\%

b_{ij}

\begin{table}[H]

\centering

\begin{tabular}{m{100pt}<{\centering} m{100pt}<{\centering} m{200pt}<{\centering}}

\toprule

序列 &  符号& 符号说明\\

\midrule

   & $t_{ij}$ &  第i个会员第j种DVD的态度\\

   & $s_j$ & 愿意观看第j张的DVD的会员数  \\

   & $p_j$ & 会员愿意观看第j种DVD的概率  \\

   & $x_{ij}$ & 第i个会员是否被分配到第j张DVD  \\

   & $a_{ij}$ & 第i个会员对第j张DVD的满意度  \\

   & $k_{i}$ & 第i个会员有没有被分配到DVD  \\

   & $c_j$ & 第j种DVD购买的数量  \\

   & $b_{ij}$ & 第i个会员是否返还第j张DVD  \\

   & $w_j$ & 两阶段共需要购买的j种DVD数量  \\

   & $z_{ij}$ & 第二阶段针第i个会员需求的第j种DVD  \\

\bottomrule

\end{tabular}

\end{table}

\begin{table}[H]

\caption{会员对5种DVD的愿意观看概率}

\centering

\begin{tabular}{|c|c|c|c|c|c|}

  \hline

  $\mbox{DVD名称}$ & $\mbox{DVD1}$ & $\mbox{DVD2}$ & $\mbox{DVD3}$ & $\mbox{DVD4}$ & $\mbox{DVD5}$\\

  \hline

  $\mbox{第j张愿意观看概率}$ & $0.2$     & 0.1 & $0.05$  & $0.025$ & $0.01$  \\

  \hline

\end{tabular}

\end{table}

\begin{table}[H]

  \centering

  \caption{前30个会员分配情况}

    \begin{tabular}{r|rrr||r|rrr}

    \toprule

    会员编号 &DVD1&DVD2&DVD3& 会员编号&DVD1&DVD2&DVD3 \\

    \midrule

    C001  & D008  & D041  & D098  & C016  & D010  & D084  & D097 \\

    C002  & D006  & D044  & D062  & C017  & D047  & D051  & D067 \\

    C003  & D032  & D050  & D080  & C018  & D041  & D060  & D078 \\

    C004  & D007  & D018  & D041  & C019  & D066  & D084  & D086 \\

    C005  & D011  & D066  & D068  & C020  & D045  & D061  & D089 \\

    C006  & D019  & D053  & D066  & C021  & D045  & D050  & D053 \\

    C007  & D026  & D066  & D081  & C022  & D038  & D055  & D057 \\

    C008  & D031  & D035  & D071  & C023  & D029  & D081  & D095 \\

    C009  & D053  & D078  & D100  & C024  & D037  & D041  & D076 \\

    C010  & D041  & D055  & D085  & C025  & D009  & D069  & D094 \\

    C011  & D059  & D063  & D066  & C026  & D022  & D068  & D095 \\

    C012  & D002  & D031  & D041  & C027  & D050  & D058  & D078 \\

    C013  & D021  & D078  & D096  & C028  & D008  & D034  & D082 \\

    C014  & D023  & D052  & D089  & C029  & D026  & D030  & D055 \\

    C015  & D013  & D052  & D085  & C030  & D037  & D062  & D098 \\

    \bottomrule

    \end{tabular}%

  \label{tab:addlabel}%

\end{table}%

\begin{equation}

E=0.6*+0.44*=1.6

\end{equation}

\begin{equation*}

t_{ij}=

  \begin{cases}

 ,&\text{第i个会员愿意观看第j种DVD}\\

 ,&\text{第i个会员不愿意观看第j种DVD}\\

  \end{cases}

\end{equation*}

$$s_j=\sum_{i=}^{}t_{ij},j=,,\ldots,$$

\begin{equation}

\lim_{n \to \infty}P(\frac{\eta_{x}-np}{\sqrt{np(-p)}}\leq x)=\int _{-\infty}^{x}\frac{}{\sqrt{\pi}}e^{-\frac{t^}{}} dt

=\Phi (x)

\end{equation}

\par 
\newpage

\textbf{()三个月内95\%}

$$X=\begin{pmatrix}

x_{,}&x_{,}&\ldots&x_{,}\\

x_{,}&x_{,}&\ldots&x_{,}\\

\vdots &\vdots & &\vdots\\

x_{,}&x_{,}&\ldots&x_{,}\\

\end{pmatrix}$$

$$ \left(\begin{array}{c}

X_1  \\

X_2 \\

\dots \\

X_p

\end{array}\right)

=

 \left(\begin{array}{cccc}

a_{} & a_{} & \dots &a_{1m} \\

a_{} & a_{} & \dots &a_{2m} \\

\dots & \dots & \dots &\dots \\

a_{p1} & a_{p2} & \dots &a_{pm} \\

\end{array}\right)

 \left(\begin{array}{c}

F_1  \\

F_2 \\

\dots \\

F_m

\end{array}\right)

\left(\begin{array}{c}

\varepsilon_1  \\

\varepsilon_2 \\

\dots \\

\varepsilon_p

\end{array}\right)

$$

\quad

\begin{center}

$$max\sum\limits_{i=}^{}\sum\limits_{j=}^{} = x_{ij}a_{ij} $$

\begin{equation*}

s.t.

\begin{cases}

\sum\limits_{j=}^{}x_{ij} = 3k_{i}\\

\sum\limits_{i=}^{}x_{ij} \leq num_j,j = ,,\ldots, \\

x_{ij},k_{ij} =  \text{或} ;  \\

i = ,,\ldots,;  \\

j = ,,\ldots,  \\

\end{cases}

\end{equation*}

\end{center}

\widehat{D_t}

\bibitem{}

\zihao{}\songti\thesection {附录1 \quad  第二题lingo实现代码}

\begin{verbatim}

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