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COMPUTER-BASED SUPPORT OF EDUCATION DECISIONS Lech Kruś Systems Research Institute, Polish Academy of Sciences Warsaw, Poland Keywords: mathematical modeling,

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1 COMPUTER-BASED SUPPORT OF EDUCATION DECISIONS Lech Kruś Systems Research Institute, Polish Academy of Sciences Warsaw, Poland Keywords: mathematical modeling, risk, utility, decision support, computer-based systems, cooperative games Systems Research Institute, Polish Academy of Sciences Lech Kruś CSM06

2 2 Presentation: current stage of the project developed in the Systems Research Institute of PAS in cooperation with the Warsaw School of Information Technology (WIT). Goal of the project: construct computer-based system, accessed by web, supporting education decisions made by candidates/students of WIT, and by authorities of the School. CONTENTS Introduction - decision problems and scope of the project Mathematical models of decision situations (examples) - candidates, students - authorities of the school System supporting education decisions Selected computational results Final remarks Systems Research Institute Polish Academy of Sciences Lech Kruś CSM06

3 3 The Warsaw School of Information Technology (WIT) established in 1996 is functioning under the auspices of the Polish Academy of Sciences (strict cooperation with the Systems Research Institute of PAS). As a private school is fully self financing. Faculty of Computer Science Offered programmes: BSc in Computer Science, MSc in Computer Science, possible further doctoral studies Specializations: computer networks, data bases, IT in telecommunication, computer supported graphics, programming techniques Studies' curriculum follows the guidelines of the American Association for Computing Machinery (a commonly recognized authority on setting standards in IT teaching) and comply with the Bologna Process recommendations which integrate European systems of higher education. Faculty of Computer Techniques for Management Offered programmes: BSc in management and marketing, MSc in management and marketing, MSc in econometrics Specializations: computer supported management, management in tele-computing, strategic management, econometrics. Currently ca 3000 students studying and 300 scholars involved in the teaching process. Intramural and extramural modes of study. Offered courses in Polish and in English. Systems Research Institute Polish Academy of Sciences Lech Kruś CSM06

4 4 Decision Situations Candidates and students starting the study: What school and direction of study should one select taking into account cost of the education, future job, risk of failure? Student during the study (after the 2-nd year in WIT): What specialization should one select? Student who has obtained BSc degree: Continue the study for MSc degree expecting better position on the labor market, but also considering additional time of studies and additional expenditures for the education? Student who has not passed exams after a given year: Repeat the academic year covering the additional expenditures or waive - accepting loss of the previous expenditures? Authorities of the school What should be tuition levels for currently offered directions of studies? Introduce a new innovative direction? What number of places prepare? What should be the tuition level? Cancel an existing direction of studies if the number of students selecting the direction decrease? Systems Research Institute Polish Academy of Sciences Lech Kruś CSM06

5 5 Objectives of the Project Developing methodology and constructing computer-based system supporting decision analysis made by students and by the authority of WIT. User friendly and effective interface to the system by the web site of WIT. Candidates/students should find on the web site information about the school. Using the system, in an interactive form, they can make financial analysis regarding the education process, including the information about: cost of education, possible job and salaries of graduates having different specializations, benefits from the education expressed in the form of utility, taking into account the risk of failure. - different students – each has own specific abilities, interests, preferences - different decision situations Systems Research Institute Polish Academy of Sciences Lech Kruś CSM06

6 6 Scope of the Research 1. Analysis of streams of students in WIT. 2. Analysis of the educational market. 3. Analysis of the labor market. 4. Methodological research using different approaches: utility function concepts - Savage, A. Tversky, R. Kulikowski multicriteria analysis – achievement function approach - A. P. Wierzbicki multiple criteria optimization and decisions under risk - W. Ogryczak multicriteria decision support in cooperative games - L. Kruś inquires methods, expert methods. 5. Constructing family of substantive models describing different decision situations. 6. Experimental versions of the system and computational experiments. Systems Research Institute Polish Academy of Sciences Lech Kruś CSM06

7 7 Streams of Students in WIT. Students are divided into several classes with respect to their abilities (example: abilities of the students starting in WIT can be measured by the level of knowledge in mathematics). For each class of students’ abilities and each specialization, historical data are collected including number of students passing the exams after the given year, - repeating, - waiving. The transition matrices, and the transition probabilities are derived. Finally, the probabilities are evaluated that the student belonging to the given ability class, studying given direction and specialization will be graduated in the planned time of studies. Systems Research Institute Polish Academy of Sciences Lech Kruś CSM06

8 8 Description of Decision Situations Goal of the model: financial analysis of the education process in the presence of risk. Considered different decision situations and the specific model is constructed for each of them. Example: Student starting the studies, selecting direction of the studies and specialization Given specializations j  [1,l] offered by the university. Discounted expenditures I e (c) during the studies can be calculated: where: T 0 – time of studies, m(t) - cost of living in the year t, c j - tuition per year, k e discount rate, j – specialization, j  [1, l ]. Effects of the university education: total, discounted increase of salaries after the studies in the period : [T 0 +1, T] : where: w e (t) increase of salaries in the year t, k n – discount rate in the time of employment till the retirement age T. Systems Research Institute Polish Academy of Sciences Lech Kruś CSM06

9 9 Utility of Sustainable Development (R. Kulikowski) (extension of the ideas proposed by Savage, Tversky, Kahneman) Utility from the risky investment, characterized by the rate of return, which is random variable with expected value R and variance  2, is described by a function of two factors: where - expected long term profit, - share of expenditures I, in the total capital P of the investor, - safety index, - worst case profit, - subjective parameter, weight prescribed to the risk of the worst case. The form applied in the model:,, where  characterizes the investor’s enterprising parameter. Systems Research Institute Polish Academy of Sciences Lech Kruś CSM06

10 10 Profit of the student Discounted increase of income minus the expenditures: W e -I e, under conditions that the student will pass entrance exams, pass the studies, will be graduated, and will find and keep the job after the studies. Utility of the student depends on the class i  [1, k] of his abilities and previous knowledge, as well as on the selected direction and specialization j  [1, l] of the studies : where x sj (c j )=I e (c j )/P s, R sej (c j ) =(W e -I e (c j ))/I e (c j ), P s - capital possessed by the student, p eij – probability that he will be graduated, and that he will find the job. Rate of return R sej is obtained with probability p eij in the case of success. Safety index S sij takes into account the risk that the student can not finish the studies in the prescribed time, and can not obtain the good job after the studies. Systems Research Institute Polish Academy of Sciences Lech Kruś CSM06

11 11 School assessment of new direction and specialization of studies Let assume: tuition c per year, operating cost c o per one place, n - number of places prepared for students, k - number of expected students, Rate of return: R uj =c/c o -1 with probability p u =k/n. It is assumed that the university has the capital P u, and part I u =n c o of it is used to prepare places for n students., where x=I u /P u Subjective parameters  u,  u, have to be evaluated interactively by the decision maker – the representative of the school authorities. Systems Research Institute Polish Academy of Sciences Lech Kruś CSM06

12 12 Systems Research Institute Polish Academy of Sciences Lech Kruś CSM06 Decision analysis in the presence of risk Student Comparison of studies on different directions, specializations, taking into account: personal predispositions, and interests, cost of the studies, difficulty of the given direction of studies and specialization, probabilities that the he will pass the exams and be graduated, probability of finding job, expected increase of wages, risk of failure. Private school Assessment of existing and new directions of studies responding to the needs of education market, taking into account cost, expected number of students, risk of failure. Derivation of tuition which is beneficial for the university, as well for students. Analyzed quantities expected rate of return, expected receipts and profit in comparison the risk free investments, assessment of risk: variance, semivariance, utilities, safety indices, impact of the risk on the cooperative solutions.

13 13 Fig. 1. Structure of the computer-based system supporting education decisions MODELS DESCRIBING PREFERENCES OF DMs Utility function of the student Utility function of the university management Interactive procedures for estimation subjective parameters of utility functions MODEL OF EDUCATION SYSTEM Database of the model Offered directions of studies, conditions, education programs and specialties. Historical information – flows of students. Information regarding labor market and employment of graduates. Inquiry information, expert’s opinions Procedures for estimation model parameters and for model verification STUDENT REPRESENTATIVE OF THE SCHOOL AUTHORITIES Graphical interface MODULE OF DECISION SUPPORT COMPUTATIONAL PROCEDURES Derivation of output variables for assumed scenarios utilities of decision makers measures of risk optimal decisions Procedures serving interactive session Graphical interface Optimization procedures Data base of generated and analyzed scenarios Decision situations of university decision variables exogenous variables model relations output variables criteria Decision situations of student decision variables exogenous variables model relations output variables criteria Systems Research Institute Polish Academy of Sciences Lech Kruś CSM06

14 Utilities of students student 1 student 2 student 3 Faculty A B Faculty A B Faculty A B Fig. 2. Computational experiment Candidates: 1,2 & 3 having different abilities (increasing) measured by the level of knowledge in mathematics. Faculties: A (marketing & management) B (computer science) Systems Research Institute Polish Academy of Sciences Lech Kruś CSM06 0 0,5 1 1,5 2 2,5 A B student 1 A B student 2 A B student 3 expected rate of return R safety index S stand. demideviation  S S S S S S R R R R R R     

15 15 Fig. 3. Students’ u tilities dependent on the tuition level Fig. 4. The parameter , safety index S and minimal probability of success dependent on the reserves of capital possessed by a student Systems Research Institute Polish Academy of Sciences Lech Kruś CSM06

16 16 Derivation of the tuition on the base of cooperation principles private school – students Students and school treated as partners in a joint venture. The concept of cooperative Nash solution : (U s N, U u N )=arg max ((U s -U sd )(U u -U ud )), dla (U s,U u )  A. In the considered case the optimization problem has to be solved: max c [(U s (c)-U sd )(U u (c)-U ud )], subject to : (U s (c), U u (c))  A. where U sd and U ud respective lower bounds of acceptable utilities of students and of the school derived on the base of BATNA concept. Systems Research Institute Polish Academy of Sciences Lech Kruś CSM06

17 17 FINAL REMARKS Current stage of the project: Functional assumptions and general structure of the system. Construction of mathematical models for selected decision situations of candidates/students and the authorities of WIT. Differentiated classes of students with respect to their abilities, differentiated directions of studies and specializations. Procedures for interactive evaluation of subjective parameters of utility functions. Procedures generating outputs for assumed scenarios of exogenous variables and decision variables with use of the optimization methods. Method for derivation of the tuition taking into account benefits of the school and benefits of students. Implementation of selected elements of the system and computational experiments. Planned research (jointly SRI PAS and WIT) Data base for mathematical models, including historical information about the streams of students in WIT enabling evaluation of transition probabilities and information enabling evaluation of labor market for graduates. Application of multicriteria approach to support the education decisions. Application of expert methods and inquires research. Systems Research Institute Polish Academy of Sciences Lech Kruś CSM06

18 18 Selected publications KRUŚ, L., Multicriteria Decision Support in Negotiations. Control&Cybernetics Vol. (1996) No. 6, KRUŚ L; A multicriteria approach to cooperation in the case of innovative activity. Control&Cybernetics, Vol. 33, No. 3, KRUŚ, L. (2004): A Computer Based System Supporting Analysis of Cooperative Strategies. In: Artificial Intelligence and Soft Computing - ICAISC 2004, Springer-Verlag, Heidelberg. KRUŚ, L. (2005): Computer-Based System Support of Individual and Cooperative Risky Decisions with Use of the Utility Concept. Int. J. of Knowledge and System Science, Vol. 2, No. 3, KULIKOWSKI R., L. KRUŚ, Support of education decisions. W: Group Decisions and Voting (J. Kacprzyk, D. Wagner eds), Akad. Oficyna Wyd. EXIT, Warszawa, KULIKOWSKI R., On general theory of risk management and decision support systems, Bulletin of the Polish Academy of Sciences, Sci. Tech., Vol. 51 (2003) No. 3. KULIKOWSKI R. (2005) Support of risky decisions by using the concept of utility which enables the implementation of sustainable development strategies. CSM OGRYCZAK, W. (2002) Multiple criteria optimization and decisions under risk. Control and Cybernetics, 31,4. TVERSKY A., KAHNEMAN D., The framing of decisions and the psychology of choice, Science, Vol. 211, (1981) January. WIERZBICKI A., MAKOWSKI M., WESSELS J., (2001) Model Based Decision Support Methodology with Environmental Applications. Kluwer Acad. Publ. Systems Research Institute Polish Academy of Sciences Lech Kruś CSM06


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