{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ebcb7d83",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-12-19T10:09:08.122602Z",
     "start_time": "2023-12-19T10:09:08.084460Z"
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    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>V1</th>\n",
       "      <th>V2</th>\n",
       "      <th>V3</th>\n",
       "      <th>V4</th>\n",
       "      <th>V5</th>\n",
       "      <th>V6</th>\n",
       "      <th>V7</th>\n",
       "      <th>V8</th>\n",
       "      <th>存货</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>W1</th>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>9</td>\n",
       "      <td>60</td>\n",
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       "    <tr>\n",
       "      <th>W2</th>\n",
       "      <td>4</td>\n",
       "      <td>9</td>\n",
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       "      <td>8</td>\n",
       "      <td>55</td>\n",
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       "    <tr>\n",
       "      <th>W3</th>\n",
       "      <td>5</td>\n",
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       "      <td>51</td>\n",
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       "      <th>W5</th>\n",
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       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "      <td>41</td>\n",
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       "      <th>W6</th>\n",
       "      <td>5</td>\n",
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       "      <td>8</td>\n",
       "      <td>1</td>\n",
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       "      <td>3</td>\n",
       "      <td>52</td>\n",
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      "text/plain": [
       "    V1  V2  V3  V4  V5  V6  V7  V8  存货\n",
       "W1   6   2   6   7   4   2   5   9  60\n",
       "W2   4   9   9   5   3   8   5   8  55\n",
       "W3   5   2   2   1   9   4   3   3  51\n",
       "W4   7   6   6   7   3   9   2   7  43\n",
       "W5   2   3   9   5   7   2   6   5  41\n",
       "W6   5   5   2   2   8   1   4   3  52"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from itertools import permutations\n",
    "import pandas as pd\n",
    "import pulp as lp\n",
    "\n",
    "\n",
    "# Defining the data\n",
    "data = {\n",
    "    \"V1\": [6, 4, 5, 7, 2, 5],\n",
    "    'V2': [2, 9, 2, 6, 3, 5],\n",
    "    \"V3\": [6, 9, 2, 6, 9, 2],\n",
    "    \"V4\": [7, 5, 1, 7, 5, 2],\n",
    "    \"V5\": [4, 3, 9, 3, 7, 8],\n",
    "    \"V6\": [2, 8, 4, 9, 2, 1],\n",
    "    \"V7\": [5, 5, 3, 2, 6, 4],\n",
    "    \"V8\": [9, 8, 3, 7, 5, 3],\n",
    "    \"存货\": [60, 55, 51, 43, 41, 52]\n",
    "}\n",
    "\n",
    "# Creating the DataFrame\n",
    "df = pd.DataFrame(data, index=[\"W1\", \"W2\", \"W3\", \"W4\", \"W5\", \"W6\"])\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "757bd77d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-12-19T10:09:08.670319Z",
     "start_time": "2023-12-19T10:09:08.538767Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     V1  V2  V3  V4  V5  V6  V7  V8    存货\n",
      "W1    6   2   6   7   4   2   5   9  60.0\n",
      "W2    4   9   9   5   3   8   5   8  55.0\n",
      "W3    5   2   2   1   9   4   3   3  51.0\n",
      "W4    7   6   6   7   3   9   2   7  43.0\n",
      "W5    2   3   9   5   7   2   6   5  41.0\n",
      "W6    5   5   2   2   8   1   4   3  52.0\n",
      "需求量  35  37  22  32  41  32  43  38   NaN\n",
      "596.0\n"
     ]
    }
   ],
   "source": [
    "# Demand\n",
    "demand = {\"V1\": 35,\"V2\":37, \"V3\": 22, \"V4\": 32, \"V5\": 41, \"V6\": 32, \"V7\": 43, \"V8\": 38}\n",
    "\n",
    "# Adding demand as a row\n",
    "df = df._append(demand, ignore_index=True)\n",
    "df.index = [\"W1\", \"W2\", \"W3\", \"W4\", \"W5\", \"W6\", \"需求量\"]\n",
    "\n",
    "print(df)\n",
    "I=list(df.index)\n",
    "I.pop()\n",
    "J=list(df.columns)\n",
    "J.pop()\n",
    "\n",
    "model = lp.LpProblem('distribution',sense=lp.LpMinimize) # 模型初始化\n",
    "x = lp.LpVariable.dicts('x',indices=[(i,j) for i in I for j in J],lowBound=0,cat='Integer')\n",
    "obj = lp.lpSum(df.loc[i,j]*x[i,j] for i in I for j in J)\n",
    "model += obj # 先添加目标函数\n",
    "for j in J:\n",
    "    model += lp.lpSum(x[i,j] for i in I)==df.loc['需求量',j]\n",
    "for i in I:\n",
    "    model += lp.lpSum(x[i,j] for j in J)<=df.loc[i,'存货'] \n",
    "model.solve()\n",
    "print(lp.value(model.objective))#result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d146227c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-12-19T10:09:11.629604Z",
     "start_time": "2023-12-19T10:09:11.604328Z"
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       "      <th>W1</th>\n",
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       "    <tr>\n",
       "      <th>W5</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>9</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "      <td>41.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>W6</th>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>8</td>\n",
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       "      <td>3</td>\n",
       "      <td>52.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>需求量</th>\n",
       "      <td>35</td>\n",
       "      <td>37</td>\n",
       "      <td>22</td>\n",
       "      <td>32</td>\n",
       "      <td>41</td>\n",
       "      <td>32</td>\n",
       "      <td>43</td>\n",
       "      <td>38</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     V1  V2  V3  V4  V5  V6  V7  V8    存货\n",
       "W1    6   2   6   7   4   2   5   9  60.0\n",
       "W2    4   9   9   5   3   8   5   8  55.0\n",
       "W3    5   2   2   1   9   4   3   3  51.0\n",
       "W4    7   6   6   7   3   9   2   7  43.0\n",
       "W5    2   3   9   5   7   2   6   5  41.0\n",
       "W6    5   5   2   2   8   1   4   3  52.0\n",
       "需求量  35  37  22  32  41  32  43  38   NaN"
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     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "006af2d5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-12-19T10:09:12.937630Z",
     "start_time": "2023-12-19T10:09:12.897242Z"
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       "    <tr>\n",
       "      <th>W5</th>\n",
       "      <td>35</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>41.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>W6</th>\n",
       "      <td>0</td>\n",
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       "      <td>22</td>\n",
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       "      <td>19</td>\n",
       "      <td>52.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>需求量</th>\n",
       "      <td>35</td>\n",
       "      <td>37</td>\n",
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       "      <td>32</td>\n",
       "      <td>41</td>\n",
       "      <td>32</td>\n",
       "      <td>43</td>\n",
       "      <td>38</td>\n",
       "      <td>NaN</td>\n",
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      ],
      "text/plain": [
       "     V1  V2  V3  V4  V5  V6  V7  V8    存货\n",
       "W1    0  37   0   0   0  21   0   0  60.0\n",
       "W2    0   0   0   0  41   0   0   0  55.0\n",
       "W3    0   0   0  32   0   0   0  19  51.0\n",
       "W4    0   0   0   0   0   0  43   0  43.0\n",
       "W5   35   0   0   0   0   0   0   0  41.0\n",
       "W6    0   0  22   0   0  11   0  19  52.0\n",
       "需求量  35  37  22  32  41  32  43  38   NaN"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = df.copy()\n",
    "for i in I:\n",
    "    for j in J:\n",
    "        df1.loc[i,j] = lp.value(x[i,j])\n",
    "df1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f3d62a0b",
   "metadata": {},
   "outputs": [],
   "source": []
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