DOI: 10.2478/V10051-010-0010-5 A System Dynamics Model for Improving Primary Education Enrollment in a Developing Country Chandra Sekhar Pedamallu1,3, Linet Ozdamar2, LS Ganesh3, Gerhard-Wilhelm Weber4, Erik Kropat5 1Currently working at New England Biolabs Inc., Ipswich, MA, USA, pcs.murali@gmail.com 2Yeditepe University, Dept. of Systems Engineering, Kayisdagi, 34755 Istanbul, Turkey, linetozdamar@lycos.com, lozdamar@hotmail.com 3Indian Institute of Technology Madras, Chennai, India, lsg@iitm.ac.in *4Institute of Applied Mathematics, Middle East Technical University, 06531 Ankara, Turkey, gweber@metu.edu.tr 5Department of Informatics, Universität der Bundeswehr, München, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany, erik.kropat@unibw.de The system dynamics approach is a holistic way of solving problems in real-time scenarios. This is a powerful methodology and computer simulation modeling technique for framing, analyzing, and discussing complex issues and problems. System dynamics modeling is often the background of a systemic thinking approach and has become a management and organizational development paradigm. This paper proposes a system dynamics approach for studying the importance of infrastructure facilities on the quality of primary education system in a developing nation. The model is built using the Cross Impact Analysis (CIA) method of relating entities and attributes relevant to the primary education system in any given community. The CIA model enables us to predict the effects of infrastructural facilities on the community's access of primary education. This may support policy makers to take more effective actions in campaigns that attempt to improve literacy. Keywords: developing countries, system modeling, cross impact analysis, simulation, system dynamics, primary education 1 Introduction The first stage of compulsory education is primary or elementary education. In most countries, it is compulsory for children to receive primary education, though in many jurisdictions it is permissible for parents to provide it. The transition to secondary school or high school is somewhat arbitrary, but it generally occurs at about eleven or twelve years of age. Some educational systems have separate middle schools with the transition to the final stage of education taking place at around the age of fourteen. The major goals of primary education are achieving basic literacy and numeracy amongst all pupils, as well as establishing foundations in science, geography, history and other social sciences. The relative priority of various areas, and the methods used to teach them, are areas of considerable political debate. Some of the expected benefits from primary education are the reduction of infant mortality rate, population growth rate, crude birth and death rate, and so on. Because of the importance of primary education, there are several models proposed to study the factors influencing the primary school enrollment and progression. These are logistic regression models (Admassu 2008), poisson regression models (Admassu 2008), system models (Altamirano and van Daalen 2004, Karadeli et al. 2001, Pedamallu 2001, Terlou et al. 1991), behavioral models (Benson 1995, Hanushek et al. 2008) constructed for the context of different countries. Several factors which influence the school enrollment and drop outs are identified in various studies. Some of the vital factors at the macro level are social, economic and logistics factors (Benson 1995), and at the micro level there are parental education, household wealth/income, distance to school, financial assistance to students and quality of school (Admassu 2008, Benson 1995, Rena 2007). An early system dynamics model to investigate the low efficiency of primary education ' Honorary affiliations: Faculty of Economics, Business and Law, University of Siegen, Germany Center for Research on Optimization and Control, University of Aveiro, Portugal Faculty of Science, Universiti Teknologi Malaysia (UTM), Skudai, Malaysia in Latin America is introduced by Terlou et al. (1991). This model investigates the progression through primary school and includes causal chains leading to progression, dropout and repetition of students. Karadeli et al. (2001) develop a model to analyze the future quality of the Turkish educational system based on the budget of the Ministry of National Education. In this model, quality of education and progression of students is influenced by the student to teacher ratio and student to class ratio. Altmirano and van Daalen (2004) propose a system dynamics model to analyze the educational system of Nicaragua and helps in identifying and analyzing the consequences of policies that are aimed at improving the coverage of the different educational programs, reducing illiteracy and increasing the average number of schooling years of the population. This study shows that implementing literacy programs and introducing a program in which families in extreme poverty receive a subsidy has an effect on school coverage as well as on the number of illiterate people. More recently, Hanushek et al. (2008) shows that school quality and grade completion by students are directly linked. The World Bank has published several reports on achieving universal primary education (Bruns et al. 2003, Serge 2009). In particular, Serge (2009) focuses on the infrastructure challenge in Sub-Saharan Africa and the constraints to scale up at an affordable cost. The model proposed in this study aims at identifying the importance of infrastructural facilities on school enrollment and progression beside factors such as quality of teaching and income level. This point is also investigated by Akar (2008) who reports about the infrastructural problems at Turkish schools and their negative impact on students. Here, we present the details about the model constructed for this purpose, the selection of attributes and entities and the simulation results that identify the variables that impact the quality of primary education. The simulation is conducted by using the Gujarat primary education data in India (Pedamallu 2001). 2 The model The model proposed here is developed by using the cross impact analysis method (CIA). The CIA method is one of the most popular systems thinking approach developed for identifying the relationships among the variables defining the systems (Gordon and Hayward 1968, Kane 2002, Weimer-Jehle 2006). This method first was developed by Theodore Gordon and Olaf Helmer in 1966 in an attempt to answer a question whether perceptions of how future events may interact with each other can be used in forecasting. As it is well known, most events and trends are interdependent in some ways. The CIA method provides an analytical approach to the probabilities of an element in a forecast set, and it helps to assess probabilities in view of judgments about potential interactions between those elements. (We refer to Lane (1999) and Mohapatra et al. (1994) for more detailed information on system dynamics modeling.) CIA has been used to model and simulate several real-time problems (for example: Pedamallu et al. 2009, Hayashi et al. 2006). Here, we briefly describe the steps of the CIA method through a block diagram given in Figure 1. 2.1 Definition of the system Systems defined based on entities, which interact with each other and produce some outputs that are either designed or natural. A system receives inputs and converts them through a process and produces outputs. All the outputs of a system need not be desirable. In the present context, the system represents the primary education system. a. Environment Every system functions in an Environment, which provides inputs to the system and receives outputs from the system. In our context, the Environment is the society. b. Structure All systems have a Structure. The 'body' of a system's structure is represented by the entities of the system and their interrelationships or linkages or connections. The entities in our system are defined as follows. 1. student, 2. teacher, 3. parents, 4. educational officials, 5. infrastructure and 6. local community. c. Linkages The linkages among entities may be physical (e.g., facilitates), electro-magnetic (e.g., electrical, electronic and communications systems, and so on), and information-based (e.g., influence, and so on). It is important to try and understand, what linkages exist in the system's structure, which entities are linked with each other, and the implications of these linkages on the behavior of the entities in particular. The entity relationship diagram of the system is illustrated in Figure 2. Exchange of matter, information and/or spirit between two entities causes a change in the state of both entities. This is reflected as system behavior. 2.2 System entities and relationships equations The dynamic change of the system state is referred to as system behavior. The state of a system is an instantaneous snapshot of levels (or, amounts) of the relevant attributes (or, characteristics) possessed by the entities that constitute the system. In all systems, every entity possesses many attributes, but only a few attributes are 'relevant' with respect to the problem at hand. Some attributes are of immediate or short-term relevance while others may be of relevance in the long run. The choice of relevant attributes has to be made carefully, keeping in mind both the short-term and long-term consequences of solutions (decisions). All attributes can be associated with given levels that may indicate quantitative or qualitative possession. The set of attributes identified for the model are given below. Entity 1: Student: 1.1 Level of Enrollment (loe). 1.2 Level of boys dropouts in a school (lbd). 1.3 Level of girls dropouts in a school (lgd). 1.4 Level of repeaters in a school (lr). Figure 1: Block diagram for the steps of the CIA method. Entity 2: Teacher: 2.1 Level of perceived quality of teaching by the Students (lts). 2.2 Level of perceived quality of teaching by the Parents (ltp). Entity 3: Parents: 3.1 Educational level of parents (elp). 3.2 Income level of parents (ilp). 3.3 Level of expectations from school by the parents (leps). Entity 4: Educational officials: 4.1 Level of perceived quality of teaching by the District educational officer (DEO) (ltd). Entity 5: Infrastructure: 5.1 Level of Space and ventilation available in a Classroom (lsv). 5.2 Level of cleanliness and other facilities such as board, mats, table/chair, educational aids (maps, toys, charts, etc.) (lc). 5.3 Level of sanitation facilities for general purpose (for both boys and girls) (ls_g). 5.4 Level of separate sanitation facilities for girls (ls_s). 5.5 Level of drinking water facility available (ldw). 5.6 Level of availability of Playground area and other equipment for children used in playing (lpa). 5.7 Level of bad organisation in the classrooms (lbo): Number of cases in which more than one class is conducted in a single instructional classroom. Number of cases in which more than 40 people are accommodating in a single instructional classroom. Figure 2: Entity relationship diagram for the primary education system. Entity 6: Local community: 6.1 Level of participation of local community (llc). 6.2 Level of awareness of local community about educational benefits (lale). When entities interact through their attributes, the levels of the attributes might change, i.e., the system behaves in certain directions. Some changes in attribute levels may be desirable while others may not be so. Each attribute influences several others, thus creating a web of complex interactions which eventually determine system behavior. In other terms, attributes are variables that vary from time to time. They can vary in the system in an unsupervised way. However, variables can be controlled directly or indirectly, and partially by introducing new intervention policies. The interrelationships among variables should be analyzed carefully before introducing new policies. The following conjectures are valid in the systems approach (the following subsection is borrowed from Kane (2002) paper). a. Modeling and forecasting the behavior of complex systems are necessary if we are to exert some degree of control over them. b. Properties of variables and interactions in large scale system variables are bounded such that: i. System variables are bounded. It is now widely recognized that any variable of human significance cannot increase indefinitely. There must be distinct limits. In an appropriate set of units these can always be set to a value between one and zero: ii. A variable increases or decreases according to whether the net impact of the other variables is positive or negative. iii. A variables' response to a given impact decreases to zero as that variable approaches its upper or lower bound. It is generally found that bounded growth and decay processes exhibit this sigmoidal character. iv. All other things being kept fixed (constant), a variable (attribute) will produce a greater impact on the system as it grows larger (ceteris paribus). v. Complex interactions are described by a looped network of binary interactions (this is the basis of the cross impact analysis). With these conditions in mind consider the following mathematical structure. Since state variables are bounded above and below, they can be rescaled to the range zero to one. This for each variable we have 0 0 for all i = 1, 2, ..., N and all t > 0. Thus the transformation (2) maps the open interval (0, 1) onto itself, preserving boundedness of the state variables (condition 1 above). Equation (3) can be made somewhat clearer if we write it in the following form: Pi«) 1 +A/1 sumof ncgativcimpacts on Xj \ 1 +Af I sumof positiveimpactson;:^ | (4) When the negative impacts are greater than the positive ones, Pi >1 and x decreases, while if the negative impacts are less than the positive ones, Pi < 1and x decreases. Finally when the negative and positive impacts are equal, Pi = 1 and x remains constant. 3 Simulating the system using cross impact analysis There are four steps to follow while implementing the cross impact analysis in our case. First, we conduct the simulation by considering the primary education system without human intervention. Then, we run the same analysis after implementing some selected policy variables such as infrastructure improvement and observe the change in system dynamics. We now describe how we construct the model in the following four steps. Step 1. Set the initial values for attributes. The initial values are obtained from published sources and surveys conducted. Here, we use the survey data reported in Pedamallu (2001). Table 1 illustrates the initial values for various attributes identified in this study. Step 2. Build a cross impact matrix with the identified relevant attributes. Summing the effects of column attributes on rows shows the effect of each attribute in the matrix. The parameters aij can be determined by creating a pairwise correlation matrix after collecting the data, and these can be adjusted by subjective assessment. In Table 2, qualitative impacts are quantified subjectively. The impact of infrastructural facilities on primary school enrollments and progression become visible by running the simulation model. A cross-impact matrix for the attributes listed above is illustrated in Table 3. Step 3. Simulate the system for a number of 50 iterations (m iterations) and tabulate the behavior of each and every attribute in each every iteration. Plot the results on a worksheet. Table 1: Initial values for attributes Attribute Initial value Level of Enrollment (loe) 0.71 Level of Space and ventilation available in a Classroom (lsv) 0.5 Level of cleanliness and other facilities such as board, mats, table/chair, educational aids (maps, toys, charts, etc.) (lc) 0.5 Educational level of parents (elp) 0.35 Income level of parents (ilp) 0.35 Level of expectations from school by the parents (leps) 0.6 Level of perceived quality of teaching by the Students (lts) 0.45 Level of perceived quality of teaching by the Parents (ltp) 0.35 Level of perceived quality of teaching by the District educational officer (DEO) (ltd) 0.35 Level of sanitation facilities for general purpose (for both boys and girls) (ls_g) 0.39 Level of separate sanitation facilities for girls (ls_s) 0.28 Level of availability of Playground area and other equipment for children used in playing (lpa) 0.3 Level of participation of local community (llc) 0.25 Level of awareness of local community about educational benefits (lale) 0.25 Level of repeaters in a school (lr) 0.05 Level of boys dropouts in a school (lbd) 0.2 Level of girls dropouts in a school (lgd) 0.29 Level of bad organisation in the classrooms (lbo) 0.69 Level of drinking water facility available (ldw) 0.34 We apply Step 3 and illustrate, in Figure 3, the simulation of the system for 50 iterations without any policy related variables. It is observed that there is sharp increase in enrollment rate at the beginning phase of the simulation (i.e., for the first 12 iterations). However, there is a steady decrease in the enrollment rate after a certain period of time. The trend is observed in the number of dropouts and repeaters. In order to observe the effect of infrastructure attributes, we include them as policy variables in our next step. The policy variable that is selected involves additional investment in the infrastructure related attributes and elements which we call it as "policy variable". Table 2: Impact rates of variables (attributes). Representation of Impact Value Description ++++ 0.8 Very strong positive effect +++ 0.6 Strong positive effect ++ 0.4 Moderate positive effect + 0.2 Mild positive effect 0 0 Neutral - -0.2 Mild negative effect - - -0.4 Moderate negative effect --- -0.6 Strong negative effect ---- -0.8 Very strong negative effect Step 4. Identify a policy variable to achieve the desired level or state and augment the cross impact matrix with this policy variable with the qualitative assessment of pairwise attribute interactions. Re-simulate the model. In this re-simulation run, we select an improvement in infrastructural facilities as the policy variable. In Table 4, we include the relationship of the policy variable to other attributes. We observe the system for 50 iterations, and check if the desired state is achieved by introducing the policy variable. We then compare the results obtained in the two simulation runs. The detailed rates of change in all variables during the two simulation runs taken before and after adding the policy variable are indicated in the Appendix. Figure 4 illustrates the results of the simulated system after adding the identified policy variable in Step 4. Here, it is observed that the policy variable is effective on improving the enrollment and dropout and repeater rates. Figure 5 illustrates the changes in important variables in detail such as the enrollment rate, level of boy dropouts, level of girl dropouts, level of repeaters, level of sanitation facilities for general purpose, level of separate sanitation facilities for girls, level of bad class organization, and level of space and ventilation available in a classroom. The initial values for these attributes are listed as 0.71, 0.2, 0.29 and 0.05 for enrollment of students, level of boy dropouts, level of girl dropouts, level of repeaters, respectively. After a simulation of 50 iterations without any policy variables, we observe that there is a rise in the enrollment level in the first 12 iterations and then, enrollment starts to decline. A similar kind of trend is observed in the level of boy dropouts in the first four iterations and in the level of girl dropouts in the first five iterations. This early amelioration in the dropout rates is short lived, and both boy and girl dropouts increase steadily thereafter. We validate the simulation results by comparing them with observed levels of enrollment, dropouts and repeaters published by Directorate of Primary Education, Gandhinagar (http://gujarat-educa-tion. gov.in/primary/mahiti/ankadakiyan mahiti/index-en g. htm). After a policy variable related to infrastructure improvements is introduced, a positive impact is observed on the level of space and ventilation available in classrooms, level of cleanliness and other facilities such as board, mats, table/ chair, educational aids (maps, toys, charts, etc.), level of separate sanitation facilities for girls, level of general sanitation facilities, level of available drinking water facilities, and class organization. These impacts are discussed with education officials, parents, students, and other local community people. By introducing this policy variable, the enrollment rate has Table 3: Cross impact matrix for primary education system. improved steadily from an initial value of 0.71 to unity in a few iterations. Further, the level of repeaters increased to a value of 0.12 from an initial value of 0.05 in first 14 iterations, and then declined thereafter. This is logical in the sense that an improvement in the infrastructure doesn't have an instant impact on the level repeaters, but it would have an instant impact on the enrollment rate because students and parents are more eager to have the children attend a nice looking healthy school. The level of bad organization in the classroom is not greatly affected by the improvement in infrastructure facilities because there are several other attributes that influence this variable such as the level of perceived quality of teaching by the district educational officer and the number of teachers available for teaching. Consequently, the level of bad classroom organization is reduced from 0.69 to 0.57 in the second simulation run. In previous studies found in the literature, it is observed that the quality and the number of teachers have significant impacts on the enrollment, dropouts and repeaters. The design of our proposed model is sufficiently flexible to accommodate those impacts in future studies. To summarize, in this study, we find that infrastructural facilities have significant impacts on the enrollment, dropout and repeater rates. This study is not meant to exclude any other important variables such as gender and parental status that affect school attendance and dropouts. Other simulations can be designed using the CIA to include parental and gender related policy variables to analyze their effects on enrollment. 5 Conclusion A cross-impact model is developed here to study the influence of infrastructure facilities on primary education enrollment and progression. The cross-impact matrix illustrates the influence of one variable over the others and it also has a provision to identify the impact variables (i.e., policy variables). Here, we construct a model based on primary education data obtained in a survey conducted in Gujarat, India. Simulation results show that infrastructure improvement would indeed increase the enrollment rate in primary education. Acknowledgments We wish to thank Mr. B. Viswanthan, Regional Manager at Tata Economic Consultancy Services, Chennai, for his valuable mentoring, and for extensive discussions. Also, we wish to thank Mrs. Anupama Pedamallu for her help in editing and formatting the paper. The authors would like to thank the anonymous referees for their valuable comments. References Admassu, K. (2008). Primary School Enrollment and Progression in Ethiopia: Family and School Factors. American Sociological Association Annual Meeting, July 31st, 2008, Boston, MA. Altamirano, M.A. & van Daalen, C.E. (2004). A system dynamics model of primary and secondary education in Nicaragua. 22nd International conference of the system dynamics society, July 25-29, 2004, Oxford, England. Akar, H. (2008). Poverty, and Schooling in Turkey: a Needs Assessment Study, Presentation at Workshop on Complex Societal Problems, Sustainable Living and Development, May 13-16, 2008, IAM, METU, Ankara. Bruns, B., Mingat, A. & Ramahatra, R. (2003). Achieving universal primary education by 2015, a chance for every child. The World Bank, Washington Dc., USA. Benson, H. (1995). Household Demand for Primary Schooling in Ethiopia: Preliminary Findings. Annual Meeting of the American Educational Research Association, April 18-22, 1995, San Francisco, CA. Gordon, T.J. and Hayward, H. (1968) Initial experiments with the cross-impact matrix method of forecasting. Futures, 1, 100-116. Hanushek, E.A., Lavy, V. & Kohtaro, H. (2008). Do Students Care about School Quality? Determinants of Dropout Behavior in Developing Countries. Journal of Human Capital, 2(1), 69-105, DOI: 10.1086/529446. Hayashi, A., Tokimatsu, K., Yamamoto, H., & Mori, S. (2006). Narrative scenario development based on cross-impact analysis for the evaluation of global-warming mitigation options. Applied Energy, 83:10, 1062-1075, D0I:10.1016/J.APENERGY. 2005.11.002. Kane, J. (2002). A Primer for a New Cross-Impact Language - KSIM. In: The Delphi Method: Techniques and Applications, Harold, A.L., and Murray, T. (eds.), Addison-Wesley. Table 4: Cross impact matrix for primary education system after adding policy variable. Figure 3: Behavior of primary educational system before adding the policy variable. Figure 4: Behavior of primary educational system after adding the policy variable. Figure 5:Important variable changes from before and after policy variable implementation. Color legend (in the electronic version of the paper): Blue line: after introducing policy variable; Red line: before introducing policy variable) Karadeli, N., Kaya, O. & Keskin, B.B. (2001). Dynamic modeling of basic education in Turkey. Senior graduation project, Bogazici University, Turkey. Lane, D.C. (1999). Social theory and system dynamics practice. European Journal of Operational Research, 113(3), 501-527, D0I:10.1016/S0377-2217(98)00192-1. Mohapatra, P.K.J., Mandal, P., & Bora, M.C. (1994). Introduction to system dynamics modeling, Universities Press (India) Limited, India. Pedamallu, C.S., Ozdamar, L., Kropat, E., & Weber, G.-W. (2009). A System Dynamics Model for Intentional Transmission of HIV/AIDS using Cross Impact Analysis, Institute of Applied Mathematics, METU, Ankara, preprint 141. Pedamallu, C.S. (2001). Externally aided construction of school rooms for primary classes- preparation of project report. Master's Dissertation, Indian Institute of Technology Madras, 2001. Rena, R. (2007). Factors affecting the enrollment and the retention of students at primary education. Essays in Education, 22. Available from: http://www.usca.edu/essays/vol22fall2008.html Serge, T. (2009). School construction strategies for universal primary education in Africa. The World Bank, Washington Dc., USA. Terlou, B., van Kuijk, E. & Vennix, J.A.M. (1991). A system dynamics model of efficiency of primary education in Latin America. In: Proceedings of the international conference of the system dynamics society, 578-587. Weimer-Jehle, W. (2006). Cross-impact balances: A system-theoretical approach to cross-impact analysis. Technological Forecasting and Social Change, 73(4), 334-361, DOI:10.1016/J. TECHFORE.2005.06.005. Chandra Sekhar Pedamallu is Postdoctoral Research Fellow at New England Biolabs, Ipswich, MA, USA; he works in the optimization, bioinformatics, computational biology, data mining, parallel computing and system modelling. He is foundation member of OR for Development and OR for computational biology, bioinformatics and medicine working groups of EURO, co-authored numerous papers and presentations, and organized many conferences (http:// globaloptimization.angelfire.com/) Linet Ozdamar is Professor at Systems Engineering Dept., Yeditepe University, Istanbul, Turkey; she works in the environmental site assessment, emergency logistics, global optimization, parallel algorithms and interval-symbolic applications in nonlinear programming. Prof. Ozdamar is permanent member of the EURO PMS Working Group and Turkish OR Society, co-authored numerous papers and presentations, and organized many conferences (http://sye. yeditepe.edu.tr/eng/academicstaff/ftfm/lozdamar.html) L. S. Ganesh holds a Bachelors degree in Mechanical Engineering of the Birla Institute of Technology and Science, Pilani, and Masters and Doctoral degrees of the Indian Institute of Technology Madras, India. He is interested in basic research in the areas of Systems Modeling and Analysis, Multi-Criteria Decision Analysis, and Forecasting, and applied research in the areas of Project, Technology, Knowledge, Operations, and Public Systems Management. His theoretical and applied research contributions have appeared (or, are to appear) in reputed international and national journals (http://www.doms.iitm.ac.in/ganesh.htm). Gerhard-Wilhelm Weber is Professor at IAM, METU, Ankara, Turkey; he works in the financial mathematics, optimization, optimal control, OR, computational statistics, life and human sciences, dynamical systems, data mining, environment and development. He has affiliations in Siegen (Germany), Aveiro (Portugal) and Skudai (Malaysia), co-authored numerous papers and presentations, and organized many conferences (http://www3.iam.metu.edu.tr/iam/ images/7/73/Willi-CVpdf ). Erik Kropat is a member of the Institute for Theoretical Computer Science, Mathematics and Operations Research at the University of the Bundeswehr Munich, Neubiberg, Germany. His main research topics are Operations Research, data mining and business intelligence with particular focus on the analysis and control of network structures under uncertainty. Model izboljšanja vpisa v osnovnošolsko izobraževanje v državi v razvoju po metodi sistemske dinamike Modeli sistemske dinamike so celovita metoda reševanja kompleksnih problemov s pomočjo scenarijev. Omogočajo, da skupaj z metodo računalniške simulacije analiziramo kompleksne probleme. Modeliranje z metodo sistemske dinamike je pogosto osnova za sistemsko razmišljanje in predstavlja managersko in organizacijsko razvojno paradigmo. V članku je opisan pristop na osnovi sistemske dinamike pri raziskavi pomembnosti infrastrukturnih zmogljivosti na kakovost osnovnega izobraževanja v državi v razvoju. Model je izdelan s pomočjo navzkrižne analize vpliva (Cross Impact Analysis - CIA), metode, ki primerja entitete in atribute značilne za osnovno izobraževanje v neki dani skupnosti. Model CIA omogoča, da predvidimo vpliv infrastrukturnih zmogljivosti na dostopnost te skupnosti do osnovnega izobraževanja. To lahko pomaga javnim odločevalcem, da bolj učinkovito planirajo akcije, ki poskušajo izboljšati pismenost. Ključne besede: države v razvoju, modeliranje sistemov, navzkrižna analiza vpliva, simulacija, sistemska dinamika, osnovno izobraževanje Appendix 1. Simulation results for attributes before adding the policy variable (attribute values are rounded off to two digits) Atlriliutes Inhial Values 1 iteration 2 iteratun 3 iteration 4 iteration 6 iteration G iteration 7 iteration 8 iretaton 9 iteration ID iteration 11 iteration 12 iteration 11 iteration 14 iteration toe 0.71 0 66 0.32 0.S5 0.9« 0.97 0.97 0 97 0.97 0.97 0.97 096 C 96 0.95 0 9S OS 0 4i 0 31 0 13 ODS 0 02 0 0 0 0 0 0 0 0 H !c o.s 042 0 31 019 0 03 0 02 0 0 0 0 0 0 0 9 d elp 0 36 0 36 0.36 0.3S Ü.3S 0 35 0 36 0 36 0 35 0 36 0.36 036 0.36 0.35 0 35 lip 0 35 0 36 0.36 0.35 0 35 0 35 0 35 0.36 0 35 0 36 0.36 036 0.36 0 35 0 35 OS ae ae 06 06 05 OS OS OS OS OS ae 06 06 OS as 0.46 04e 0 43 0 35 023 0 1 0.03 0 0 0 0 0 0 0 a «0 0 36 027 0.17 o.oe 0 02 0 0 0 0 0 0 0 0 0 a ad 0 35 0 27 018 0 09 03 0 0 0 0 0 0 0 0 0 0 ls_g 0 39 032 0 24 0 IS 0 07 0 02 0.01 0 0 0 0 0 0 0 d IS s 0 26 022 0.16 O.OB 0.3 0 01 0 0 0 0 0 0 0 0 a IPS 0.3 019 01 004 0 01 0 0 0 0 0 0 0 0 0 a lie 0 25 027 0 29 0 31 0 33 0 35 0 33 04 043 0.46 9.51 9.63 0.56 0 6 0 53 Isle 0 2S 027 029 0 31 0 33 0 3S 0 3B 0.41 0 44 0.47 0.51 064 ose 0 61 0 ss Ir 0 06 007 0 11 0 19 0 33 0 51 0 63 0 61 0.39 0 94 096 096 099 0 99 1 IM 0 2 0 06 0.01 0 0 0.01 0.02 0.06 0.1 0.19 0.29 0.41 0 62 0.62 0.7 /sd 0 29 D.1 0.03 001 0 91 0 01 0.03 0 07 0 14 0 23 9.36 o.4e O.ST 0 66 0.7« Iba 0.69 077 0 66 0 91 0 95 0.97 0 93 0 99 0.99 1 1 1 1 1 1 0.3J 023 0 13 0 06 0 D2 0 0 0 0 0 0 0 0 0 a Attributes iteration 1& iteration 17itsration 18 iteration 19 itsration 20 iteration 21 iteration Z2 iteration 23 iteration 24 iteration 29 iteration 26 iteration 27 iteration 2e iteration 29 iteration roe 0.94 0.S3 091 0.9 0.S6 0.35 0.62 0.7S 0.75 0.7 0.64 o.sa 0.51 0.43 0 3S 0 C 0 0 0 0 0 0 0 0 0 0 0 0 0 .'t 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 s.ip 0 35 0 35 0 35 0 35 0.35 0.35 0 35 0 35 0 35 0 35 035 0 35 D 35 0 35 0 35 ■If 0 35 0 35 0 35 0 35 0 36 0 35 0 35 0 35 0 35 0 35 035 0 35 0 36 0 35 0 35 'SPS 0.6 06 0.6 OS 0.6 0.6 0.6 0.6 06 0.6 0.6 06 0.6 0.6 OS 'Ii 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 M 0 0 D 0 0 0 0 0 0 0 0 0 0 0 a rs 0 0 0 0 0 0 0 0 0 D 0 0 0 o' 0 a '5 s 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d (JB 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a ita 0 6? 07 0 73 0 76 0.79 032 064 oe6 0 66 09 0 91 0 93 094 0 95 095 lals ose 0 n 0 74 0 77 0 79 0.33 0 65 0B7 ÜS9 09 0 92 0 93 094 0 95 096 Ir 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Ibö 0.77 0t2 0S7 09 0.92 094 0.9S 097 0 97 0 96 0.99 0.99 0.99 0 99 1 JSK 079 O.iS 03B 0.91 0.93 09S 0.9S 0.97 0 96 0.96 9.99 0.99 0.99 0 99 1 IM 1 1 1 1 1 1 t 1 1 t 1 1 i 1 1 D C D 0 0 0 0 D 0 0 0 0 0 D a Attributes 30 iteration 31 iteration 32 iteration 33 iteration 34 Iteration 35 iteration 36 iteration 37 iteraUon 3S iteration 39 iteration 40 iteration 41 iteration 42 iteration 43 iteration 44 iteration los 0.26 0 21 014 0.09 OOS 0 03 0.01 0 0 0 0 0 0 0 0 lav 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Is 0 0 0 0 0 0 0 0 0 0 0 0 D 0 0 cto 0 35 0 36 0 35 0.36 0 35 0 36 0.35 0 35 0.36 0 35 0 36 0 35 0.36 0 35 0 36 •ip 035 0 35 035 0 35 035 0 35 0.3S 0 35 0.36 0 35 0 36 0 35 0 35 035 0 35 iBpS 0.6 0.6 0.6 0 6 0.6 0 6 0.6 06 06 0.5 06 0.6 0 6 0.6 OS Its 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a I!p 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d IM 0 0 0 0 0 0 0 0 0 0 0 0 D 0 d Is 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d Ii S 0 0 0 0 0 0 0 0 0 0 0 0 0 d (f» 0 0 0 0 0 0 0 0 0 0 0 0 0 d lic 0.96 0 97 097 0 98 09B 0 93 0.99 0 99 0.39 0 99 0 99 0 99 lale 0.96 097 0 90 0.96 099 0.99 0.99 0.99 O.S9 0 99 0.99 Ir 1 1 1 1 1 1 1 t IM 1 1 t 1 1 1 1 1 t inä 1 1 1 t 1 1 1 1 1 1 t Ii» 1 1 1 1 1 1 1 1 1 1 .w» 0 0 0 0 0 0 0 0 0 0 0 D 0 d Attributes 49 iteration 46 iteration 47 ire tation 46 iteration 49 iteration SO iteration laB 0 0 0 0 0 0 lsy 0 0 0 0 0 D Ic 0 0 0 0 0 0 elB 035 035 0.36 0.35 0.36 0.35 •Ip 0 35 0 35 036 0 36 0 36 0 35 laps 0.6 0.6 OS O.S O.S 06 lis 0 0 0 0 0 «p 0 0 0 0 D IM 0 0 0 0 a Is a 0 0 0 0 0 Is s 0 0 0 0 D (pa 0 0 0 0 D ite 1 1 l3le 1 1 Ir 1 1 Ibö 1 1 ISK 1 1 11» 1 1 IdK 0 0 0 0 0 ü 2. Simulation results for attributes after adding the policy variable (attribute values are rounded off to two digits) Acribuläa 1 il^raüon 2 iieraüt^rt J ircralion 4 ircraiion 6 lieraiion 6 btfrraüfin 7 iTfrraiifirt 6 irtlau^rt 9 Merwian 10 iitraiion 11 htraiian 12 ii4ra[ion 13 it«ratiün 11 itaraiidrt ■oe 0 f. 0 49 1 1 1 1 1 1 1 1 1 1 .'it His gu 0 73 D7G 0 79 0 02 D!U 0 96 ose 04 0 91 0 92 091 it use oei 0 69 1] 73 0 76 0 79 0)2 OW 0 36 0 38 04 0 91 0 9i 091 0 35 0 3S a 35 0 35 0 35 0 35 D3S D 35 0 3S 0 35 0 35 0 35 0 35 0 35 If 0 35 0 36 0 36 0 36 0 35 035 035 036 036 0 3S 0 36 0 35 0 36 0 35- ICfB 0 6 0 6 06 06 0.6 0.6 06 06 0.6 0.6 06 06 0.6 06. lis 0.43 0.65 0.61 0.67 0.73 0.76 0.83 D.S7 O.S 0S3 0S6 0.96 0.87 0 9$ llf 027 0 2 0.14 0.09 0.05 0 03 0.01 0 0 0 0 0 0 » M 0 2a 0 21 016 0 11 OOB 0 05 003 002 0 01 0 01 0 0 0 » Is ( 0.47 0.61 0.5S 06 0.63 066 0.69 0.71 0.74 0 76 0 ^4 0.81 0 83 0 85. Is J 0.!S 0.42 0.47 0.61 0.S4 D.5S 0.61 0.64 C.67 0.7 0 3 0 75 07S 081 IPS 0J4 ose 04 0.13 016 019 0S2 0S6 OH OK 0 >6 0 ) 0 72 »C ()?7 0 31 0 33 0 35 038 04 013 C16 OS 0 3 0 6 06 06^ Isla 017 OM 0 31 0 33 036 036 Oil 014 017 0S1 0 0 S 0 61 065. Ir 0.06 o.os 01 0.11 0.13 0 14 0.1£ 0.1S 0 1S ou 0 1 0 1 013 O.ii IM 004 0 0 0 0 0 0 0 0 0 0 0 0 » KU 0 07 0 0 0 D 0 0 0 0 0 0 0 0 » liK 0.65 0.62 0.6 0.69 0.6B 066 0.67 0.67 0.S7 0.57 0 57 0 57 0.57 0.57" Id« 0.39 0.42 0.45 0.4S 0.61 064 0.6S 0.61 064 0 67 0 71 0 74 0 77 OS Anribu[E^ 15 iteration 16 ileralion 17fterBtian IB »teratlDn 14 ileralion 20 ileratrt}r 21 iteration 22 iloralion 23 iteration 24 iteration 2^ iieraiion 26 iteration 27 iteration 28 iie ration 24 rteration 1'» 1 1 1 1 1 1 1 1 1 1 1 1 i'5-r- 0 35 9.46 096 037 IK 0.93 033 039 0 33 O.SS 0 3? 0 33 1 1 1 IC 0 95 145 0 96 0 97 444 0 98 0 9e 444 0 99 9 44 0 99 0 99' 1 1 1 eb 0 35 D 35 a 35 0 35 4 35 Ü 35 9 35 035 0 36 9 35 035 9 36 135 435 9 35 0 35 »35 0 35 0 35 035 0 35 0 35 03S 0 36 9 35 035 0 36 135 03S 03S leEHff 06 0.6 0.6 06 0.6 06 0.6 06 O.S 06 0.6 0.6 16 0.6 0.£ 0 99 4 44 0 99 1 1 1 1 1 1 1 1 1 1 1 1 IfD 0 0 a D 4 0 0 0 0 9 0 9 0 D .■id 0 0 0 0 0 0 0 t 0 0 0 0 0 0 U g 0 57 4»4 C9 0 32 4 45 09J 0.45 ow 0.97 0.47 048 0.96 144 039 09» 0 63 D an 0 37 0 69 4 41 0 92 044 445 096 946 447 098 148 498 9 9» IM 0 76 g SI OM 0 56 049 03 042 043 054 945 096 037 157 0 6! 0 9B ive 0 67 07 0 n 0 76 on 0S2 0S4 0» O.SS J.S 051 1.« 0.35 0 36. laii 0 88 4 71 C u 0 77 04 0 83 0 65 4 87 0 89 14 0 42' 0 93 144 0 95 09S IT 0 11 »11 C I 0 09 444 0.07 0.07 406 0 06 9 0S 401 004 143 0 03 9 93 JM 0 0 0 0 0 0 9 0 0 0 0 0 0 0 u rsa 0 0 0 0 0 0 0 0 0 0 0 0 0 0 D Ii« 0 57 4 57 0 57 0 57 4 67 0 57 0 67 4 57 0 57 167 4 57 0 57 157 0S7 0 57- Iti» 0 82 9 85 a a? 0!9 041 0 92 9.43 045 096 1.4E 047 0 9S 148 0 9! 9.5;i AnributE^ 30 iteration 31 iteration 32ileratior 33 iteration 34 iteration 35 iieratit}r 36 iteration 37 iteration 38 iteration 34 iteration 40 iteration 11 iteration 42 iteration UitEratinn 41 rteration it» 1 1 1 1 1 1 1 1 1 1 1 1» 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Ii; 1 1 1 1 1 1 1 at. 9 35 135 43 93 035 03 9 35 035 03 935 035 9 36 135 0 35 9 35 if 0 35 135 03 03 035 03 0 35 035 03 9 35 035 0 35 135 0 35 035 II" 06 0.6 0 0. 06 0. 1.6 06 0. 1.6 0.6 0.6 1.6 0.6 OS Its 1 1 1 1 1 1 1 1 1 Jtn 9 0 0 0 0 0 0 0 9 0 0 IM 0 0 0 0 0 0 0 0 0 0 0 0 g 0 99 144 03 1 1 1 1 1 1 1 1 1 1 5 9 99 144 4 9! 0.49 1 1 1 1 1 1 1 1 laj 9 95 144 06 0.43 044 1 1 1 1 1 1 1 1 l-.t la.'e 0 36 096 137 4.47 03 09 0.3B 040 0.3 0.99 099 0.33 0 99 199 144 099 0.33 t 1 1 1 0 4B 048 09 049 444 044 1 St 0 92 449 0.0 0.91 401 0.0 9 01 001 0 01 101 0 0 0 IM 0 0 0 0 0 0 0 0 0 0 0 0 0 I> rga 0 0 0 0 0 0 0 0 0 0 0 0 0 U tbo 0 57 0 67 0 57 0 57 4 57 0 57 0 57 0 57 0 57 167 4 57 0 57 167 0 57 0 57 Iti» 9.99 044 0.99 9.19 1 1 1 1 1 1 1 1 1 1 1 Attributes 45 iteration 46 iteratron 17 iteration 48 irtsralinn 49 iteratron ^ iteration 1« 1 1 1 1 1 1 tsv 1 1 1 1 1 Ic 1 1 1 1 1 1 Slß 035 0 35 0 35 0 35 0 35 035. rit D.3S 0.35 0 35 0 35 0.35 0.35 ISflS 06 06 0.6 OS OS oe lis 1 1 1 1 1 1 lie 0 0 0 0 0 0 iia 0 0 0 0 0 a Is t, 1 1 1 1 1 1 Is f 1 1 1 1 1 1 lea 1 1 1 1 1 1 lie 1 1 1 1 1 1 lale 1 1 1 1 1 1 Ir 0 0 0 0 0 0 IW 0 0 0 0 0 a 0 0 0 0 9 0 57 0 57 0 57 0 57 0.57 OST' Itfir 1. 1 1 1 1 1