﻿ 面向高校内部的平行两阶段运营效率评价模型
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 同济大学学报(自然科学版)  2019, Vol. 47 Issue (4): 575-582.  DOI: 10.11908/j.issn.0253-374x.2019.04.018 0

### 引用本文

LIU Run, YOU Jianxin, YU Anyu. Parallel Two-stage Operational Efficiency Evaluation Model for Inner University[J]. Journal of Tongji University (Natural Science), 2019, 47(4): 575-582. DOI: 10.11908/j.issn.0253-374x.2019.04.018

### 文章历史

Parallel Two-stage Operational Efficiency Evaluation Model for Inner University
LIU Run , YOU Jianxin , YU Anyu
School of Economics and Management, Tongji University, Shanghai 200092, China
Abstract: An efficiency evaluation of inner structure for universities was proposed based on data envelopment analysis (DEA). The operational efficiency of the universities was divided into operational stage and profitability stage. The efficiency of the profitability stage was decomposed into educational and research efficiencies. Both efficiencies were estimated for parallel structure system. To prove the rationality and effectiveness, the case study of a specific 985-project university was investigated based on the data of its inner colleges. The method provides more effective operational management suggestions for the universities.
Key words: efficiency evaluation    university operational efficiency    data envelopment analysis (DEA)    parallel system    two-stage network model

1 方法

 图 1 高校内部两阶段系统效率转化过程 Fig.1 Efficiency conversion for two-stage system of inner university

 $\begin{array}{l} {\theta _i} = \min \frac{{{\omega _1}\left( {1 - \frac{1}{3}\left( {\frac{{s_T^ - }}{{{T_i}}} + \frac{{s_E^ - }}{{{E_i}}} + \frac{{s_{{R_i}}^ - }}{{{R_{{\rm{i}}i}}}}} \right)} \right) + {\omega _2}}}{{{\omega _1}\left( {1 + \frac{1}{3}\left( {\frac{{s_P^ + }}{{{P_i}}} + \frac{{s_A^ + }}{{{A_i}}} + \frac{{s_L^ + }}{{{L_i}}}} \right)} \right) + {\omega _2}\left( {1 + \frac{1}{2}\left( {\frac{{s_{{E_{\rm{m}}}}^ + }}{{{E_{{\rm{m}}i}}}} + \frac{{s_{{R_{\rm{p}}}}^ + }}{{{R_{{\rm{p}}i}}}}} \right)} \right)}}\\ {\rm{s}}{\rm{.}}\;{\rm{t}}{\rm{.}}\;\;\;\sum\limits_{j = 1}^n {{\lambda _j}} {T_j} + s_T^ - = {T_i}, \sum\limits_{j = 1}^n {{\lambda _j}} {E_j} + s_E^ - = {E_i}, \sum\limits_{j = 1}^n {{\lambda _j}} {R_{ij}} + s_{{R_i}}^ - = {R_{ii}}, \\ \;\;\;\;\;\;\;\sum\limits_{j = 1}^n {{\lambda _j}} {P_j} - s_P^ + = {P_i}, \sum\limits_{j = 1}^n {{\lambda _j}} {A_j} - s_A^ + = {A_i}, \sum\limits_{j = 1}^n {{\lambda _j}} {L_j} - s_L^ + = {L_i}, \\ \;\;\;\;\;\;\;\sum\limits_{j = 1}^n {{\lambda _j}} {L_j} = \sum\limits_{j = 1}^n {{\eta _j}} {L_j}, \sum\limits_{j = 1}^n {{\lambda _j}} {P_j} = \sum\limits_{j = 1}^n {{\eta _j}} {P_j}, \sum\limits_{j = 1}^n {{\lambda _j}} {A_j} = \sum\limits_{j = 1}^n {{\eta _j}} {A_j}, \\ \;\;\;\;\;\;\;{L_i} = \sum\limits_{j = 1}^n {{\eta _j}} {L_j}, \sum\limits_{j = 1}^n {{\eta _j}} {R_{{\rm{p}}j}} - s_{{R_{\rm{p}}}}^ + = {R_{{\rm{p}}i}}, {P_i} = \sum\limits_{j = 1}^n {{\eta _j}} {P_j}, \\ \;\;\;\;\;\;\;{A_i} = \sum\limits_{j = 1}^n {{\eta _j}} {A_j}, \sum\limits_{j = 1}^n {{\eta _j}} {E_{{\rm{m}}j}} - s_{{E_{\rm{m}}}}^ + = {E_{{\rm{m}}i}}, \sum\limits_{j = 1}^n {{\eta _j}} = 1, \\ \;\;\;\;\;\;\;{\lambda _j}, {\eta _j}, s_T^ - , s_E^ - , s_{{R_{\rm{i}}}}^ - , s_P^ + , s_A^ + , s_L^ + , s_{{E_{\rm{m}}}}^ + , s_{{R_{\rm{p}}}}^ + \ge 0, j = 1, 2, \cdots , n \end{array}$ (1)

 $\begin{array}{*{20}{c}} {{\omega _1}\left( {t + \frac{1}{3}\left( {\frac{{S_P^ + }}{{{P_i}}} + \frac{{S_A^ + }}{{{A_i}}} + \frac{{S_L^ + }}{{{L_i}}}} \right)} \right) + }\\ {{\omega _2}\left( {t + \frac{1}{2}\left( {\frac{{S_{{E_{\rm{m}}}}^ + }}{{{E_{{\rm{m}}i}}}} + \frac{{S_{{R_{\rm{p}}}}^ + }}{{{R_{{\rm{p}}i}}}}} \right)} \right) = 1} \end{array}$

 $\begin{array}{l} {\theta _i} = \min \left( {{\omega _1}\left( {t - \frac{1}{3}\left( {\frac{{S_T^ - }}{{{T_i}}} + \frac{{S_E^ - }}{{{E_i}}} + \frac{{S_{{R_{\rm{i}}}}^ - }}{{{R_{{\rm{i}}i}}}}} \right)} \right) + t{\omega _2}} \right)\\ {\rm{s}}.\;{\rm{t}}.\;\;\;{\omega _1}\left( {t + \frac{1}{3}\left( {\frac{{S_P^ + }}{{{P_i}}} + \frac{{S_A^ + }}{{{A_i}}} + \frac{{S_L^ + }}{{{L_i}}}} \right)} \right) + {\omega _2}\left( {t + \frac{1}{2}\left( {\frac{{S_{{E_{\rm{m}}}}^ + }}{{{E_{{\rm{m}}i}}}} + \frac{{S_{{R_{\rm{p}}}}^ + }}{{{R_{{\rm{p}}i}}}}} \right)} \right) = 1\\ \;\;\;\;\;\;\;\sum\limits_{j = 1}^n {\lambda _j^\prime } {T_j} + S_T^ - = t{T_i}, \sum\limits_{j = 1}^n {\lambda _j^\prime } {E_j} + S_E^ - = t{E_i}, \sum\limits_{j = 1}^n {\lambda _j^\prime } {R_{{\rm{i}}j}} + S_{{R_{\rm{i}}}}^ - = t{R_{{\rm{i}}i}}, \\ \;\;\;\;\;\;\;\sum\limits_{j = 1}^n {\lambda _j^\prime } {P_j} - S_P^ + = t{P_i}, \sum\limits_{j = 1}^n {\lambda _j^\prime } {A_j} - S_A^ + = t{A_i}, \sum\limits_{j = 1}^n {\lambda _j^\prime } {L_j} - S_L^ + = t{L_i}, \\ \;\;\;\;\;\;\;\sum\limits_{j = 1}^n {\lambda _j^\prime } {L_j} = \sum\limits_{j = 1}^n {\eta _j^\prime } {L_j}, \sum\limits_{j = 1}^n {\lambda _j^\prime } {P_j} = \sum\limits_{j = 1}^n {\eta _j^\prime } {P_j}, \sum\limits_{j = 1}^n {\lambda _j^\prime } {A_j} = \sum\limits_{j = 1}^n {\eta _j^\prime } {A_j}, \\ \;\;\;\;\;\;\;t{L_i} = \sum\limits_{j = 1}^n {\eta _j^\prime } {L_j}, \sum\limits_{j = 1}^n {\eta _j^\prime } {R_{{\rm{p}}j}} - S_{{R_{\rm{p}}}}^ + = t{R_{{\rm{p}}i}}, \\ {P_i} = \sum\limits_{j = 1}^n {\eta _j^\prime } {P_j}, \\ \;\;\;\;\;\;\;t{A_i} = \sum\limits_{j = 1}^n {\eta _j^\prime } {A_j}, \sum\limits_{j = 1}^n {\eta _j^\prime } {E_{{\rm{m}}j}} - S_{{E_{\rm{m}}}}^ + = t{E_{{\rm{m}}i}}, \sum\limits_{j = 1}^n {\eta _j^\prime } = t, \\ \;\;\;\;\;\;\;\lambda _j^\prime , \eta _j^\prime , S_T^ - , S_E^ - , S_{{R_i}}^ - , S_P^ + , S_A^ + , S_L^ + , S_{{E_{\rm{m}}}}^ + , S_{{R_{\rm{p}}}}^ + \\ \ge 0, t\;无取值约束, j = 1, 2, \cdots , n \end{array}$ (2)

 图 2 高校内部平行系统效率转化过程 Fig.2 Efficiency conversion for parallel system of inner university

 $\begin{array}{l} {\theta _i} = \min \frac{{{\omega _1}\left( {1 - \frac{1}{3}\left( {\frac{{S_T^ - }}{{{T_i}}} + \frac{{S_E^ - }}{{{E_i}}} + \frac{{S_{{R_{\rm{i}}}}^ - }}{{{R_{{\rm{i}}i}}}}} \right)} \right) + {\omega _2} + {\omega _3}}}{{{\omega _1}\left( {1 + \frac{1}{3}\left( {\frac{{s_P^ + }}{{{P_i}}} + \frac{{s_A^ + }}{{{A_i}}} + \frac{{s_L^ + }}{{{L_i}}}} \right)} \right) + {\omega _2}\left( {1 + \frac{{s_{\rm{m}}^ + }}{{{E_{{\rm{m}}i}}}}} \right) + {\omega _3}\left( {1 + \frac{{s_{{R_{\rm{p}}}}^ + }}{{{R_{{\rm{p}}i}}}}} \right)}}\\ {\rm{s}}.\;{\rm{t}}.\;\;\;\sum\limits_{j = 1}^n {{\lambda _j}} {T_j} + {s_T} = {T_i}, \sum\limits_{j = 1}^n {{\lambda _j}} {E_j} + s_E^ - = {E_i}, \sum\limits_{j = 1}^n {{\lambda _j}} {R_{{\rm{i}}j}} + s_{{R_{\rm{i}}}}^ - = {R_{{\rm{i}}i}}, \\ \;\;\;\;\;\;\;\sum\limits_{j = 1}^n {{\lambda _j}} {P_j} - s_P^ + = {P_i}, \sum\limits_{j = 1}^n {{\lambda _j}} {A_j} - s_A^ + = {A_i}, \sum\limits_{j = 1}^n {{\lambda _j}} {L_j} - s_L^ + = {L_i}, \\ \;\;\;\;\;\;\;\sum\limits_{j = 1}^n {{\lambda _j}} {L_j} = \sum\limits_{j = 1}^n {{\mu _j}} {L_j}, \sum\limits_{j = 1}^n {{\lambda _j}} {P_j} = \sum\limits_{j = 1}^n {{\gamma _j}} {P_j}, \sum\limits_{j = 1}^n {{\lambda _j}} {A_j} = \sum\limits_{j = 1}^n {{\gamma _j}} {A_j}, \\ \;\;\;\;\;\;\;{L_i} = \sum\limits_{j = 1}^n {{\mu _j}} {L_j}, \sum\limits_{j = 1}^n {{\mu _j}} {E_{{\rm{m}}j}} - s_{{E_{\rm{m}}}}^ + = {E_{{\rm{m}}i}}, \sum\limits_{j = 1}^n {{\mu _j}} = 1, \\ \;\;\;\;\;\;\;{P_i} = \sum\limits_{j = 1}^n {{\gamma _j}} {P_j}, {A_i} = \sum\limits_{j = 1}^n {{\gamma _j}} {A_j}, \sum\limits_{j = 1}^n {{\gamma _j}} {R_{{\rm{p}}j}} - s_{{R_{\rm{p}}}}^ + = {R_{{\rm{p}}i}}, \sum\limits_{j = 1}^n {{\gamma _j}} = 1, \\ \;\;\;\;\;\;\;{\lambda _j}, {\mu _j}, {\gamma _j}, s_T^ - , s_E^ - , s_{{R_{\rm{i}}}}^ - , s_P^ + , s_A^ + , s_L^ + , s_{{E_{\rm{m}}}}^ + , s_{{R_{\rm{p}}}}^ + \ge 0, j = 1, 2, \cdots , n \end{array}$ (3)

 $\begin{array}{l} {\theta _i} = \min \left( {{\omega _1}t - \frac{{{\omega _1}}}{3}\left( {\frac{{S_T^ - }}{{{T_i}}} + \frac{{S_E^ - }}{{{E_i}}} + \frac{{S_{{R_i}}^ - }}{{{R_{{\rm{i}}i}}}}} \right) + {\omega _2}t + {\omega _3}t} \right)\\ {\rm{s}}.\;{\rm{t}}.\;\;\;{\omega _1}t + \frac{{{\omega _1}}}{3}\left( {\frac{{S_P^ + }}{{{P_i}}} + \frac{{S_A^ + }}{{{A_i}}} + \frac{{S_L^ + }}{{{L_i}}}} \right) + {\omega _2}t + {\omega _2}\frac{{S_{{E_{\rm{m}}}}^ + }}{{{E_{{\rm{m}}i}}}} + {\omega _3}t + \\ {\omega _3}\frac{{S_{{R_{\rm{p}}}}^ + }}{{{R_{{\rm{p}}i}}}} = 1\\ \;\;\;\;\;\;\;\sum\limits_{j = 1}^n {\lambda _j^\prime } {T_j} + {S_T} = t{T_i}, \sum\limits_{j = 1}^n {\lambda _j^\prime } {E_j} + \\ S_E^ - = t{E_i}, \sum\limits_{j = 1}^n {\lambda _j^\prime } {R_{{\rm{i}}j}} + S_{{R_{\rm{i}}}}^ - = t{R_{{\rm{i}}i}}, \\ \;\;\;\;\;\;\;\sum\limits_{j = 1}^n {\lambda _j^\prime } {P_j} - S_P^ + = t{P_i}, \sum\limits_{j = 1}^n {\lambda _j^\prime } {A_j} - S_A^ + \\= t{A_i}, \sum\limits_{j = 1}^n {\lambda _j^\prime } {L_j} - S_L^ + = t{L_i}, \\ \;\;\;\;\;\;\;\sum\limits_{j = 1}^n {\lambda _j^\prime } {L_j} = \sum\limits_{j = 1}^n {\mu _j^\prime } {L_j}, \sum\limits_{j = 1}^n {\lambda _j^\prime } {P_j} = \sum\limits_{j = 1}^n {\gamma _j^\prime } {P_j}, \sum\limits_{j = 1}^n {\lambda _j^\prime } {A_j} = \sum\limits_{j = 1}^n {\gamma _j^\prime } {A_j}, \\ \;\;\;\;\;\;\;t{L_i} = \sum\limits_{j = 1}^n {\mu _j^\prime } {L_j}, \sum\limits_{j = 1}^n {\mu _j^\prime } {E_{{\rm{m}}j}} - S_{{E_{\rm{m}}}}^ + = t{E_{{\rm{m}}i}}, \sum\limits_{j = 1}^n {\mu _j^\prime } = t, \\ \;\;\;\;\;\;\;t{P_i} = \sum\limits_{j = 1}^n {\gamma _j^\prime } {P_j}, t{A_i} = \sum\limits_{j = 1}^n {\gamma _j^\prime } {A_j}, \sum\limits_{j = 1}^n {\gamma _j^\prime } {R_{{\rm{p}}j}} - S_{{R_{\rm{p}}}}^ + \\ = t{R_{{\rm{p}}i}}, \sum\limits_{j = 1}^n {\gamma _j^\prime } = t, \\ \;\;\;\;\;\;\;\lambda _j^\prime , \mu _j^\prime , \gamma _j^\prime , S_T^ - , S_E^ - , S_{{R_{\rm{i}}}}^ - , S_P^ + , S_A^ + , S_L^ + , S_{{E_{\rm{m}}}}^ + , \\ S_{{R_{\rm{p}}}}^ + \ge 0, t\;无取值约束, j = 1, 2, \cdots , n \end{array}$ (4)

 ${E_{{\rm{p}}i}} = \frac{{1 - \frac{1}{3}\left( {\frac{{s_T^ - }}{{{T_i}}} + \frac{{s_E^ - }}{{{E_i}}} + \frac{{s_{{R_{\rm{i}}}}^ - }}{{{R_{{\rm{i}}i}}}}} \right)}}{{1 + \frac{1}{3}\left( {\frac{{s_P^ + }}{{{P_i}}} + \frac{{s_A^ + }}{{{A_i}}} + \frac{{s_L^ + }}{{{L_i}}}} \right)}}$
 ${E_{{\rm{e}}i}} = \frac{1}{{1 + \frac{{s_{{E_{\rm{m}}}}^ + }}{{{E_{{\rm{m}}i}}}}}}$
 ${E_{{\rm{r}}i}} = \frac{1}{{1 + \frac{{s_{{R_{\rm{p}}}}^ + }}{{{R_{{\rm{p}}i}}}}}}$
 ${E_{{\rm{o}}i}} = \frac{{{\omega _1}\left( {1 - \frac{1}{3}\left( {\frac{{s_T^ - }}{{{T_i}}} + \frac{{s_E^ - }}{{{E_i}}} + \frac{{s_{{R_{\rm{i}}}}^ - }}{{{R_{{\rm{i}}i}}}}} \right)} \right) + {\omega _2} + {\omega _3}}}{{{\omega _1}\left( {1 + \frac{1}{3}\left( {\frac{{s_P^ + }}{{{P_i}}} + \frac{{s_A^ + }}{{{A_i}}} + \frac{{s_L^ + }}{{{L_i}}}} \right)} \right) + {\omega _2}\left( {1 + \frac{{s_{{E_{\rm{m}}}}^ + }}{{{E_{{\rm{m}}i}}}}} \right) + {\omega _3}\left( {1 + \frac{{s_{{R_{\rm{p}}}}^ + }}{{{R_{{\rm{p}}i}}}}} \right)}}$

 $\frac{{{\omega _1}\left( {1 - \frac{1}{3}\left( {\frac{{s_T^ - }}{{{T_i}}} + \frac{{s_E^ - }}{{{E_i}}} + \frac{{s_{{R_{\rm{i}}}}^ - }}{{{R_{{\rm{i}}i}}}}} \right)} \right) + {\omega _2} + {\omega _3}}}{{{\omega _1}\left( {1 + \frac{1}{3}\left( {\frac{{s_P^ + }}{{{P_i}}} + \frac{{s_A^ + }}{{{A_i}}} + \frac{{s_L^ + }}{{{L_i}}}} \right)} \right) + {\omega _2}\left( {1 + \frac{{s_{{E_{\rm{m}}}}^ + }}{{{E_{{\rm{m}}i}}}}} \right) + {\omega _3}\left( {1 + \frac{{s_{{R_{\rm{p}}}}^ + }}{{{R_{{\rm{p}}i}}}}} \right)}}$

 $\frac{{1 - \frac{{{\omega _1}}}{3}\left( {\frac{{s_T^ - }}{{{T_i}}} + \frac{{s_E^ - }}{{{E_i}}} + \frac{{s_{{R_{\rm{i}}}}^ - }}{{{R_{{\rm{i}}i}}}}} \right)}}{{1 + \frac{1}{3}\left( {\frac{{s_P^ + }}{{{P_i}}} + \frac{{s_A^ + }}{{{A_i}}} + \frac{{s_L^ + }}{{{L_i}}}} \right) + \frac{{s_{{E_{\rm{m}}}}^ + }}{{{E_{{\rm{m}}i}}}} + \frac{{s_{{R_{\rm{p}}}}^ + }}{{{R_{{\rm{p}}i}}}}}}$

 $\begin{array}{*{20}{c}} {\frac{{{\omega _1}}}{3}\left( {\frac{{s_T^ - }}{{{T_i}}} + \frac{{s_E^ - }}{{{E_i}}} + \frac{{s_{{R_{\rm{i}}}}^ - }}{{{R_{{\rm{i}}i}}}}} \right) \ge 0}\\ {\frac{1}{3}\left( {\frac{{s_P^ + }}{{{P_i}}} + \frac{{s_A^ + }}{{{A_i}}} + \frac{{s_L^ + }}{{{L_i}}}} \right) + \frac{{s_{{E_{\rm{m}}}}^ + }}{{{E_{{\rm{m}}i}}}} + \frac{{s_{{R_{\rm{p}}}}^ + }}{{{R_{{\rm{p}}i}}}} \ge 0} \end{array}$

 $\frac{{1 - \frac{{{\omega _1}}}{3}\left( {\frac{{s_T^ - }}{{{T_i}}} + \frac{{s_E^ - }}{{{E_i}}} + \frac{{s_{{R_{\rm{i}}}}^ - }}{{{R_{{\rm{i}}i}}}}} \right)}}{{1 + \frac{1}{3}\left( {\frac{{s_P^ + }}{{{P_i}}} + \frac{{s_A^ + }}{{{A_i}}} + \frac{{s_L^ + }}{{{L_i}}}} \right) + \frac{{s_{{E_{\rm{m}}}}^ + }}{{{E_{{\rm{m}}i}}}} + \frac{{s_{{R_{\rm{p}}}}^ + }}{{{R_{{\rm{p}}i}}}}}} \le 1$

2 高校学院运营效率分析

3 结语

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