2022高教社杯数学建模思路 - 复盘:中小微企业的信贷决策

2022 高教社杯(国赛数学建模)思路解析

2022高教社杯ABCD赛题思路解析：

https://blog.csdn.net/dc_sinor/article/details/126211983

数据

数据一用提供了3个csv文件：

• 附件1：123家有信贷记录企业的相关数据.xlsx
• 附件2：302家无信贷记录企业的相关数据.xlsx
• 附件3：银行贷款年利率与客户流失率关系的统计数据.xlsx

观察数据

import pandas as pd 
import numpy as np


df1_1 = pd.read_excel('../data/附件1：123家有信贷记录企业的相关数据.xlsx',sheet_name=0)
df1_2 = pd.read_excel('../data/附件1：123家有信贷记录企业的相关数据.xlsx',sheet_name=1)
df1_3 = pd.read_excel('../data/附件1：123家有信贷记录企业的相关数据.xlsx',sheet_name=2)

df2_1 = pd.read_excel('../data/附件2：302家无信贷记录企业的相关数据.xlsx',sheet_name=0)
df2_2 = pd.read_excel('../data/附件2：302家无信贷记录企业的相关数据.xlsx',sheet_name=1)
df2_3 = pd.read_excel('../data/附件2：302家无信贷记录企业的相关数据.xlsx',sheet_name=2)

df3 = pd.read_excel('../data/附件3：银行贷款年利率与客户流失率关系的统计数据.xlsx',sheet_name=0)

display(df1_1.head())
display(df1_2.head())
display(df1_3.head())

display(df2_1.head())
display(df2_2.head())
display(df2_3.head())

建模

每个企业生存年限

'''
每家公司的成立年限，第一张发票时间到最后一张发票时间的差值，以月为单位
'''
# 支出表生存年限
live_time2 = df1_2[['企业代号','开票日期']]
live_time2_min = live_time2.groupby('企业代号').min().reset_index()
live_time2_max = live_time2.groupby('企业代号').max().reset_index()
live_time2 = pd.merge(live_time2_max,live_time2_min,on='企业代号')
live_time2['生存年限1'] = live_time2['开票日期_x'] - live_time2['开票日期_y']

# 收入表生存年限
live_time3 = df1_3[['企业代号','开票日期']]
live_time3_min = live_time3.groupby('企业代号').min().reset_index()
live_time3_max = live_time3.groupby('企业代号').max().reset_index()
live_time3 = pd.merge(live_time3_max,live_time3_min,on='企业代号')
live_time3['生存年限2'] = live_time3['开票日期_x'] - live_time3['开票日期_y']

# 找出生存年限最大的值作为生存年限
live_time = pd.merge(live_time2,live_time3,on='企业代号')[['企业代号','生存年限1','生存年限2']]
x1 = list(live_time['生存年限1'])
x2 = list(live_time['生存年限2'])
x = []
for i in range(len(x1)):
    if x1[i] >= x2[i]:
        x.append(x1[i])
    else:
        x.append(x2[i])
company_id = pd.DataFrame(live_time['企业代号'])
x = pd.DataFrame(x,columns=['生存年限'])
live_time = company_id.join(x)

# 生存年限转为月份
live_time['生存年限'] = live_time['生存年限'].astype(str)
live_time['生存年限'] = live_time['生存年限'].str.split().str.get(0)
live_time['生存年限'] = live_time['生存年限'].map(lambda x: str(int(x) // 30) + '月')
live_time.head()

客户量

计算收入的发票数有多少

ustomer = df1_3[['企业代号','购方单位代号','发票状态']]
customer = customer[customer['发票状态'] == '有效发票']
customer = customer.drop_duplicates(subset=['企业代号','购方单位代号'])
customer = customer.groupby('企业代号')['购方单位代号'].count().reset_index()
customer.rename(columns={'购方单位代号': '客户数'},inplace=True)
customer.head()

公司类别

# 查看公司名字中都有哪些词
company = df1_1[['企业代号','企业名称']]
company_name = list(company['企业名称'])
company_name = ' '.join(company_name).replace('*','').\
                    replace('有限公司','').replace('责任公司','').\
                    replace('分公司','')

# 词云
import jieba
import wordcloud
from scipy.misc import imread
w = wordcloud.WordCloud(background_color = 'white',
                        width = 1000,height = 700,
                        font_path = 'msyh.ttc',
                        )
w.generate(company_name)
w.to_file('../output/公司名称词云.png')

# 定义企业类型，销项，中小微
table = {
    '餐饮业':{'销项价税合计(年)':{'中':[2000,'正无穷'],
                               '小':[100,2000],
                               '微':['负无穷',100]}},
    '仓储业':{'销项价税合计(年)':{'中':[1000,'正无穷'],
                               '小':[100,1000],
                               '微':['负无穷',100]}},
    '信息传输业':{'销项价税合计(年)':{'中':[1000,'正无穷'],
                               '小':[100,1000],
                               '微':['负无穷',100]}},
    '软件和信息技术服务业':{'销项价税合计(年)':{'中':[1000,'正无穷'],
                               '小':[50,1000],
                               '微':['负无穷',50]}},
    '房地产开发经营':{'销项价税合计(年)':{'中':[5000,'正无穷'],
                               '小':[2000,5000],
                               '微':['负无穷',2000]}},
    '物业管理':{'销项价税合计(年)':{'中':[1000,'正无穷'],
                               '小':[500,1000],
                               '微':['负无穷',500]}},
    '租赁和上午服务业':{'销项价税合计(年)':{'中':[8000,'正无穷'],
                               '小':[100,8000],
                               '微':['负无穷',100]}},
    '农林牧渔业':{'销项价税合计(年)':{'中':[500,'正无穷'],
                               '小':[50,500],
                               '微':['负无穷',50]}},
    '工业':{'销项价税合计(年)':{'中':[2000,'正无穷'],
                               '小':[300,2000],
                               '微':['负无穷',300]}},
    '建筑业':{'销项价税合计(年)':{'中':[5000,'正无穷'],
                               '小':[300,5000],
                               '微':['负无穷',300]}},
    '批发业':{'销项价税合计(年)':{'中':[5000,'正无穷'],
                               '小':[1000,5000],
                               '微':['负无穷',1000]}},
    '零售业':{'销项价税合计(年)':{'中':[500,'正无穷'],
                               '小':[100,500],
                               '微':['负无穷',100]}},
    '交通运输业':{'销项价税合计(年)':{'中':[3000,'正无穷'],
                               '小':[200,3000],
                               '微':['负无穷',200]}},
    '邮政业':{'销项价税合计(年)':{'中':[2000,'正无穷'],
                               '小':[100,2000],
                               '微':['负无穷',100]}},
    '住宿业':{'销项价税合计(年)':{'中':[2000,'正无穷'],
                               '小':[100,2000],
                               '微':['负无穷',100]}},
    '其他':{'销项价税合计(年)':{'中':[2562,'正无穷'],
                               '小':[325,2562],
                               '微':['负无穷',325]}},
}

    if ('工程' in s):
        return '建筑业'
    if ('木' in s) or ('林' in s) or ('花' in s) or ('农' in s):
        return '农、林、牧、渔业'
    if ('矿' in s):
        return '采矿业'
    else:
        return '其他'
company['企业类别'] = company['企业名称'].map(kind)
company

信誉等级时序图

ank = df1_3[df1_3['发票状态'] == '有效发票']
rank = rank[['企业代号','开票日期','价税合计']]

# 开票日期转换为年月
rank['year'] = rank['开票日期'].dt.year
rank['year'] = rank['year'].astype(str)
rank['month'] = rank['开票日期'].dt.month
rank['month'] = rank['month'].astype(str)
rank['开票日期'] = rank['year'] + '-' + rank['month']

rank = rank.groupby(['企业代号','开票日期'])['价税合计'].sum().reset_index()
rank = pd.merge(rank,df1_1,on='企业代号',how='left')
rank.head()

rank_a = rank[rank['信誉评级'] == 'A'] 

import seaborn as sns
import matplotlib.pyplot as plt

# 设置这些配置，图标才能正常显示
#%matplotlib inline # 让图表直接在 jupyter notebook 中展现出来
plt.rcParams['font.sans-serif'] = ['SimHei'] # 解决中文乱码问题
plt.rcParams['axes.unicode_minus'] = False # 解决负号无法正常显示的问题
%config InlineBackend.figure_format = 'svg' # 将图标设置成矢量图格式显示，会更清晰
plt.style.use('ggplot') # 设置绘图样式
#display(plt.style.available) # 风格

fig = plt.figure(figsize=(5,4), dpi=100)
sns_line_a=sns.lineplot(x="开票日期", y="价税合计",
                  hue="企业代号",data=rank_a,
                  markers=True, dashes=False)
sns_line_a

rank_b = rank[rank['信誉评级'] == 'B']
fig = plt.figure(figsize=(5,4), dpi=100)
sns_line_b=sns.lineplot(x="开票日期", y="价税合计",
                  hue="企业代号",data=rank_b,
                  markers=True, dashes=False)
sns_line_b

rank_c = rank[rank['信誉评级'] == 'C']
fig = plt.figure(figsize=(5,4), dpi=100)
sns_line_c=sns.lineplot(x="开票日期", y="价税合计",
                  hue="企业代号",data=rank_c,
                  markers=True, dashes=False)
sns_line_c

rank_d = rank[rank['信誉评级'] == 'D']
fig = plt.figure(figsize=(5,4), dpi=100)
sns_line_d=sns.lineplot(x="开票日期", y="价税合计",
                  hue="企业代号",data=rank_d,
                  markers=True, dashes=False)
sns_line_d

企业进项，作废发票数，有效发票数

bill_outcome = df1_2[['企业代号','价税合计','发票状态']]

# 有效发票数
yes_bill_outcome = bill_outcome[bill_outcome['发票状态'] == '有效发票']
yes_bill_outcome = yes_bill_outcome.groupby('企业代号')['发票状态'].count()
yes_bill_outcome = yes_bill_outcome.reset_index()

# 作废发票数
no_bill_outcome = bill_outcome[bill_outcome['发票状态'] == '作废发票']
no_bill_outcome = no_bill_outcome.groupby('企业代号')['发票状态'].count()
no_bill_outcome = no_bill_outcome.reset_index()

# 进项有效，作废发票数汇总
bill_outcome = pd.merge(yes_bill_outcome,no_bill_outcome,on='企业代号',
                       how='left')
bill_outcome.rename(columns={'发票状态_x' : '进项有效发票数',
                            '发票状态_y' : '进项作废发票数'},
                            inplace=True)
bill_outcome.head()

企业销项作废发票数，有效发票数

bill_income = df1_3[['企业代号','价税合计','发票状态']]

# 有效发票数
yes_bill_income = bill_income[bill_income['发票状态'] == '有效发票']
yes_bill_income = yes_bill_income.groupby('企业代号')['发票状态'].count()
yes_bill_income = yes_bill_income.reset_index()

# 作废发票数
no_bill_income = bill_income[bill_income['发票状态'] == '作废发票']
no_bill_income = no_bill_income.groupby('企业代号')['发票状态'].count()
no_bill_income = no_bill_income.reset_index()

# 进项有效，作废发票数汇总
bill_income = pd.merge(yes_bill_income,no_bill_income,on='企业代号',
                      how='left')
bill_income.rename(columns={'发票状态_x' : '销项有效发票数',
                            '发票状态_y' : '销项作废发票数'},
                            inplace=True)
bill_income.head()

企业进项价,销项税合计

# 进项
outcome_sum = df1_2[['企业代号','价税合计']]
outcome_sum = outcome_sum.groupby('企业代号')['价税合计'].sum().reset_index()

# 销项
income_sum = df1_3[['企业代号','价税合计']]
income_sum = income_sum.groupby('企业代号')['价税合计'].sum().reset_index()

# 进项，销项汇总
outcome_income_sum = pd.merge(outcome_sum,income_sum,on='企业代号')
outcome_income_sum.rename(columns={'价税合计_x' : '进项价税合计',
                                  '价税合计_y' : '销项价税合计'},inplace=True)
outcome_income_sum.head()

变量汇总

'''
字段为：企业代号，企业名称，信誉评级，是否违约，进项合计，销项合计，进项有效
发票数，进项作废发票数,销项有效发票数，进项作废发票数，成立时间，客户量
'''
import math
data = pd.merge(df1_1,live_time,on='企业代号')
data = pd.merge(data,customer,on='企业代号')
data = pd.merge(data,bill_outcome,on='企业代号')
data = pd.merge(data,bill_income,on='企业代号')
data = pd.merge(data,outcome_income_sum,on='企业代号')
data['利润'] = data['销项价税合计'] - data['进项价税合计']
data['生存年限'] = data['生存年限'].map(lambda x: int(x.replace('月','')))
data['生存年限'] = data['生存年限'].map(lambda x: math.ceil(x / 12))
data['收益率'] = (data['销项价税合计'] - data['进项价税合计']) / data['进项价税合计']
data['收益率'] = data['收益率'] / data['生存年限']
data.to_excel('../data/data.xlsx',encoding='utf8',index=False)

LCR 模型，KMeans 聚类

LCR 建模

data.head()

'''
LCR 模型变量选取
L 成立年限
C 客户数 
R 收益率 
'''
LCR = data[['生存年限','客户数','收益率']]
#LCR['生存年限'] = LCR['生存年限'].map(lambda x: int(x.replace('月','')))
LCR.head()

聚类模型对企业分类
'''
from sklearn.cluster import KMeans
kms = KMeans(n_clusters=4)
kms.fit(LCR)
label = kms.labels_
label = pd.DataFrame(list(label))

# 把企业类别汇总到 data.xlsx，并保存为 new_data.xlsx
data['种类'] = label
data.to_excel('../data/data_Kmeans.xlsx')
data.head()

聚类结果可视化

# 0 类型
kind_0 = data[data['种类'] == 0]
#kind_0['生存年限'] = kind_0['生存年限'].map(lambda x: int(x.replace('月','')))
kind_0 = kind_0[["生存年限","客户数","收益率"]].mean()
kind_0
# 1 类型
kind_1 = data[data['种类'] == 1]
#kind_1['生存年限'] = kind_1['生存年限'].map(lambda x: int(x.replace('月','')))
kind_1 = kind_1[["生存年限","客户数","收益率"]].mean()
kind_1
# 2 类型
kind_2 = data[data['种类'] == 2]
#kind_2['生存年限'] = kind_2['生存年限'].map(lambda x: int(x.replace('月','')))
kind_2 = kind_2[["生存年限","客户数","收益率"]].mean()
kind_2

kind_3 = data[data['种类'] == 3]
#kind_3['生存年限'] = kind_3['生存年限'].map(lambda x: int(x.replace('月','')))
kind_3 = kind_3[["生存年限","客户数","收益率"]].mean()
kind_3


# 雷达图
from pyecharts import options as opts
from pyecharts.globals import ThemeType
from pyecharts.charts import Radar

value_0 = [
    list(kind_0.values)
]
value_1 = [
    list(kind_1.values)
]
value_2 = [
    list(kind_2.values)
]
value_3 = [
    list(kind_3.values)
]
c_schema = [
    {"name": "成立年限", "max": 5, "min": 0},
    {"name": "客户数", "max": 8500, "min": 0},
    {"name": "收益率", "max": 4425, "min": 0},
]
c = (
    Radar(init_opts=opts.InitOpts(theme=ThemeType.DARK))
    .add_schema(schema=c_schema, shape="circle")
    .add("0", value_0, color="#f9713c")
    .add("1", value_1, color="#b3e4a1")
    .add("2", value_2, color="#bd10e0")
    .add("3", value_3, color="#FFFF00")
    .set_series_opts(label_opts=opts.LabelOpts(is_show=False))
    .set_global_opts(title_opts=opts.TitleOpts(title="企业聚类结果"))
)
c.render('../output/聚类结果.html')
c.render_notebook()

建立 KNN 分类模型预测附件2 企业等级

附件1最终数据作为训练集

data = data.fillna(0)

x_train = data.drop(columns=['企业代号','企业名称','信誉评级','是否违约','种类'])
y_train = data['信誉评级']

# 模型建立
from sklearn.neighbors import KNeighborsClassifier as KNN
knn = KNN(n_neighbors=2) # 当有一个新样本时，选取离他最近的 3 个，类别最多的，那新样本也属于这个类别
knn.fit(x_train,y_train)

# 预测准确度评估
an = knn.predict(x_train)
from sklearn.metrics import accuracy_score
score = accuracy_score(an, y_train)
score

附件2处理为需要用到的数据

'''
每家公司的成立年限，第一张发票时间到最后一张发票时间的差值，以月为单位
'''
# 支出表生存年限
live_time2 = df2_2[['企业代号','开票日期']]
live_time2_min = live_time2.groupby('企业代号').min().reset_index()
live_time2_max = live_time2.groupby('企业代号').max().reset_index()
live_time2 = pd.merge(live_time2_max,live_time2_min,on='企业代号')
live_time2['生存年限1'] = live_time2['开票日期_x'] - live_time2['开票日期_y']

# 收入表生存年限
live_time3 = df2_3[['企业代号','开票日期']]
live_time3_min = live_time3.groupby('企业代号').min().reset_index()
live_time3_max = live_time3.groupby('企业代号').max().reset_index()
live_time3 = pd.merge(live_time3_max,live_time3_min,on='企业代号')
live_time3['生存年限2'] = live_time3['开票日期_x'] - live_time3['开票日期_y']

# 找出生存年限最大的值作为生存年限
live_time = pd.merge(live_time2,live_time3,on='企业代号')[['企业代号','生存年限1','生存年限2']]
x1 = list(live_time['生存年限1'])
x2 = list(live_time['生存年限2'])
x = []
for i in range(len(x1)):
    if x1[i] >= x2[i]:
        x.append(x1[i])
    else:
        x.append(x2[i])
company_id = pd.DataFrame(live_time['企业代号'])
x = pd.DataFrame(x,columns=['生存年限'])
live_time = company_id.join(x)

# 生存年限转为月份
live_time['生存年限'] = live_time['生存年限'].astype(str)
live_time['生存年限'] = live_time['生存年限'].str.split().str.get(0)
live_time['生存年限'] = live_time['生存年限'].map(lambda x: str(int(x) // 30) + '月')


'''
客户量：计算收入的发票数有多少
'''
customer = df2_2[['企业代号','购方单位代号','发票状态']]
customer = customer[customer['发票状态'] == '有效发票']
customer = customer.drop_duplicates(subset=['企业代号','购方单位代号'])
customer = customer.groupby('企业代号')['购方单位代号'].count().reset_index()
customer.rename(columns={'购方单位代号': '客户数'},inplace=True)


'''
每个企业的进项，作废发票数，有效发票数
'''
bill_outcome = df2_3[['企业代号','价税合计','发票状态']]

# 有效发票数
yes_bill_outcome = bill_outcome[bill_outcome['发票状态'] == '有效发票']
yes_bill_outcome = yes_bill_outcome.groupby('企业代号')['发票状态'].count()
yes_bill_outcome = yes_bill_outcome.reset_index()

# 作废发票数
no_bill_outcome = bill_outcome[bill_outcome['发票状态'] == '作废发票']
no_bill_outcome = no_bill_outcome.groupby('企业代号')['发票状态'].count()
no_bill_outcome = no_bill_outcome.reset_index()

# 进项有效，作废发票数汇总
bill_outcome = pd.merge(yes_bill_outcome,no_bill_outcome,on='企业代号',
                       how='left')
bill_outcome.rename(columns={'发票状态_x' : '进项有效发票数',
                            '发票状态_y' : '进项作废发票数'},
                            inplace=True)


'''
每个企业的销项作废发票数，有效发票数
'''
bill_income = df2_3[['企业代号','价税合计','发票状态']]

# 有效发票数
yes_bill_income = bill_income[bill_income['发票状态'] == '有效发票']
yes_bill_income = yes_bill_income.groupby('企业代号')['发票状态'].count()
yes_bill_income = yes_bill_income.reset_index()

# 作废发票数
no_bill_income = bill_income[bill_income['发票状态'] == '作废发票']
no_bill_income = no_bill_income.groupby('企业代号')['发票状态'].count()
no_bill_income = no_bill_income.reset_index()

# 进项有效，作废发票数汇总
bill_income = pd.merge(yes_bill_income,no_bill_income,on='企业代号',
                      how='left')
bill_income.rename(columns={'发票状态_x' : '销项有效发票数',
                            '发票状态_y' : '销项作废发票数'},
                            inplace=True)


'''
每个企业进项价,销项税合计
'''
# 进项
outcome_sum = df2_2[['企业代号','价税合计']]
outcome_sum = outcome_sum.groupby('企业代号')['价税合计'].sum().reset_index()

# 销项
income_sum = df2_3[['企业代号','价税合计']]
income_sum = income_sum.groupby('企业代号')['价税合计'].sum().reset_index()

# 进项，销项汇总
outcome_income_sum = pd.merge(outcome_sum,income_sum,on='企业代号')
outcome_income_sum.rename(columns={'价税合计_x' : '进项价税合计',
                                  '价税合计_y' : '销项价税合计'},inplace=True)


'''
变量汇总
'''
import math
data1 = pd.merge(df2_1,live_time,on='企业代号')
data1 = pd.merge(data1,customer,on='企业代号')
data1 = pd.merge(data1,bill_outcome,on='企业代号')
data1 = pd.merge(data1,bill_income,on='企业代号')
data1 = pd.merge(data1,outcome_income_sum,on='企业代号')
data1['利润'] = data1['销项价税合计'] - data1['进项价税合计']
data1['生存年限'] = data1['生存年限'].map(lambda x: int(x.replace('月','')))
data1['生存年限'] = data1['生存年限'].map(lambda x: math.ceil(x / 12))
data1['收益率'] = (data1['销项价税合计'] - data1['进项价税合计']) / data1['进项价税合计']
data1['收益率'] = data1['收益率'] / data['生存年限']
data1.to_excel('../data/data2.xlsx',encoding='utf8',index=False)

2022 高教社杯(国赛数学建模)思路解析

2022高教社杯ABCD赛题思路解析：

https://blog.csdn.net/dc_sinor/article/details/126211983