds\n",
      "Thread count was 4 (of 4 available processors)\n",
      "\n",
      "Solution count 10: 7.6 12.8 16.8 ... 131.6\n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 7.599999999999e+00, best bound 7.599999999999e+00, gap 0.0000%\n",
      "\n",
      "\n",
      "_________________________________________________________________________________\n",
      "The optimal allocation of retailers to Division 1 is:\n",
      "_________________________________________________________________________________\n",
      "Retailer2\n",
      "Retailer6\n",
      "Retailer7\n",
      "Retailer9\n",
      "Retailer12\n",
      "Retailer13\n",
      "Retailer14\n",
      "Retailer15\n",
      "Retailer23\n",
      "\n",
      "The optimal objective function value is 7.599999999999427\n",
      "             Goal  Min_35  Actual   Max_45\n",
      "  Delivery points  255.50   290.0   328.50\n",
      "    Spirit market  838.25   957.0  1077.75\n",
      "      Oil market1   46.90    55.0    60.30\n",
      "      Oil market2   75.25    84.0    96.75\n",
      "      Oil market3   35.00    39.0    45.00\n",
      "          Group A    2.80     3.0     3.60\n",
      "          Group B    5.25     6.0     6.75\n"
     ]
    }
   ],
   "source": [
    "MarketSharing(retailers, deliveryPoints, spiritMarket,retailers1,  oilMarket1,retailers2,  oilMarket2,\\\n",
    "                 retailers3,  oilMarket3,groupA,  retailerA,groupB,  retailerB,deliveryPoints40,deliveryPoints5,\\\n",
    "                 spiritMarket40,spiritMarket5,oilMarket1_40,oilMarket1_5,oilMarket2_40,oilMarket2_5,oilMarket3_40,\\\n",
    "                  oilMarket3_5,retailerA40,retailerA5,retailerB40,retailerB5)"
   ]
  },
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   "execution_count": null,
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     "end_time": "2020-12-11T08:04:44.054459Z",
     "start_time": "2020-12-11T08:04:44.003788Z"
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
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    "ExecuteTime": {
     "end_time": "2020-12-11T08:06:46.099803Z",
     "start_time": "2020-12-11T08:06:46.088806Z"
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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