2023年全国大学生数学建模竞赛C题 蔬菜类商品的自动定价与补货决策
本文仅含数据处理（编程位），且c++
题目
在生鲜商超中，一般蔬菜类商品的保鲜期都比较短，且品相随销售时间的增加而变差，大部分品种如当日未售出，隔日就无法再售。因此，商超通常会根据各商品的历史销售和需求情况每天进行补货。
由于商超销售的蔬菜品种众多、产地不尽相同，而蔬菜的进货交易时间通常在凌晨 3:00-4:00，为此商家须在不确切知道具体单品和进货价格的情况下，做出当日各蔬菜品类的补货决策。蔬菜的定价一般采用“成本加成定价”方法，商超对运损和品相变差的商品通常进行打折销售。可靠的市场需求分析，对补货决策和定价决策尤为重要。从需求侧来看，蔬菜类商品的销售量与时间往往存在一定的关联关系；从供给侧来看，蔬菜的供应品种在 4 月至 10月较为丰富，商超销售空间的限制使得合理的销售组合变得极为重要。
附件 1 给出了某商超经销的 6 个蔬菜品类的商品信息；附件 2 和附件 3 分别给出了该商超 2020 年 7 月 1 日至 2023 年 6 月 30 日各商品的销售流水明细与批发价格的相关数据；附件 4 给出了各商品近期的损耗率数据。请根据附件和实际情况建立数学模型解决以下问题：
问题 1 蔬菜类商品不同品类或不同单品之间可能存在一定的关联关系，请分析蔬菜各品类及单品销售量的分布规律及相互关系。
问题 2 考虑商超以品类为单位做补货计划，请分析各蔬菜品类的销售总量与成本加成定价的关系，并给出各蔬菜品类未来一周(2023 年 7 月 1-7 日)的日补货总量和定价策略，使得商超收益最大。
问题 3 因蔬菜类商品的销售空间有限，商超希望进一步制定单品的补货计划，要求可售单品总数控制在 27-33 个，且各单品订购量满足最小陈列量 2.5 千克的要求。根据 2023年 6 月 24-30 日的可售品种，给出 7 月 1 日的单品补货量和定价策略，在尽量满足市场对各品类蔬菜商品需求的前提下，使得商超收益最大。
问题 4 为了更好地制定蔬菜商品的补货和定价决策，商超还需要采集哪些相关数据，这些数据对解决上述问题有何帮助，请给出你们的意见和理由。
附件 1 6 个蔬菜品类的商品信息
附件 2 销售流水明细数据
附件 3 蔬菜类商品的批发价格
附件 4 蔬菜类商品的近期损耗率
注 (1) 附件 1 中，部分单品名称包含的数字编号表示不同的供应来源。
(2) 附件 4 中的损耗率反映了近期商品的损耗情况，通过近期盘点周期的数据计算得到。
问题一
计算单品的总销售额
#include
ifstream data2("annex2.csv",ios::in);
string line2;
istringstream sin2;
vector<string> words2;
string word2;
getline(data2, line2);
while (getline(data2, line2))
{
sin2.clear();
sin2.str(line2);
words2.clear();
int i=0;
while (getline(sin2, word2, ','))
{
words2.push_back(word2);
}
double res=stold(words2[3])*stold(words2[4]);
mp[words2[2]]+=res;
}
data2.close();
// map< string,double>::iterator it;
// for(it=mp.begin();it!=mp.end();it++)cout<first<<" "<second<
map<string,double>::iterator it;
for(it=mp.begin();it!=mp.end();it++){
fer(i,0,k){
if(it->first==g[i].s[0]){
g[i].money=it->second;
break;
}
}
}
ofstream outFile;
outFile.open("salesVolume.csv",ios::out|ios::trunc);
outFile<<"code,name,typeCode,typeName,money,typeMoney"<<endl;
fer(i,0,k){
outFile<<g[i].s[0]<<","<<g[i].s[1]<<","<<g[i].s[2]<<","<<g[i].s[3]<<",";
outFile<<g[i].money<<endl;
}
outFile.close();
return 0;
}
计算品类及单品的每月销售额
#include
// fer(i,0,k)cout<
ifstream data2("annex2.csv",ios::in);
string line2;
istringstream sin2;
vector<string> words2; //分别是日期，编码，销量，单价的字符串
string word2;
getline(data2, line2);
while (getline(data2, line2))
{
sin2.clear();
sin2.str(line2);
words2.clear();
int i=0;
while (getline(sin2, word2, ','))
{
words2.push_back(word2);
}
double res=stold(words2[3])*stold(words2[4]);
int time=0;
int year=words2[0][3]-'0';
int month=(words2[0][5]-'0')*10+words2[0][6]-'0';
int day=(words2[0][8]-'0')*10+words2[0][9]-'0';
//cout<
if(year==0)time=month-7;
else if(year==1){
time=month+5;
}else if(year==2)time=month+17;
else time=month+29;
string tmp=words2[2];
if(time<10)tmp+="0";
tmp+=to_string(time);
mp[tmp]+=res;
}
data2.close();
//map< string,double>::iterator it;
//for(it=mp.begin();it!=mp.end();it++)cout<first<<" "<second<
map<string,double>::iterator it;
for(it=mp.begin();it!=mp.end();it++){
string tmp=it->first;
string code=tmp.substr(0,15);
string strtime=tmp.substr(15);
int time=atoi(strtime.c_str());
//cout<second<
fer(i,0,k){
if(code==g[i].s[0]){
//cout<<"success"<
g[i].money[time]=it->second;
break;
}
}
}
// fer(i,0,k){
// cout<
// fer(j,0,36)cout<
// cout<
// }
ofstream outFile;
outFile.open("salesTypeMonthly.csv",ios::out|ios::trunc);
outFile<<"type"<<",";
fer(i,0,36){
if(i<=5)outFile<<"2020 -"<<i+7<<",";
else if(i<=17)outFile<<"2021 -"<<i-5<<",";
else if(i<=29)outFile<<"2022 -"<<i-17 <<",";
else if(i<35)outFile<<"2023 -"<<i-29<<",";
else outFile<<"2023 -"<<i-29<<endl;
}
//输出品类按月的销售额
fer(i,0,k){
fer(j,0,6){
if(g[i].s[3]==type[j]){
fer(t,0,36)money[j][t]+=g[i].money[t];
}
}
}
fer(i,0,6){
outFile<<type[i]<<",";
fer(j,0,36){
outFile<<money[i][j];
if(j!=35)outFile<<",";
else outFile<<endl;
}
}
//输出单品按月的销售额
// fer(i,0,k){
// outFile<
// fer(j,0,36){
// outFile<
// if(j!=35)outFile<<",";
// else outFile<
// }
// }
outFile.close();
return 0;
}
问题二
打折商品的售价和销量
#include
}
}
data2.close();
cout<<"success2"<<endl;
ifstream data3("annex1.csv",ios::in);
string line3;
istringstream sin3;
vector<string> words3;
string word3;
getline(data3, line3);
while (getline(data3, line3))
{
sin3.clear();
sin3.str(line3);
words3.clear();
while (getline(sin3, word3, ','))
{
words3.push_back(word3);
}
type[words3[0]]=words3[3];
// cout<
}
data3.close();
cout<<"success3"<<endl;
map<string,node>::iterator it;
for(it=mp.begin();it!=mp.end();it++){
string key=it->first;
string date=key.substr(0,10);
string code=key.substr(10);
string tp=type[code];
string pinleiKey=date+tp;
if(pinlei.find(pinleiKey)==pinlei.end()){//没找见
node solve;
solve.price=it->second.price*it->second.salesV;
solve.salesV=it->second.salesV;
pinlei[pinleiKey]=solve;
}else{//找见了
node solve=pinlei[pinleiKey];
solve.price+=it->second.price*it->second.salesV;
solve.salesV+=it->second.salesV;
pinlei[pinleiKey]=solve;
}
}
for(it=pinlei.begin();it!=pinlei.end();it++){
node solve=it->second;
solve.price/=solve.salesV;
it->second=solve;
}
ofstream outFile;
outFile.open("discountSS.csv",ios::out|ios::trunc);
string typeName="水生根茎类";
outFile<<typeName<<endl;
outFile<<"日期,平均销售价格,销量（kg）"<<endl;
int monthday[12]={31,28,31,30,31,30,31,31,30,31,30,31};
int year=0,month=7,day=1;
for(it=pinlei.begin();it!=pinlei.end();it++){
string tmp=it->first;
string date=tmp.substr(0,10);
string typ=tmp.substr(10);
//cout<
int nowyear=(tmp[3]-'0');
int nowmonth=(tmp[5]-'0')*10+tmp[6]-'0';
int nowday=(tmp[8]-'0')*10+tmp[9]-'0';
//cout<
while(year<nowyear||(nowyear==year&&month<nowmonth)||(year==nowyear&&nowmonth==month&&day<nowday)){
if(year>=3&&month>=7)break;
outFile<<"202"<<year<<"-";
if(month<10)outFile<<"0";
outFile<<month<<"-";
if(day<10)outFile<<"0";
outFile<<day<<",";
outFile<<"0,0"<<endl;
day++;
if(day>monthday[month-1]){
month++;day=1;
}
if(month>12){
year++;month=1;
}
}
if(typ==typeName){
node solve=it->second;
outFile<<date<<","<<solve.price<<","<<solve.salesV<<endl;
day++;
if(day>monthday[month-1]){
month++;day=1;
}
if(month>12){
year++;month=1;
}
}
}
outFile.close();
cout<<"success4";
return 0;
}
各品类平均损耗率
这个处理得比较粗糙，直接对损耗率求平均，没有加权重
#include
}
data1.close();
cout<<"success1"<<endl;
ifstream data2("annex4.csv",ios::in);
string line2;
istringstream sin2;
vector<string> words2;
string word2;
getline(data2, line2);
while (getline(data2, line2))
{
sin2.clear();
sin2.str(line2);
words2.clear();
while (getline(sin2, word2, ','))
{
words2.push_back(word2);
}
string tmp=words2[0]+" ";
//cout<
fer(i,0,6){
if(type[tmp]==typeName[i]){
tp[i].loss+=stod(words2[2]);
tp[i].n++;
//cout<
break;
}
}
}
data2.close();
cout<<"success2"<<endl;
ofstream outFile;
outFile.open("typeLoss.csv",ios::out|ios::trunc);
outFile<<"损耗率(%)与1-损耗率"<<endl;
fer(i,0,6){
tp[i].loss/=tp[i].n;
outFile<<typeName[i]<<","<<tp[i].loss<<","<<1-tp[i].loss<<endl;
}
outFile.close();
cout<<"success3"<<endl;
return 0;
}
计算各品类的利润
#include
}
data3.close();
cout<<"success3"<<endl;
map<string,node>::iterator it;
for(it=mp.begin();it!=mp.end();it++){
string key=it->first;
string date=key.substr(0,10);
string code=key.substr(10);
string tp=type[code];
string pinleiKey=date+tp;
if(pinlei.find(pinleiKey)==pinlei.end()){//没找见
node solve;
solve.cost=it->second.cost * it->second.salesV;
solve.price=it->second.price*it->second.salesV;
solve.salesV=it->second.salesV;
pinlei[pinleiKey]=solve;
}else{//找见了
node solve=pinlei[pinleiKey];
solve.cost+=it->second.cost*it->second.salesV;
solve.price+=it->second.price*it->second.salesV;
solve.salesV+=it->second.salesV;
pinlei[pinleiKey]=solve;
}
}
for(it=pinlei.begin();it!=pinlei.end();it++){
node solve=it->second;
solve.cost/=solve.salesV;solve.price/=solve.salesV;
solve.profitM=(solve.price-solve.cost)/solve.cost;
it->second=solve;
}
ofstream outFile;
outFile.open("averageLaJiao.csv",ios::out|ios::trunc);
string typeName="辣椒类";
outFile<<typeName<<endl;
outFile<<"日期,平均批发价格,平均销售价格,总销量（kg）,利润率"<<endl;
for(it=pinlei.begin();it!=pinlei.end();it++){
string tmp=it->first;
string date=tmp.substr(0,10);
string typ=tmp.substr(10);
if(typ==typeName){
node solve=it->second;
outFile<<date<<","<<solve.cost<<","<<solve.price<<","<<solve.salesV<<","<<solve.profitM<<endl;
}
}
outFile.close();
cout<<"success4";
return 0;
}
问题三
问题三成本与售价
#include
//i++;
}
//cout<
data1.close();
cout<<"success1";
ifstream data2("annex2.csv",ios::in);
string line2;
istringstream sin2;
vector<string> words2;
string word2;
getline(data2, line2);
while (getline(data2, line2))
{
sin2.clear();
sin2.str(line2);
words2.clear();
while (getline(sin2, word2, ','))
{
words2.push_back(word2);
}
string tmp=words2[0]+words2[2];
mp2[tmp]=words2[4];
//cout<
}
data2.close();
cout<<"success2";
ifstream data3("annex1.csv",ios::in);
string line3;
istringstream sin3;
vector<string> words3;
string word3;
getline(data3, line3);
while (getline(data3, line3))
{
sin3.clear();
sin3.str(line3);
words3.clear();
while (getline(sin3, word3, ','))
{
words3.push_back(word3);
}
cdnm[words3[0]]=words3[1];
type[words3[0]]=words3[3];
// cout<
}
data3.close();
cout<<"success3";
// map< string,double>::iterator it;
// for(it=mp.begin();it!=mp.end();it++)cout<first<<" "<second<
// ofstream outFile;
// outFile.open("salesPrice2.csv",ios::out|ios::trunc);
// outFile<<"日期,单品编码,单品名称,类别,批发价格,售价"<
map<string,string>::iterator it;
for(it=mp.begin();it!=mp.end();it++){
string tmp=it->first;
string date=tmp.substr(0,10);
string code=tmp.substr(10);
// outFile<
// //outFile<
// outFile<
cout<<date<<","<<code<<","<<cdnm[code]<<","<<type[code]<<","<<mp[tmp]<<","<<mp2[tmp]<<endl;
// cout<first<<" "<second<
break;
}
//outFile.close();
cout<<"success4";
return 0;
}
问题三单品销量
#include
node single;
single.cost=stold(words1[2]);
single.price=0;single.salesV=0;
mp[tmp]=single;
cout<<tmp<<","<<mp[tmp].cost<<endl;
}
data1.close();
cout<<"success1"<<endl;
ifstream data2("624-630annex2.csv",ios::in);
string line2;
istringstream sin2;
vector<string> words2;
string word2;
while (getline(data2, line2))//获取当日单品销售额及销量
{
sin2.clear();
sin2.str(line2);
words2.clear();
while (getline(sin2, word2, ','))
{
words2.push_back(word2);
}
string tmp=words2[0]+words2[2];
// tmp.pop_back();
struct node single=mp[tmp];
single.price+=stod(words2[4])*stod(words2[3]);
single.salesV+=stod(words2[3]);
mp[tmp]=single;
//cout<
}
data2.close();
cout<<"success2"<<endl;
ifstream data3("annex1.csv",ios::in);
string line3;
istringstream sin3;
vector<string> words3;
string word3;
getline(data3, line3);
while (getline(data3, line3))//编号映射单品名和种类名
{
sin3.clear();
sin3.str(line3);
words3.clear();
while (getline(sin3, word3, ','))
{
words3.push_back(word3);
}
//words3[0].pop_back();
type[words3[0]]=words3[3];
name[words3[0]]=words3[1];
}
data3.close();
cout<<"success3"<<endl;
map<string,node>::iterator it;
for(it=mp.begin();it!=mp.end();it++){
string key=it->first;
string date=key.substr(0,10);
string code=key.substr(10);
//cout<
if(mp2.find(code)==mp2.end()){//没找见
node solve;
solve.cost=it->second.cost * it->second.salesV;
solve.price=it->second.price;
solve.salesV=it->second.salesV;
mp2[code]=solve;
}else{//找见了
node solve=mp2[code];
solve.cost+=it->second.cost*it->second.salesV;
solve.price+=it->second.price;
solve.salesV+=it->second.salesV;
mp2[code]=solve;
}
}
for(it=mp2.begin();it!=mp2.end();it++){
node solve=it->second;
if(solve.salesV!=0){
solve.cost/=solve.salesV;solve.price/=solve.salesV;
solve.profitM=(solve.price-solve.cost)/solve.cost;
solve.salesV/=7;
it->second=solve;
}
}
ofstream outFile;
outFile.open("Q3.csv",ios::out|ios::trunc);
outFile<<"单品编号,单品名称,单品种类,平均批发价格,平均销售价格,总销量（kg）,利润率,真实成本,每日总利润"<<endl;
for(it=mp2.begin();it!=mp2.end();it++){
node solve=it->second;
if(solve.salesV!=0){
string code=it->first;
outFile<<code<<","<<name[code]<<","<<type[code]<<",";
outFile<<solve.cost<<","<<solve.price<<","<<solve.salesV<<","<<solve.profitM<<",";
outFile<<solve.cost/loss[type[code]]*100<<endl;
}
}
outFile.close();
cout<<"success4";
return 0;
}
问题三品类对应
#include
}
data2.close();
cout<<"success2"<<endl;
ifstream data1("type.csv",ios::in);
string line1;
istringstream sin1;
string word1;
vector<string> words1;
getline(data1, line1);
ofstream outFile;
outFile.open("typeMatch.csv",ios::out|ios::trunc);
outFile<<"单品名称,单品类型,总销量（kg）,真实成本,实际利润率,平均销售价格,成本,销售额,利润"<<endl;
while (getline(data1, line1))
{
//cout<<1;
sin1.clear();
sin1.str(line1);
words1.clear();
while (getline(sin1, word1, ','))
{
words1.push_back(word1);
}
//cout<
outFile<<words1[0]<<","<<type[words1[0]]<<",";
fer(i,1,7)outFile<<words1[i]<<",";
outFile<<words1[7]<<endl;
}
data1.close();
cout<<"success1"<<endl;
outFile.close();
cout<<"success3"<<endl;
return 0;
}