A Slack-Based Measures within Group Common Benchmarking using DEA for Improving the Efficiency Performance of Departments in Universitas Malikussaleh

Measurement of the efficiency of the university performance. Data Envelopment Analysis (DEA) is a data-based performance evaluation method used when multiple inputs and outputs are represented in the Decision-Making Unit (DMU) set. In DEA, when there is a value of Non-Zero Input and Output Slacks then this often means inefficiency. This scalar measure directly with the input of surplus and the output of the short decision of the decision-making unit (DMU). DEA Structure usually apply in general settings, actually DMUs can fall into distinct groups whose members experience similar circumstances. The targets of the Ministry of Research, Technology and Higher Education of the Republic of Indonesia (KEMENRISTEKDIKTI), one of which is the measurement of the efficiency based on the number of lecturers’ research, the efficient use of resources. This study will group each department at the Universitas Malikussaleh using the Group Common Benchmarking approach and then provide suggestions for improvements to each group by using Slack-Based Measures.


Introduction
Data Envelopment Analysis (DEA) is an optimization framework proposed to measure the relative performance of a set of Decision Making Units (DMUs) [1].In recent years, educational institutions such as universities have increasingly focused on improving quality as an effort to improve their prestige.Within the university, the study program is also increasingly focused on ranking especially related to the quality of publications and graduates [2].The result of benchmarking that get from the DEA method in the form of benchmarking values can be studies as a pattern when there is a new data can be directly predicted [3].Data Envelopment Analysis (DEA) is a mathematical model for evaluating Decision Making Units (DMUs) that have multiple inputs and multiple outputs.Note that adding or removing an inefficient DMU will not necessarily change the efficiency of DMU and efficient frontier.Inefficiency scores can only be changed if the efficient frontier is changed.The performance of each DMU depends on the identification of the Efficient Frontier expressed through slack measurement [4].In DEA, when there is a value of Non-Zero Input and Output Slacks then this often means inefficiency [5].If there is a DMU with an efficiency score of one even if it has a zero slack value, it remains categorized as having the same efficiency level as an efficient DMU, even if it is inefficient [4].
Slack Based Measure can measure the efficiency of each department in University and if there is an inefficient department then it will be measured based on slack-based measures to advise aspects that need attention so that the department can be efficient [6].In the DEA Method, we can identify the Efficient Frontier based on a certain subset of efficient DMU, which can be viewed as a common reference set and will minimize the paretoefficient frontier [7].From this new efficient frontier this will find the closest targets to each of DMU [8].This study will group each department at the Universitas Malikussaleh using the Group Common Benchmarking approach and then provide suggestions for improvements to each group by using Slack-Based Measures.In grouping based on efficient frontier it is necessary to pay attention to the quality of grouping [9] and need to pay https://doi.org/10.1051/matecconf/201819716005AASEC 2018 attention to the new patterns that will emerge based on the trend patterns that exist in the process of grouping [10].The results of the study using Slack Based Measure and Group Common Benchmarking are expected to be the entire study program available at Malikussaleh University to be efficient.

Related works
Data Envelopment Analysis (DEA) is a method of performance evaluation and benchmarking of a collection of Decision Making Units (DMU) that are settlementbased with mathematical programming methods [11].O'Neal et al. [12] proposed DMU exclusion of indefinite data to calculate efficiency.This affects the relative effectiveness of other DMU.Undetected data in DEA can use stochastic approaches.Stochastic programming has undergone many theoretical developments since the 1950s, beginning with the pioneering work in Dantzig [13].A Common Set of Weights is the basis for comparing and ranking all decision-making units under the same conditions [14].While CSW and DEA offer two "opposite" approaches to analyzing efficiency, in some situations would be desirable intermediate access between them.For example, Cook and Zhu [15] claim that in many real-world applications where DEA is used, DMUs can be grouped into groups whose members have similar circumstances, and therefore each DMU as a separate entity may not be suitable.Cook et al. [7] develop models that are based on the idea of minimizing distance from the DMU group to the DEA effective limit.On the other side, Tone [5] proposed a method to evaluate the effectiveness based on the deceleration values, a measure based on free movement (SBM) was introduced.When using SBM to evaluate the context, we can have a reasonable stratification of the DMU performance levels.

Methodology
Linear programming model of DEA proposed by CCR can be written as follows.

Slack based measures
We will deal with n DMUs (Decision Making Units) with the input and output matrices  = (  ) ∈   and  = (  ) ∈   , respectively.We assume that the data set is positive, i.e., X > 0 and Y > 0. The production possibility set P is defined as We consider an expression for describing a certain DMU (x 0, y0) as

Group common benchmarking in linear programming
Group common benchmarking model will find the closest targets for the DMU in a given group by minimizing globally weighted distance to their actual inputs and outputs.

Slack based measure within common group benchmarking
Using (8) we can calculate the distance to their paretto efficient frontier for each DMU.For each in efficient DMU, we calculate the distance for input and output.We assume that the DMU Information Technology as the best DMU.The Result can be seen in Table 4.According to (8) the minimum distance to paretto efficient frontier are Input Number of Lecturers and Output Number of Research.For the input we use the maximum distance to subtract with its slack value and the output we use the minimum distance to add with its slack value.
For example we can see the DMU Civil Engineering with the slack value 0.301756.We can increase the output of U2 (Number of Research) according to the slack value using (4) U2 = 5 + 5*0.301756 = 7 We can decrease the input of V2 (Number of Students) according to the slack value using (4) V2 = 747 -747*0.301756= 522 The result of Recomendation of Input and Output for become efficient can be seen in Table 5.

Conclusion
First, the Common Group Benchmarking can be used to determine the minimum value of each input and the inefficient output to the paretto efficient frontier value so that it can be used as a basis for using slack based measure.Second, slack based measure can be used to reduce the maximum value of inputs based on Common Group Benchmarking and can also increase the minimum value of output based on Common Group Benchmarking.Third, the results show that each department can be efficient if we increase the output and reduce the input according to the slack value.Future research is expected

Experimental process 4.1 Data Description Universitas
Malikussaleh has 30 Departments with around 20000 students.The data of 19 Departments (DMU) with two outputs and two inputs is shown in Table1.There are 11 departments are still new, therefore they do not have graduates yet.As a consequence, these 11 departments are not included in Table 1.

Table 1 .
List of DMU with input and output data.It can be seen that DMU1 is efficient, as the value of β is 1.The score of efficiency for all DMUs can be found in Table2.

Table 2 .
Efficiency Score of Each DMU Using DEA

Table 5 .
Recomendation of input and output for every DMU to become efficient.