Agent-Based Simulation of School Choice in Bandung, Indonesia: The by xld14276

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                              The Asian Journal of Technology Management

                                 Volume 2, Number 1, June 2009, 14-24


      Agent-Based Simulation of School Choice in Bandung, Indonesia:
     The Emergence of Enrollment Pattern Trough Individual Preferences


                Dhanan Sarwo Utomo, Utomo Sarjono Putro and Pri Hermawan
           School of Business and Management, Institut Teknologi Bandung, Indonesia


                                           ABSTRACT

This study is motivated by the reality that school choice programs that is currently implemented in
Bandung that, always resulting student deficit (lack of student) in some schools. In this study, a
mechanism that can describe how the enrollment pattern in a school choice program emerge as a
result of individual preferences of the prospective students, is constructed. Using computer
simulation, virtual experiments are conducted. In these experiments, the enrollment patterns and
the number of student deficit that were resulted by various school choice program configurations
are analyzed. Based on the experiment results, modification of the current program that can
minimize the number of student deficit can be purposed.

Keywords: agent-based simulation, school choice, computer simulation

1.    Introduction                                         The information technology that is used to
                                                            manage applicants administration data. For
1.1 School Choice Problem in Indonesia                      example, central data base that can be
     As an impact of the implementation of                  accessed via internet is used to manage
Indonesian Republic Law No.32 2004, each                    applicants administration data in Jogjakarta
local government has an obligation to design                and DKI Jakarta (Rusqiyati, 2008).
suitable education policy for their region. One            They way the schools are classified or
of the obligations that should be met is to                 clustered. For example, in Bogor the
design a school choice program that is suitable             schools are categorized or clustered based
to be implemented in their region. School                   on their achievement from previous year
choice program is a program that facilitates the            experience while in Takengon the schools
parents and their children to select schools                are clustered based on their geographic
(Brown, 2004; Betts, Rice, Zau, Tang, &                     location (Muisman, 2003).
Koedel, 2006). In Indonesia this kind of                   The number of school to which the
program is also known as the acceptance of                  prospective students may enroll. For
new students program (is abbreviated as PSB in              example, students in Yogyakarta may
Bahasa).                                                    enroll to three schools while in Bandung,
                                                            students is only allowed to enroll to two
    From year to year, school choice program                schools (Kompas, 2007).
in every region, especially for senior high                Admission criteria that is used to determine
school, is vary in the term of:                             whether an applicant is accepted or not.


                                                   14
    For instance, a number of regions in                 Simulation: Dealing with Complexity, 2004).
    Indonesia use national examination score as          This non linear interaction is caused by human
    the admission criteria. In another region            societies characteristic that can recognized and
    like Bekasi a combination between national           changed their behavior (adaptive) in order to
    examination score and test score that held           respond to (Gilbert, Emergence in Social
    by each school is used as admission criteria         Simulation, 1995) the new implemented
    (Pos Kota, 2008).                                    system. Because of this human society
                                                         characteristic, the impact that will occur from
    Education experts and practitioners in               the experiment will be very hard to predict
Indonesia argue that, there are two criteria of a        (Agar, 2004).
good high school choice program, namely:
                                                         1.1 Purpose of the Study
       Fair and free from corruption, collusion
                                                               This study aims to purpose a mechanism
        and nepotism practice (Junaidi, 2008;
                                                         that can describe how the enrollment pattern in
        Suwarja, 2003; Vardhana, 2008).
                                                         a school choice program, can emerge from the
       The incoming students are distributed
                                                         individual preferences of prospective students.
        evenly to all public and private school
                                                         The case that is selected in this study is the
        in that region (Suryadi, 2008; Fathoni,
                                                         school choice program in Bandung in 2008.
        2008).
                                                         Using computer simulation, experiments with
     Unfortunately, school choice programs               various system configuration and agent’s
that are currently applied in many cities in             characteristics are conducted. Specifically,
Indonesia still cannot meet these criteria. There        these experiments aim to show the enrollment
are many schools that suffer from lack of                patterns and the number of student deficit that
students (Antara, 2008; Radar Cirebon, 2008;             may occur. Based on the experiments results,
Banjarmasin Post, 2009). On the other hand,              school choice program that can minimize the
many prospective students were rejected                  number of student deficit can be purposed.
because the schools to which they enroll have
                                                         2.   Modeling Process
lack of space (Kompas, 2007; Sumatera
Ekspres, 2007; Surya, 2009). In addition, there
                                                         2.1 Description of School Choice Program
are gaps in the quality of incoming students
                                                               in Bandung
between the favorite schools and less favorite
schools (Siahaan, 2008).                                       In 2008 there are 26 high schools in
                                                         Bandung that participate in the school choice
                                                         program. All of these schools are public high
      To improve the performance of school               school. The rest of the high school and the
choice program, the city governments                     private high schools have obligation to hold
continuously modify the program that is                  their own selection process.
applied. These modifications are usually made
based on the evaluation of the program’s                      26 high schools that participate in the
performance in the previous year (Suara                  school choice program are clustered into five.
Merdeka, 2008; Radar Bogor, 2009). This                  These clusters were made based on the school’s
mode is no other than an experiment that is              previous achievement. Prestigious high schools
conducted in real system. Experimentation in             are placed in the first cluster and less favorite
real system was very risky because a school              schools are placed in the last cluster. Each
choice program involves a complex social                 applicant may only choose two schools from
process. A complex social process consists of            different cluster. They have seven days to
many non linear interactions among elements,             consider and submit their application to the
in this case human (Gilbert, Agent-based Social          selected school. Each applicant was able to
                                                         access daily information about the number and


                                                    15
national examination score of all applicants that        all school and, they will update this information
already submit their application.                        regularly.

      There is no specific standard that have to              In the second step, the applicant will
be met by an applicant. The lowest national              consider the school that is most appropriate for
examination score of a student that was                  them. This process can be represents by the
accepted in the previous year (known as                  process of maximizing school’s aggregate
passing grade) usually become guidance for the           benefit according to applicant (Belfield &
applicants to select a school. Schools with high         Levin, 2002).
passing grade usually interpreted as a
prestigious schools, which is commonly
avoided applicants with low national                          In the last step the applicant will consider
examination score.                                       whether he or she will be qualified in the
                                                         selected schools (Belfield & Levin, 2002). This
2.2 Applicant Decision Making Process                    process can be considered as the process of
     There are three general steps that are              comparing applicant’s national examination
usually taken by an applicant to decide schools          score to the school’s passing grade.
to which he or she will apply. In the first step,
an applicant will gather information about the           2.3 Purposed Agent-Based Simulation
schools (Tatar & Oktay, 2006). There are six                  The purposed simulation is constructed
kind of information that usually gathered by the         using SOARS (Spot Oriented Agent Role
applicants in this step, namely:                         Simulator) that was developed by Deguchi
                                                         Laboratory in Tokyo Institute of Technology.
   Applicant’s residence location (Henrickson,          There are two types of object in SOARS, spot
    2003)                                                and agent.
   Distance travelled to school ( (Henrickson,
    2003; Tatar & Oktay, 2006)                                 In this model an agent represents an
   The number of application that have been             applicant in the school choice program. The
    sent, represent the number of competitors            total number of agents is 2850, that represent
    they will face.                                      6% of the total applicants in 2008. Agents are
   Applicant’s achievement represent by the             categorized into three types:
    national examination score.
                                                            Neutral agents: represent applicants who
   Applicant’s expectation about the school’s               believe that the minimum score they should
    quality (Henrickson, 2003; Tatar & Oktay,                have to be qualified in a school can fully be
    2006), that is based on the school’s                     described by the previous year passing
    previous achievements.                                   grade. Therefore, they will apply to a
   The minimum qualifications that are                      school only if their score is higher than the
    accepted in that school (Tatar & Oktay,                  previous year passing grade of that school.
    2006).                                                  Pessimistic agents: represent the applicants
     Applicants have autonomy to determine                   who disbelieve that the minimum score
the importance of each school attributes.                    they should have can be fully represented
                                                             by the previous year passing grade.
     In reality, the applicants will not have                Therefore, they make some adjustment to
complete information of all available schools.               anticipate in case the minimum the
But, in order to simplify the problem at hand                minimum score needed to be qualified
the simulation that will be constructed is based             increase.
on the assumption that, all applicants (agents)             Optimistic agents: this type of agent also
are able to gather complete information about                disbelieve that the minimum score they


                                                    16
     should have can be fully represented by the         in Indonesia revealed that there is a linear
     previous year passing grade. But, they dare         relationship between the passing grade score
     to make speculation and apply to the top            and the school’s expected education quality
     school of their choice.                             (Muisman, 2003; Purnawan, 2005; Priyanta,
                                                         2008; Rijanto, Hadi, & Relisa, 2008).
     There are two types of spot that are                Therefore, the following linear relationship is
defined in this model. The first is the home             used to assign image score to each school spot
spot in which the participants stored all                in the simulation.
information during the simulation and the
second, school spot to which the applicants                   ������������ = 7.651������������ − 114.765             (1)
enroll. The number of school spot is 26 (equal
to the number of schools that participate in the               The fifth attribute of the school spot is the
school choice program in 2008) and the number            number of applicants (���������������� ). This variable is an
of home spot is 2850 (equal to the number of             integer counter of the agents who enroll to
agent). The next section describes mechanisms            school j at each time step. At the beginning of
and attributes owned by each spot and agent.             the simulation, this variable is initiated as zero.
1)   Attributes of School Spot                                The sixth attribute of the school is the
     The first attribute for the schools is x and        cluster number (������������ ). This attribute is put into
y position in a grid of Bandung City. In order           the simulation as integer based on the school’s
to assign schools position, Bandung city is              cluster data in 2008.
divided into 6 X 4 grids. Then, the x and y
position for school spot is assigned based on the             The seventh attribute of the school is the
actual position of the given school in the real          minimum applicant’s score ( ���������������� ). This
world.                                                   variable indicates the lowest national
     The second attribute of the schools is              examination score of all agents who enroll at
passing grade score (PGj). A passing grade               school j at time t. At the beginning of the
score indicate the lowest national examination           simulation, this variable is initiated as zero.
score that was accepted in a certain school in
the previous year. In this study, passing grade
score of each school is assign based on the
result of the school choice program in 2007.

     The third attributes of the school spot is
capacity (Cj). School’s capacity indicates the
number of student that can be admitted by a
certain school. The capacity of each school
spot is assigned based on the data in 2008.

     The fourth attributes of school spot is
image score (IMj). Image score indicates the
expected education quality of schools based on                  Figure 1 6 x 4 grid of Bandung city
the perception of the agents. This attributes is
assigned as a real number from 0 to 100. The                   The eighth attribute of the school spot is
higher image score, the higher the expected              the competitor score (���������������� ). Competitor score is
education quality of the given school. Although          a real number that range from 0 to 100. This
there is no research that directly measure image         variable indicates the degree of competition that
of the schools in Bandung city, some research            will be faced by agents if they enroll to school


                                                    17
j. This variable is inserted in the simulation as                     of 0 is assign if ������������ is equal to the diameter of
a function of the capacity of school j and, the                       the grid (7.211). In order to assign the distance
number of applicants in school j in the previous                      score of each school the following equation is
day.                                                                  used.


                       100 ∗ �������� − ����������������               (2)              ������������ = −13.867 ∗ ������������ + 100           (4)
        ����������������+1   =
                              ��������
                                                                           The third attribute of the home spot are
      The last attribute of the school spot are                       two arrays to record index of the schools that
                                                                      are chosen by agent his or her first (��������1���� ) and
two arrays to store the indexes ������������ and
                                                                      second (��������2���� ) choice. At the beginning of the
national examination scores ������������ of the agents                      simulation, both of these arrays are initiated as
who have enroll to school j. At the beginning                           .
of the simulation both of these arrays are
initiated as .
                                                                            The last attribute of the home spot are two
2)     Attributes of Home Spot                                        arrays to record cluster code of the schools that
                                                                      are chosen by agent as his or her first (��������1���� )
      Just like the school spots, each home spot                      and second (��������2���� ) choice. At the beginning of
is also equipped with the x and y position. To                        the simulation, both of these arrays are initiated
assign the x and y position of home spots, the                        as .
population densities at each point on the grid
are calculated. The population densities are                          3)   Agent’s Attributes
calculated by dividing the population in each                              The first attribute of the agents is their
point by the total population in Bandung. After                       national examination score (�������� ). The minimum
that, the coordinate of each home spot is                             national examination score that should be
assigned using roulette wheel method in which,                        achieved in order to be graduated from junior
the population density serves as the probability.                     high school is 22 while, the maximum national
                                                                      examination score that can be achieved is 40.
     The second attribute of the home spot is its                     Therefore, in this study the national
distance to each school (������������ ). This attribute is                  examination score of each agent is assigned as a
calculated using Euclidean distance formula as                        random number from 22 to 40.
the following:
                                                                           The second attribute of the agents is the
                                                                      weights for each school attribute namely,
                                   2                   2   (3)        distance weight (������������ ), image weight (���������������� )
     ������������ =        �������� − ��������       + �������� − ��������                  and competitor weight (���������������� ). All of these
                                                                      weights are assigned as a random number from
        Where, ������������ is the distance from home i to                  0 to 1 but, the total of all weights may not
school j, �������� is the position of school j in x axis,                 exceed 1. In order to fulfill this constraint, the
                                                                      following steps are taken.
 �������� is the position of home i in x axis, �������� is the
position of school j in y axis and �������� is the
position of home i in y axis.                                                 ������������ = ������������������������[0,1]            (5.a)
    The distance to each school is then                                             ∆= 1 − ������������                   (5.b)
converted into a score ( ������������ ) from 0 to 100.                             ���������������� = ������������������������[0, ∆]          (5.c)
Score of 100 is assign if the ������������ = 0 and score                             ���������������� = ∆ − ����������������              (5.d)


                                                                 18
                                                                      The aggregate benefit scores of all schools
     The third attribute for the agents is agent’s              are then sorted from the school with the highest
tolerance ( �������� ). Agent's tolerance indicates                 aggregate benefit to the school with the lowest
agent’s boldness to speculate on the                            aggregate benefit. Agent i then determines the
fluctuations of passing grade score that may                    school to which he or she will enroll. The
occur. For neutral agents, tolerance value is set               evaluation process is started from the school
as zero.                                                        with the highest aggregate benefit to the school
                                                                with the lowest aggregate benefit. In this
                     �������� = 0                      (6.a)        process agent i will calculate the difference
                                                                between his or her national examination score
      For optimistic agents, tolerance value is                 and the passing grade of school j plus agent’s
initiated as a negative random number with                      tolerance.
restriction that, the total of tolerance value and
agent’s national examination score may not less
than 22 (since there will be no school which                             ����1�������� = �������� − ������������ + ��������          (8)
passing grade is less than 22).
                                                                     If ����1�������� > 0 then, agent i will chose school
     �������� = ������������������������ [0, 22 − �������� ]           (6.b)        j. If ����1�������� < 0 then, agent i will not chose
                                                                school j and, will continue the evaluation
      For pessimistic agents, tolerance value is
                                                                process to the next best school. If ����1�������� = 0
initiated as a positive random number with
restriction that, the total of tolerance value and              then, agent i evaluate whether he or she has
agent’s national examination score may not                      better chance to be admitted than the applicant
                                                                with the lowest national examination score at
greater than 40 (since there will be no school
                                                                school j.
which passing grade is greater than 40).

     �������� = ������������������������ [0, 40 − �������� ]           (6.c)                     ����2�������� = �������� − ����������������           (9)

4)    Simulation Process                                             If ����2�������� > 0 then, agent i will chose school
      At every time step, from the 1st day until                j else, agent i will continue the evaluation
the 7th day, as long as ��������1���� = ∅ or ��������2���� = ∅,             process to the next best school.
agent i will visit all school. Agent i then will
record the passing grade score ( ������������ ),                             Every time an agent chose a school, he or
                                                                she will check whether he or she is able to
competitor score ( ���������������� ), image score ( ������������ ),
                                                                enroll to the chosen school. If ��������1���� = ∅ and
cluster code (������������ ) and the minimum applicant’s              ��������2���� = ∅ then, agent i will store the index of
score (���������������� ) from each school. These variables             school j in array of first choice index ��������1���� =
are then stored in agent i’s home.                              ���� and, the cluster code of school j in the array of
                                                                first choice cluster ��������1���� = ������������ . If ��������1���� ≠
     In each home spot, agents calculated the
                                                                ∅ and ��������2���� = ∅ and ������������ ! ∈ ��������1���� then, agent i
aggregate benefit of all school using additive
model (Goodwin & Wright, 2004).                                 will store the index of school j in array of
                                                                second choice index ��������2���� = ���� and, the
                                                                cluster code of school j in the array of second
      ���������������� = ������������ ������������ + ���������������� ������������    (7)         choice cluster ��������2���� = ������������ . If school j
                             + ���������������� ����������������                cannot satisfy these conditions then, agent i will
                                                                chose new school.
    Where, ���������������� is the aggregate benefit of                      After the evaluation process, agents will
school j according to agent i.                                  enroll to the schools whose index is stored in


                                                           19
array ��������1���� and ��������2���� . Each agent who enrolls                only pessimistic agents, the third involve only
to school j will increase the number of applicant                 optimistic agents and in the last scenario all
at school j (���������������� ) by 1. Agent’s index and                   types of agents are involved with equal
national examination score then will be stored                    proportion.
in array of applicant index ������������ and array of
                                                                       In the first experiment observed that in the
applicant score ������������ at school j.                               current school choice program, student deficit
                                                                  are always occurred in every scenario. The
     After agents enroll to the schools of their                  number of student deficit increases drastically
choice, each school then will update the                          in the second scenario, when all agents are
competitor score ���������������� and the minimum                         pessimistic. This is happened because
applicant’s score ���������������� for the next iteration.                pessimistic agents tend to avoid competition,
The new competitor score in each school is                        indicated by a low total number of applicants in
calculated using (2).                                             each cluster.

         To update the minimum applicant’s score                        In the second experiment, the number of
in each school, both ������������ and ������������ are sorted                 cluster is reduced into three clusters. This
based on the applicant’s score, from the highest                  program performs better in eliminating the
score to the lowest score. If ���������������� ≤ �������� then, the           number of student deficit in the second and
                                                                  fourth scenario. But, this program performs
���������������� is equal to the applicant’s score who is in
                                                                  worse than the current school program in the
the ���������������� rank. If ���������������� > �������� then the ���������������� is        first and third scenario.
equal to the applicant’s score who is in the ��������
rank. After these processes are finished, the
                                                                                                               Number of Applicant in Each
iteration counter is increased by 1.
                                                                                                                        Cluster
       At the end of the school choice program,                                                              1000
both ������������ and ������������ in all schools are sorted based
                                                                                       Number of applicant




                                                                                                                                              Scenario 1
on the applicant’s score, from the highest score
                                                                                                               500                            Scenario 2
to the lowest score. If ���������������� ≤ �������� then, the
school j will admit all agents who enroll to                                                                                                  Scenario 3
school j. If ���������������� > �������� then, the school j will                                                               0
                                                                                                                                              Scenario 4
admit agents whose rank is less than or equal to                                                                            I   II III IV V
�������� .
                                                                            Figure 2 The enrollment pattern in the first
                                                                                           experiment
3.    Experiment Process
     In this study three experiments are                                                                     Number of Student Deficit in each
                                                                        100
                                                                                                                         cluster
                                                                   Number of deficit




conducted. The aim of the first experiment is to
test the performance of the current program                                                                                                   Scenario 1
(five clusters with two choices) under various                                   50                                                           Scenario 2
population variations. The second and third                                                                                                   Scenario 3
experiment aimed to test the performance of the                                                                                               Scenario 4
                                                                                           0
school choice program using different number
of cluster.                                                                                                    I       II       III  IV   V
                                                                                                                                Cluster
     In each experiment, four kinds of                               Figure 3 Student deficit in each cluster in the
scenarios are carried out. The first scenario                                      first experiment
involve only neutral agents, the second involve


                                                             20
                                                         4.       Conclusions and Further Research
           Number of Applicant in Each
                    Cluster                              4.1 Conclusions
  1000                                                        In this study mechanism that can describe
                                      Scenario 1         how the enrollment pattern in a school choice
   500                                Scenario 2         program can emerge from the individual
                                                         preferences of prospective students is purposed.
                                      Scenario 3
       0                                                 Using computer simulation virtual experiments
                 I       II   III     Scenario 4         can be conducted. These experiments can give
                                                         insight to the decision maker about the
Figure 4 The enrollment pattern in the second            enrollment pattern and the number of student
                experiment                               deficit in each cluster under the variation of
                                                         population proportion and number of cluster.
       Number of Student deficit in Each                      From the experiment results it can be
                   Cluster                               concluded that the current school choice
  20                                                     program is very sensitive to the variation of
                                       Scenario 1        population proportion and the number of
  10                                   Scenario 2        cluster. The current school choice program is
                                                         vulnerable in resulting high number of student
   0                                   Scenario 3
                                                         deficit especially, when the number of
             I          II     III     Scenario 4        pessimistic agents is high. In order to minimize
                                                         the number of student deficit in each cluster,
 Figure 5 Student deficit in each cluster in the         the decision maker in Bandung can increase the
              second experiment                          number of cluster that is used, from five
                                                         clusters to six clusters.
     In the third experiment, the number of
cluster is increased into six clusters. This             4.2 Further Research
program performs better in minimizing student                 This study has several limitations that
deficit in all scenarios. The deficit only               should be improved in the future. The first
occurred in the third scenario, with less number         limitation is that the experiment result is still
compare to the two previous programs.                    not yet validated externally. In the next study,
                                                         we aim to compare the enrollment pattern and
                                                         the number of student deficit in each cluster, to
                                                         the data taken from the real world.
           Number of Applicant in Each
                    Cluster                                             Number of Student Deficit in
  1000                                 Scenario 1                             Each Cluster
   500                                 Scenario 2             6
                                                                                                   Scenario 1
       0                               Scenario 3             4
                                                                                                   Scenario 2
             I       II III IV V VI    Scenario 4             2
                                                                                                   Scenario 3
                                                              0
  Figure 6 The enrollment pattern in the third                                                     Scenario 4
                 experiment                                         I     II   III   IV   V   VI

                                                          Figure 7 Student deficit in each cluster in the
                                                                        third experiment


                                                    21
      The second limitation of this study is that,        Brown, D. J. (2004). School Choice Under
the agents are only interact each other through           Open Enrollment. Kelowna, Canada: Society of
the school spots. The agents are also assumed             the Advancement of Excellence in Education.
to have complete information about all schools
attributes. Studies have revealed that in a               Dillon, E. (2008). Plotting School Choice: The
school choice program, agents have incomplete             Challenges of Crossing District Lines.
information about the school’s attribute.                 Washington, D.C.: Education Sector.
Agents will rely on their social networks (for
example: ex-schoolmate, parent’s co-worker, or            Dougherty, J., Harrelson, J., Maloney, L.,
family member) in gathering more information              Murphy, D., Smith, R., Snow, M., et al. (2007).
about the school attributes (Holme, 2002;                 School Choice in Suburbia: Public School
Ramsay & Sanchez, 2006; Dougherty, et al.,                Testing and Private Real Estate Markets.
2007; Dillon, 2008). In the next study we aim             “Mapping School Choice” panel, Division L.
to improve the purposed mechanism, in order to            American Educational Research Association.
facilitate these behaviors.
                                                          Fathoni. (2008, July 1). Sistem penerimaan
                                                          siswa baru sepanjang tahun. Retrieved July 25,
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