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Program allocation process improvement by an assignment model

Program allocation process improvement by an assignment model 10.7603/s40690-015-0011-y JOURNAL OF AERONAUTICS AND SPACE TECHNOLOGIES JULY 2015 VOLUME 8 NUMBER 2 (7-13) PROGRAM ALLOCATION PROCESS IMPROVEMENT BY AN ASSIGNMENT MODEL Okay Iù IK* Muhammet Bø LGE YÕ ldÕ rÕ m KILIÇARSLAN 2nd Main Jet Base, ø zmir, Turkey, 2nd Main Jet Base, Izmir, Turkey, TurAF Headquarters, Cost Analysis bilge4003@harbiyeli.hho.edu.tr 4004kilicarslan@harbiyeli.hho.edu.tr and Statistics Department, Ankara, Turkey, o.isik@hho.edu.tr th rd Received: 29 April 2015, Accepted: 23 July 2015 ABSTRACT As the only source of jet pilot candidates for Turkish Air Force, Air Force Academy (TuAFA) applies several screening processes in order to acquire an average group of 150 cadets from civilian high school graduates each year. Besides the nationwide examinations (YGS-LYS), there are several others such as medical, flight, athletics evaluations and etc. Because the number of criteria for screening is large, the spread of the distribution of YGS-LYS scores of the candidates, which is assumed to be the aptitude towards college education, is a lot wider than those of other universities. Although admission to faculty for civilian high school students is regulated by the YGS-LYS score; in order to provide a balance distribution among different programs in terms of YGS-LYS score, placement to aerospace, electronics, computer and Industrial engineering programs of the Faculty is governed by a special directive. Although the directive considers candidates’ preferences, the ultimate goal of the algorithm in the directive is to keep the balance of academic success among different programs in the allocation process. In this study, we propose an alternative assignment model which tries to minimize the deviations from students’ preferences while maintaining the balance of the distribution among programs. Through simulation from different preference distributions with different number of students, it has been showed that regardless of the number of students and distribution of preferences,first choice allocation performance of the proposed model is significantly better than the directive’s algorithm. Keywords: Balanced Assignment Problem, Process Improvement, Stable Marriage Problem. HHO BÖLÜMLERE AYIRMA SÜRECøN ø N ATAMA MODELø YLE ø Yø LEù TøR øLMES ø ÖZET Türk Hava Kuvvetlerinin pilot adaylarÕ nÕ n yetiúti ÷ i tek kurum olan Hava Harp Okulu (HHO), her yÕ l, bünyesinde e÷ itim verece÷ i sivil lise mezunu yaklaúÕ k 150 ö÷ renciyi seçebilmek amacÕ yla, ülke çapÕ nda uygulanan YGS-LGS sÕ navlarÕ na ek olarak uçuú, spor, sa ÷ lÕ k ve psikomotor gibi çok sayÕ da eleme aú amasÕ uygulamaktadÕ r. Bunun nedeni HHO’nun ö÷ rencilerinde akademik beceriler yanÕ nda liderlik becerileri de aramasÕ , mezunlarÕ na hem mühendislik hem de subaylÕ k diplomasÕ vermesi, daha da önemlisi, 4 yÕ llÕ k e÷ itim-ö÷ retim dönemi sonunda pilot adayÕ olarak mezun olabilenlerin son teknoloji ile donatÕ lmÕ ú süpersonik uçaklara kumanda etmesidir. Ek olarak, HHO mezunlarÕ , NATO üyesi seçkin bir hava kuvvetinde kariyer yapabilme garantisi elde etmektedir. Ö÷ renci alÕ mlarÕ nda seçim kriteri sayÕ sÕ nÕ n fazla olmasÕ nedeniyle, adaylarÕ n üniversite ö÷ renimine hazÕ r bulunuúluklar Õ nÕ n bir göstergesi olan YGS-LGS puanÕ nÕ n da÷ Õ lÕ mÕ nÕ n varyansÕ , di÷ er üniversite bölümlerinin varyansÕ ndan daha büyüktür. Bu yüzden ö÷ rencilerin HHO DekanlÕ ÷ Õ bünyesindeki 4 farklÕ mühendislik bölümüne ayrÕ lmalarÕ , özel bir yönergeyle düzenlenmiútir. Yönerge, adaylar Õ n tercihlerini dikkate almakla birlikte asÕ l amaç, bölümler arasÕ akademik baú arÕ yÕ dengeli da÷ Õ tmaktÕ r. Bu çalÕ úmada, bölümlere ay Õ rma sürecinde ö÷ rencinin ilk tercihinden sapmalarÕ minimize eden ve aynÕ zamanda bölümler arasÕ dengeyi de sa÷ layan alternatif bir atama modeli önerilmiútir. Önerilen modelin ilk tercihe yerle útirme performans Õ nÕ n, yönergedeki algoritmadan anlamlÕ úekilde üstün oldu ÷ u ve bu üstünlü÷ ün ö÷ renci sayÕ sÕ ndan ve tercih da÷ Õ lÕ mÕ ndan ba÷ Õ msÕ z oldu÷ u, farklÕ tercih da÷ Õ lÕ mlarÕ ndan yaratÕ lan benzetim verileriyle gösterilmiútir. Anahtar Kelimeler: Dengeli Atama Modeli, Süreç ø yileútirme, Dengeli Evlilik Problemi (Stable Marriage Problem, SPA). Iù IK, Bø LGE, KILIÇARSLAN Corresponding Author 7 Program Allocation Process Improvement By An Assignment Model 1. INTRODUCTION x B also prefers A over the element to which B is already matched. Graduation from a reputable university is assumed to be the key to succeed in life. On the other hand, in In other words, a matching is stable when there does most of the developing countries, competition is fierce not exist any alternative pairing (A, B) in which both because the number of seats is disproportionally A and B are individually better off than they would be scarce against the population of students. In Turkey, with the element to which they are currently matched. match between the students and the programs is Hospital/residence problem is a special case of SMP, basically determined via the national exams, LGS – also known as the college admissions problem – (Transition to Higher Education Examination) and differs from the stable marriage problem in that the LYS (Undergraduate Placement Examination). In "women" can accept "proposals" from more than one 2013, 38.2% of the students who passed the pre- "man" (e.g., a hospital can take multiple residents, or a elimination exam LGS and had the right to choose a college can take an incoming class of more than one program, did not attempt to do so, because they were student). Algorithms to solve the college admissions sure that their combined score (40%LGS+60%LYS) problem can be college-oriented (female-optimal) or would not allow them to get a seat in their order of student-oriented (male-optimal). preference. Hence they kept their position instead of making a choice in vain. In [1], it has been proved that, for any equal number of men and women, it is always possible to solve the To our knowledge, there has been little quantitative SMP and make all marriages stable. However, research on LYS type placement exams in terms of the stability does not necessarily mean optimality. In [4], match between student preference and the overall it has been shown that finding a maximum stable value to society. It is assumed that a student who is matching for the problem of allocating students to placed to the first program in his/her order of projects, where both students and lecturers have preference will be more successful or willing to do so preferences over projects, and both projects and during his/her entire career. As an example in Turkey, lecturers have capacities is NP-hard. Therefore, many after the announcement of combined YGS-LYS of the literature focus on approximation algorithms scores, students are allowed to choose 30 alternative [5]. programs to form their order of preference. They usually sort the programs on the basis of previous Program placement problem discussed here is similar years’ ground scores. The allocation is simple; the one to college admissions problem where programs who has higher score is more likely to place to his/her establish priorities according to students’ combined first slot in the preference list. However due to the academic score and students’ preferences can follow time limit and waste number of programs, student arbitrary distributions.We applied the proposed choices and the resulting placement are subject to method to TuAFA’s Faculty which has four different discussion. Most of the students choose programs programs. thinking of theirself-economic interest or career, some for academic interest and some just follow the crowd. This paper consists of five sections. Section 1 is the There is no concern about the demand in the economy introduction, in section 2 TuAFA’s current placement or the overall welfare of the society. As a result, algorithm is presented, which is followed by the intellectual capital distribution is not balanced, leaving proposed assignment model in Section 3. Section 4 some economic segments underdeveloped and some reserved for the empirical findings of our model and skyrocketed. finallythe concluding remarks provided in Section 5. College admission problem can be modeled as an 2. TuAFA PROGRAM PLACEMENT assignment problem, where students and universities ALGORITHM have preferences over each other. In the literature [1- 4], assignment problem where two sets of elements In order to overcome the problem of uneven given a set of preferences for each element, known as distribution of intellectual capital among different the stable marriage problem (SMP). A matching is a programs, Turkish Air Force Academy (TuAFA) mapping from the elements of one set to the elements follows a different placement strategy for its of the other set. A matching is stable whenever it is programs. Applying to the Turkish Air Force not the case that both: Academy (TuAFA) is considerably more involved than applying to a typical university in Turkey. There x Some given element A of the first matched are many steps and challenges an applicant must meet. set prefers some given element B of the TuAFA seeks individuals who possess good academic second matched set over the element to skills besides leadership potential. This is because which A is already matched, and TuAFA offers both university degree and officer diploma for its graduates, and more importantly, at the Iù IK, Bø LGE, KILIÇARSLAN 8 Program Allocation Process Improvement By An Assignment Model end of the 4 year education, those who are qualified as 3. PROPOSED ASSIGNMENT MODEL a jet pilot candidate can fly supersonic aircraft equipped with cutting edge technology. Moreover, a In order to provide a compromising solution for all life time career is guaranteed in one of the World’s stakeholders, a preference score, p which is a measure distinguished NATO allied air force. of candidate’s disappointment is introduced to penalize deviations from candidate’s first preference. Because of its unique offerings and intense evaluation Let strategy, the number of applicants for TuAFA’s freshman class pools an average of 6,000 high school Sets: graduates to enroll only 150 cadets each year. As a result, the spread of the distribution of YGS-LYS ሼ ሽ R Set of programs, ܥܧǡܧܧǡܫܧǡܣܧ score of the applicants is wider than those of similar ݌ ith candidate’s preference score for jth ௜௝ colleges in Turkey, but representative of the initial program, א ሼ ʹǡ͵ ሽ , א ሼ ǥǡ݊ ሽ א ܴ pool. TuAFA Faculty has four alternative engineering wheren is the number of candidates. If ith candidate programs namely, Aerospace (AE), Electronics (EE), has a preference score array {1, 3, 2, 0}, his order of Computer (CE) and Industrial Engineering (IE). A preference is actually AE pCE pIE p EE. His/her first poorly administered program allocation in a boarding choice is AE, then CE, then IE and then EE. We school, may result undesirable preference information, checked that the solution is not sensitive to different in a sense all the students follow the same preference choices of values for p: structure which makes it hard to find a compromise between programs’ quota and student preferences. Parameters: Because they would basically sort programs depending on the previous year’s graduation rate, ݏ ith candidate’s combined academic score, follow the leader, or word of mouth. ܾ jth program’s quota, ܽ average academic score of all ݏ ௜ ௜ Current program placement algorithmis presented ܽൌ candidates, below: Variables: 1. Record candidates’ order of preference in order from most to least preferable, A binary variable is used if ith candidate assigned to 2. Sort candidates descending order according his/her jth preference, to academic score and split them into groups according to class requirement, ‘‡ 3. Take the first group and place the first ݕ ൌ൜ ௜௝ candidate to his/her first choice, 4. Place the next candidate according to his/her ି ା ߝ ǡߝ deviations of average academic score of jth order of preference if it is not occupied by the ௝ ௝ program from ܽ previous, 5. Go to step 4 until all candidates placed. The objective function is: Advantage of the above placement algorithm is, ି ା academic scores or intellectual capital will definitely ܼ ൌ ሺ ݂ ǡߝ ǡߝ ሻ (1) ௝ ௝ be distributed evenly among programs but also within variance of the programs will almost be equal. Minimizing f, which is a measure of total However, a candidate who has higher score can be disappointment weighted by the academic score of placed to the last spot in his/her preference list. For candidates, will move the search process towards example, if there exist 8 classes and 2 classes for each candidates’ first preferences, while minimizing ߝ and th program, according to academic score 8 candidate ߝ , will provide a balanced academic success th st can be placed to his 4 preference, while 121 student distribution among programs. will be placed to his/her first preference. This is not fair and penalizes successful candidates. The question Subject to: is can there be any other approach satisfying distributional constraints and also reasonable for ௡ ସ (2) diligent students. In other words, the outcome is ݂ ൌ෍෍ݏ ݌ ݕ ௜ ௜௝ ௜௝ female-optimal and in the next section we propose an ௜ୀଵ ௝ୀଵ alternative assignment model, where the student preferences are considered and Pareto optimality can Average academic score for jth program is: be achieved. σ ݕ ݏ (3) ௜௝ ௜ ௜ୀଵ ି ା ൅ߝ െߝ ൌܽ ௝ ௝ Iù IK, Bø LGE, KILIÇARSLAN ܯ݅݊ ‘–Š‡”™‹•‡ǡ Ͳǡ ‹ˆ݅–Š…ƒ†‹†ƒ–ƒ••‹‰‡†–݆–Š’”‘‰”ƒ ͳǡ The programs’quotas must be met: Despite some preference listings highly cited than others, all possible permutations are recorded by the students. For 4 programs, 4! = 24 different preference ෍ݕ ൌܾ (4) listings are possible. In order to generalize the results ௜௝ ௝ ௜ for the proposed model, 10 different data sets are generated from the same distribution for 137 cadets Each candidate must be assigned to exactly one and results are tabulated in Table 2. On the average, program: the proposed model produces 67% less disappointment than the directive’s algorithm. (5) ෍ݕ ൌͳǡ ௜௝ The performance of the proposed method can change ௝ୀଵ depending on the distribution of cadets’ preferences. We expect similar results with uniform or almost ି ା ݕ ൌ ‘”ͳͲ , ߝ ǡߝ ൒Ͳ uniform preference distributions. 10 data sets each ௜௝ ௝ ௝ having 250 cadets with equally likely preference IBM ILOG CPLEX optimization software is used to listings are generated. The results of both methods in run above model for different data sets. The results are disappointment metric are tabulated in Table 3. summarized in the next section. 4. EMPIRICAL FINDINGS The proposed multi-objective model is applied to 137 candidates who applied in 2012fall admission period. Next, in order to generalize the performance of the model, same number of candidates with same preference distribution is generated. Then to see the effect of number of students and preference distribution, 250 students from uniform and skewed preference distributions are generated.Academic scores are also generated and assigned to students from the normal distribution with mean 53.21 and standard deviation 18.98, as 2012 fall semester. Program placement results of the proposed model and the directive’s algorithm are compared on the basis of Figure 1. Placement results for 2012 fall semester disappointment metric. data. In Figure 1, comparison of proposed model and the Table 1. ANOVA of the mean academic scores with directive’s algorithm is presented for 2012 fall the proposed model placement. semester. The proposed model placed significantly more students to his/her first preference than the directive. Moreover unlike the directive, no students Programs: Count Mean Variance placed to his/her last preference. In disappointment Score scale, the proposed model produced 62% less Computer Eng. 34 53.52 1819.60 disappointment than the directive. The mean academic Electronics score of the programs are almost equal. ANOVA in Eng. 35 51.49 1802.04 Table 1, showing the mean scores according to Industrial proposed model placement, revealed no significant Eng. 35 54.67 1913.35 Aerospace differences among programs. Eng. 33 53.19 1755.36 In Figure 2, the distribution of preference listings is ANOVA presented for 2012 fall semester. Here, horizontal axis represents students’ order of preference in descending Source SS df MS F p – value Between order and vertical axis represents frequency of the groups 181.47 3 60.49 0.165 0.920 students who picked that preference. For example, Within first column in the graph represents 16 students who Groups 48819.73 133 367.07 picked {3, 1, 0, 2} order (IE, EE, AE, CE). Total 49001.20 136 Iù IK, Bø LGE, KILIÇARSLAN Figure 2. Preference frequency in descending order for 2012 fall semester. optimization model is shown significant improvement Table 2. Results for the 2012 fall reference opportunities without violating system constraints. distribution (137 cadets). The proposed model can be extended to solve the assignment problem of graduates of TuAFA who will Proposed Relative assign to branches other than pilotage. The Directive Data Method Disappointment Disappointment Set Disappointment Efficiency of Table 3. Results for the uniform preference Score Score Proposed distributions (250 cadets). 1 110 39 65 2 124 37 70 Relative Proposed 3 114 37 68 The Directive Disappointment Data Method 4 129 35 73 Disappointment Efficiency of Set Disappointment 5 144 58 60 Score Proposed Score 6 134 45 66 Method (%) 7 146 43 71 1 324 99 8 117 40 66 2 318 105 9 113 36 68 3 313 106 10 131 45 66 4 328 109 Mean 126.2 41.5 67 5 331 107 6 317 109 For uniform and skewed preference distributions, our 66 assignment model produces 66% and 59% less 7 308 105 Disappointment accordingly. Proposed model is 8 318 111 relatively more efficient in Disappointment metric for 9 324 115 both of the distributions. We showed that regardless of 10 313 108 the preference distribution proposed assignment Mean 319.4 107.4 model is superior to the algorithm in the directive and also provide a balanced academic score distribution among programs. 5. CONCLUDING REMARKS In this study we have considered an alternative model for the student-program allocation problem, in which students have preferences over programs and balanced academic score distribution among programs need to be maintained. A practical and easy to apply Iù IK, Bø LGE, KILIÇARSLAN 11 Program Allocation Process Improvement By An Assignment Model Figure 3. Preference probabilities in descending order for simulated skewed distribution (250 cadets). Table 4. Results for the skewed preference 7. REFERENCES distribution (250 cadets). [1] Gale, D., Shapley, L.S., 1962, College Relative admissions and the stability of marriage, American Proposed The Directive Disappointment Mathematical Monthly, 69–1, 9–15 . Data Method Disappointment Efficiency of [2] Saito, Y., Fujimoto, T.,Matsuo, T., 2008, Set Disappointment Score Proposed Multi-sided Matching Lecture Allocation Mechanism, Score Method (%) New Challenges in Applied Intelligence Technologies, 1 323 155 52% volume 134 of Studies in Computational Intelligence, 2 328 172 48% Springer. 3 340 182 46% [3] Gusfield, D., Irving R.W., 1989, “The stable 4 333 172 48% marriage problem: structure and algorithms”, MIT 5 335 166 50% Press, Cambridge, MA, USA. 6 330 171 48% [4] Manlove, D.F., O'Malley, G., 2005, Student 7 319 166 48% project allocation with preferences over projects. In 8 319 160 50% Proceedings of ACID2005: the 1st Algorithms and 9 315 153 51% Complexity in Durham, 4, 69 – 80, KCL Publications. 10 327 160 51% [5] Marx, D., Schlotter, I., 2009, Parameterized Mean 326.9 165.7 49% Complexity and Local Search Approaches for the Stable Marriage Problem with Ties, Algorithmica, 6. ACKNOWLEDGEMENT 58(1), 170–187. This study was started as part of a quality VITAE improvement project in TuAFA and accomplished by senior cadets. The Authors express their gratitude Okay Iù IK to officials at Human Resources Evaluation and Col.Iù IK(Ph.D.) is the chief of Financial Accounting Admission Center in TuAFA, for their close support. and Statistics Office in Turkish Air Force Hq. He has B.S. in Electronics Engineering and received his M.S. “Open Access: This article is distributed under the and Ph.D. in Industrial Engineering and Engineering terms of the Creative Commons Attribution License Management from Middle East Technical University (CC-BY 4.0) which permits any use, distribution, and reproduction in any medium, provided the original and Old Dominion University in 2001 and 2009 author(s) and the source are credited.” respectively. His research interest is in statistical Iù IK, Bø LGE, KILIÇARSLAN 12 Program Allocation Process Improvement By An Assignment Model quality control, design for six sigma, QFD, multiple response surface optimization methodology, decision theory and mathematical modeling. Muhammet BøLGE Lt. Bø LGE had his B.S. degree in Industrial Engineering from Turkish Air Force Academy, in 2013. Recently he is following advance pilot training nd program as a pilot candidate in 2 Main Jet Base Com., ø zmir, Turkey. YÕ ldÕ rÕ m KILIÇARSLAN Lt. KILIÇARSLAN had his B.S. degree in Industrial Engineering from Turkish Air Force Academy, in 2013. Recently he is following advance pilot training nd program as a pilot candidate in 2 Main Jet Base Com., ø zmir, Turkey. Iù IK, Bø LGE, KILIÇARSLAN http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Aeronautics and Space Technologies (Havacilik ve Uzay Teknolojileri Dergisi) Springer Journals

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10.7603/s40690-015-0011-y JOURNAL OF AERONAUTICS AND SPACE TECHNOLOGIES JULY 2015 VOLUME 8 NUMBER 2 (7-13) PROGRAM ALLOCATION PROCESS IMPROVEMENT BY AN ASSIGNMENT MODEL Okay Iù IK* Muhammet Bø LGE YÕ ldÕ rÕ m KILIÇARSLAN 2nd Main Jet Base, ø zmir, Turkey, 2nd Main Jet Base, Izmir, Turkey, TurAF Headquarters, Cost Analysis bilge4003@harbiyeli.hho.edu.tr 4004kilicarslan@harbiyeli.hho.edu.tr and Statistics Department, Ankara, Turkey, o.isik@hho.edu.tr th rd Received: 29 April 2015, Accepted: 23 July 2015 ABSTRACT As the only source of jet pilot candidates for Turkish Air Force, Air Force Academy (TuAFA) applies several screening processes in order to acquire an average group of 150 cadets from civilian high school graduates each year. Besides the nationwide examinations (YGS-LYS), there are several others such as medical, flight, athletics evaluations and etc. Because the number of criteria for screening is large, the spread of the distribution of YGS-LYS scores of the candidates, which is assumed to be the aptitude towards college education, is a lot wider than those of other universities. Although admission to faculty for civilian high school students is regulated by the YGS-LYS score; in order to provide a balance distribution among different programs in terms of YGS-LYS score, placement to aerospace, electronics, computer and Industrial engineering programs of the Faculty is governed by a special directive. Although the directive considers candidates’ preferences, the ultimate goal of the algorithm in the directive is to keep the balance of academic success among different programs in the allocation process. In this study, we propose an alternative assignment model which tries to minimize the deviations from students’ preferences while maintaining the balance of the distribution among programs. Through simulation from different preference distributions with different number of students, it has been showed that regardless of the number of students and distribution of preferences,first choice allocation performance of the proposed model is significantly better than the directive’s algorithm. Keywords: Balanced Assignment Problem, Process Improvement, Stable Marriage Problem. HHO BÖLÜMLERE AYIRMA SÜRECøN ø N ATAMA MODELø YLE ø Yø LEù TøR øLMES ø ÖZET Türk Hava Kuvvetlerinin pilot adaylarÕ nÕ n yetiúti ÷ i tek kurum olan Hava Harp Okulu (HHO), her yÕ l, bünyesinde e÷ itim verece÷ i sivil lise mezunu yaklaúÕ k 150 ö÷ renciyi seçebilmek amacÕ yla, ülke çapÕ nda uygulanan YGS-LGS sÕ navlarÕ na ek olarak uçuú, spor, sa ÷ lÕ k ve psikomotor gibi çok sayÕ da eleme aú amasÕ uygulamaktadÕ r. Bunun nedeni HHO’nun ö÷ rencilerinde akademik beceriler yanÕ nda liderlik becerileri de aramasÕ , mezunlarÕ na hem mühendislik hem de subaylÕ k diplomasÕ vermesi, daha da önemlisi, 4 yÕ llÕ k e÷ itim-ö÷ retim dönemi sonunda pilot adayÕ olarak mezun olabilenlerin son teknoloji ile donatÕ lmÕ ú süpersonik uçaklara kumanda etmesidir. Ek olarak, HHO mezunlarÕ , NATO üyesi seçkin bir hava kuvvetinde kariyer yapabilme garantisi elde etmektedir. Ö÷ renci alÕ mlarÕ nda seçim kriteri sayÕ sÕ nÕ n fazla olmasÕ nedeniyle, adaylarÕ n üniversite ö÷ renimine hazÕ r bulunuúluklar Õ nÕ n bir göstergesi olan YGS-LGS puanÕ nÕ n da÷ Õ lÕ mÕ nÕ n varyansÕ , di÷ er üniversite bölümlerinin varyansÕ ndan daha büyüktür. Bu yüzden ö÷ rencilerin HHO DekanlÕ ÷ Õ bünyesindeki 4 farklÕ mühendislik bölümüne ayrÕ lmalarÕ , özel bir yönergeyle düzenlenmiútir. Yönerge, adaylar Õ n tercihlerini dikkate almakla birlikte asÕ l amaç, bölümler arasÕ akademik baú arÕ yÕ dengeli da÷ Õ tmaktÕ r. Bu çalÕ úmada, bölümlere ay Õ rma sürecinde ö÷ rencinin ilk tercihinden sapmalarÕ minimize eden ve aynÕ zamanda bölümler arasÕ dengeyi de sa÷ layan alternatif bir atama modeli önerilmiútir. Önerilen modelin ilk tercihe yerle útirme performans Õ nÕ n, yönergedeki algoritmadan anlamlÕ úekilde üstün oldu ÷ u ve bu üstünlü÷ ün ö÷ renci sayÕ sÕ ndan ve tercih da÷ Õ lÕ mÕ ndan ba÷ Õ msÕ z oldu÷ u, farklÕ tercih da÷ Õ lÕ mlarÕ ndan yaratÕ lan benzetim verileriyle gösterilmiútir. Anahtar Kelimeler: Dengeli Atama Modeli, Süreç ø yileútirme, Dengeli Evlilik Problemi (Stable Marriage Problem, SPA). Iù IK, Bø LGE, KILIÇARSLAN Corresponding Author 7 Program Allocation Process Improvement By An Assignment Model 1. INTRODUCTION x B also prefers A over the element to which B is already matched. Graduation from a reputable university is assumed to be the key to succeed in life. On the other hand, in In other words, a matching is stable when there does most of the developing countries, competition is fierce not exist any alternative pairing (A, B) in which both because the number of seats is disproportionally A and B are individually better off than they would be scarce against the population of students. In Turkey, with the element to which they are currently matched. match between the students and the programs is Hospital/residence problem is a special case of SMP, basically determined via the national exams, LGS – also known as the college admissions problem – (Transition to Higher Education Examination) and differs from the stable marriage problem in that the LYS (Undergraduate Placement Examination). In "women" can accept "proposals" from more than one 2013, 38.2% of the students who passed the pre- "man" (e.g., a hospital can take multiple residents, or a elimination exam LGS and had the right to choose a college can take an incoming class of more than one program, did not attempt to do so, because they were student). Algorithms to solve the college admissions sure that their combined score (40%LGS+60%LYS) problem can be college-oriented (female-optimal) or would not allow them to get a seat in their order of student-oriented (male-optimal). preference. Hence they kept their position instead of making a choice in vain. In [1], it has been proved that, for any equal number of men and women, it is always possible to solve the To our knowledge, there has been little quantitative SMP and make all marriages stable. However, research on LYS type placement exams in terms of the stability does not necessarily mean optimality. In [4], match between student preference and the overall it has been shown that finding a maximum stable value to society. It is assumed that a student who is matching for the problem of allocating students to placed to the first program in his/her order of projects, where both students and lecturers have preference will be more successful or willing to do so preferences over projects, and both projects and during his/her entire career. As an example in Turkey, lecturers have capacities is NP-hard. Therefore, many after the announcement of combined YGS-LYS of the literature focus on approximation algorithms scores, students are allowed to choose 30 alternative [5]. programs to form their order of preference. They usually sort the programs on the basis of previous Program placement problem discussed here is similar years’ ground scores. The allocation is simple; the one to college admissions problem where programs who has higher score is more likely to place to his/her establish priorities according to students’ combined first slot in the preference list. However due to the academic score and students’ preferences can follow time limit and waste number of programs, student arbitrary distributions.We applied the proposed choices and the resulting placement are subject to method to TuAFA’s Faculty which has four different discussion. Most of the students choose programs programs. thinking of theirself-economic interest or career, some for academic interest and some just follow the crowd. This paper consists of five sections. Section 1 is the There is no concern about the demand in the economy introduction, in section 2 TuAFA’s current placement or the overall welfare of the society. As a result, algorithm is presented, which is followed by the intellectual capital distribution is not balanced, leaving proposed assignment model in Section 3. Section 4 some economic segments underdeveloped and some reserved for the empirical findings of our model and skyrocketed. finallythe concluding remarks provided in Section 5. College admission problem can be modeled as an 2. TuAFA PROGRAM PLACEMENT assignment problem, where students and universities ALGORITHM have preferences over each other. In the literature [1- 4], assignment problem where two sets of elements In order to overcome the problem of uneven given a set of preferences for each element, known as distribution of intellectual capital among different the stable marriage problem (SMP). A matching is a programs, Turkish Air Force Academy (TuAFA) mapping from the elements of one set to the elements follows a different placement strategy for its of the other set. A matching is stable whenever it is programs. Applying to the Turkish Air Force not the case that both: Academy (TuAFA) is considerably more involved than applying to a typical university in Turkey. There x Some given element A of the first matched are many steps and challenges an applicant must meet. set prefers some given element B of the TuAFA seeks individuals who possess good academic second matched set over the element to skills besides leadership potential. This is because which A is already matched, and TuAFA offers both university degree and officer diploma for its graduates, and more importantly, at the Iù IK, Bø LGE, KILIÇARSLAN 8 Program Allocation Process Improvement By An Assignment Model end of the 4 year education, those who are qualified as 3. PROPOSED ASSIGNMENT MODEL a jet pilot candidate can fly supersonic aircraft equipped with cutting edge technology. Moreover, a In order to provide a compromising solution for all life time career is guaranteed in one of the World’s stakeholders, a preference score, p which is a measure distinguished NATO allied air force. of candidate’s disappointment is introduced to penalize deviations from candidate’s first preference. Because of its unique offerings and intense evaluation Let strategy, the number of applicants for TuAFA’s freshman class pools an average of 6,000 high school Sets: graduates to enroll only 150 cadets each year. As a result, the spread of the distribution of YGS-LYS ሼ ሽ R Set of programs, ܥܧǡܧܧǡܫܧǡܣܧ score of the applicants is wider than those of similar ݌ ith candidate’s preference score for jth ௜௝ colleges in Turkey, but representative of the initial program, א ሼ ʹǡ͵ ሽ , א ሼ ǥǡ݊ ሽ א ܴ pool. TuAFA Faculty has four alternative engineering wheren is the number of candidates. If ith candidate programs namely, Aerospace (AE), Electronics (EE), has a preference score array {1, 3, 2, 0}, his order of Computer (CE) and Industrial Engineering (IE). A preference is actually AE pCE pIE p EE. His/her first poorly administered program allocation in a boarding choice is AE, then CE, then IE and then EE. We school, may result undesirable preference information, checked that the solution is not sensitive to different in a sense all the students follow the same preference choices of values for p: structure which makes it hard to find a compromise between programs’ quota and student preferences. Parameters: Because they would basically sort programs depending on the previous year’s graduation rate, ݏ ith candidate’s combined academic score, follow the leader, or word of mouth. ܾ jth program’s quota, ܽ average academic score of all ݏ ௜ ௜ Current program placement algorithmis presented ܽൌ candidates, below: Variables: 1. Record candidates’ order of preference in order from most to least preferable, A binary variable is used if ith candidate assigned to 2. Sort candidates descending order according his/her jth preference, to academic score and split them into groups according to class requirement, ‘‡ 3. Take the first group and place the first ݕ ൌ൜ ௜௝ candidate to his/her first choice, 4. Place the next candidate according to his/her ି ା ߝ ǡߝ deviations of average academic score of jth order of preference if it is not occupied by the ௝ ௝ program from ܽ previous, 5. Go to step 4 until all candidates placed. The objective function is: Advantage of the above placement algorithm is, ି ା academic scores or intellectual capital will definitely ܼ ൌ ሺ ݂ ǡߝ ǡߝ ሻ (1) ௝ ௝ be distributed evenly among programs but also within variance of the programs will almost be equal. Minimizing f, which is a measure of total However, a candidate who has higher score can be disappointment weighted by the academic score of placed to the last spot in his/her preference list. For candidates, will move the search process towards example, if there exist 8 classes and 2 classes for each candidates’ first preferences, while minimizing ߝ and th program, according to academic score 8 candidate ߝ , will provide a balanced academic success th st can be placed to his 4 preference, while 121 student distribution among programs. will be placed to his/her first preference. This is not fair and penalizes successful candidates. The question Subject to: is can there be any other approach satisfying distributional constraints and also reasonable for ௡ ସ (2) diligent students. In other words, the outcome is ݂ ൌ෍෍ݏ ݌ ݕ ௜ ௜௝ ௜௝ female-optimal and in the next section we propose an ௜ୀଵ ௝ୀଵ alternative assignment model, where the student preferences are considered and Pareto optimality can Average academic score for jth program is: be achieved. σ ݕ ݏ (3) ௜௝ ௜ ௜ୀଵ ି ା ൅ߝ െߝ ൌܽ ௝ ௝ Iù IK, Bø LGE, KILIÇARSLAN ܯ݅݊ ‘–Š‡”™‹•‡ǡ Ͳǡ ‹ˆ݅–Š…ƒ†‹†ƒ–ƒ••‹‰‡†–݆–Š’”‘‰”ƒ ͳǡ The programs’quotas must be met: Despite some preference listings highly cited than others, all possible permutations are recorded by the students. For 4 programs, 4! = 24 different preference ෍ݕ ൌܾ (4) listings are possible. In order to generalize the results ௜௝ ௝ ௜ for the proposed model, 10 different data sets are generated from the same distribution for 137 cadets Each candidate must be assigned to exactly one and results are tabulated in Table 2. On the average, program: the proposed model produces 67% less disappointment than the directive’s algorithm. (5) ෍ݕ ൌͳǡ ௜௝ The performance of the proposed method can change ௝ୀଵ depending on the distribution of cadets’ preferences. We expect similar results with uniform or almost ି ା ݕ ൌ ‘”ͳͲ , ߝ ǡߝ ൒Ͳ uniform preference distributions. 10 data sets each ௜௝ ௝ ௝ having 250 cadets with equally likely preference IBM ILOG CPLEX optimization software is used to listings are generated. The results of both methods in run above model for different data sets. The results are disappointment metric are tabulated in Table 3. summarized in the next section. 4. EMPIRICAL FINDINGS The proposed multi-objective model is applied to 137 candidates who applied in 2012fall admission period. Next, in order to generalize the performance of the model, same number of candidates with same preference distribution is generated. Then to see the effect of number of students and preference distribution, 250 students from uniform and skewed preference distributions are generated.Academic scores are also generated and assigned to students from the normal distribution with mean 53.21 and standard deviation 18.98, as 2012 fall semester. Program placement results of the proposed model and the directive’s algorithm are compared on the basis of Figure 1. Placement results for 2012 fall semester disappointment metric. data. In Figure 1, comparison of proposed model and the Table 1. ANOVA of the mean academic scores with directive’s algorithm is presented for 2012 fall the proposed model placement. semester. The proposed model placed significantly more students to his/her first preference than the directive. Moreover unlike the directive, no students Programs: Count Mean Variance placed to his/her last preference. In disappointment Score scale, the proposed model produced 62% less Computer Eng. 34 53.52 1819.60 disappointment than the directive. The mean academic Electronics score of the programs are almost equal. ANOVA in Eng. 35 51.49 1802.04 Table 1, showing the mean scores according to Industrial proposed model placement, revealed no significant Eng. 35 54.67 1913.35 Aerospace differences among programs. Eng. 33 53.19 1755.36 In Figure 2, the distribution of preference listings is ANOVA presented for 2012 fall semester. Here, horizontal axis represents students’ order of preference in descending Source SS df MS F p – value Between order and vertical axis represents frequency of the groups 181.47 3 60.49 0.165 0.920 students who picked that preference. For example, Within first column in the graph represents 16 students who Groups 48819.73 133 367.07 picked {3, 1, 0, 2} order (IE, EE, AE, CE). Total 49001.20 136 Iù IK, Bø LGE, KILIÇARSLAN Figure 2. Preference frequency in descending order for 2012 fall semester. optimization model is shown significant improvement Table 2. Results for the 2012 fall reference opportunities without violating system constraints. distribution (137 cadets). The proposed model can be extended to solve the assignment problem of graduates of TuAFA who will Proposed Relative assign to branches other than pilotage. The Directive Data Method Disappointment Disappointment Set Disappointment Efficiency of Table 3. Results for the uniform preference Score Score Proposed distributions (250 cadets). 1 110 39 65 2 124 37 70 Relative Proposed 3 114 37 68 The Directive Disappointment Data Method 4 129 35 73 Disappointment Efficiency of Set Disappointment 5 144 58 60 Score Proposed Score 6 134 45 66 Method (%) 7 146 43 71 1 324 99 8 117 40 66 2 318 105 9 113 36 68 3 313 106 10 131 45 66 4 328 109 Mean 126.2 41.5 67 5 331 107 6 317 109 For uniform and skewed preference distributions, our 66 assignment model produces 66% and 59% less 7 308 105 Disappointment accordingly. Proposed model is 8 318 111 relatively more efficient in Disappointment metric for 9 324 115 both of the distributions. We showed that regardless of 10 313 108 the preference distribution proposed assignment Mean 319.4 107.4 model is superior to the algorithm in the directive and also provide a balanced academic score distribution among programs. 5. CONCLUDING REMARKS In this study we have considered an alternative model for the student-program allocation problem, in which students have preferences over programs and balanced academic score distribution among programs need to be maintained. A practical and easy to apply Iù IK, Bø LGE, KILIÇARSLAN 11 Program Allocation Process Improvement By An Assignment Model Figure 3. Preference probabilities in descending order for simulated skewed distribution (250 cadets). Table 4. Results for the skewed preference 7. REFERENCES distribution (250 cadets). [1] Gale, D., Shapley, L.S., 1962, College Relative admissions and the stability of marriage, American Proposed The Directive Disappointment Mathematical Monthly, 69–1, 9–15 . Data Method Disappointment Efficiency of [2] Saito, Y., Fujimoto, T.,Matsuo, T., 2008, Set Disappointment Score Proposed Multi-sided Matching Lecture Allocation Mechanism, Score Method (%) New Challenges in Applied Intelligence Technologies, 1 323 155 52% volume 134 of Studies in Computational Intelligence, 2 328 172 48% Springer. 3 340 182 46% [3] Gusfield, D., Irving R.W., 1989, “The stable 4 333 172 48% marriage problem: structure and algorithms”, MIT 5 335 166 50% Press, Cambridge, MA, USA. 6 330 171 48% [4] Manlove, D.F., O'Malley, G., 2005, Student 7 319 166 48% project allocation with preferences over projects. In 8 319 160 50% Proceedings of ACID2005: the 1st Algorithms and 9 315 153 51% Complexity in Durham, 4, 69 – 80, KCL Publications. 10 327 160 51% [5] Marx, D., Schlotter, I., 2009, Parameterized Mean 326.9 165.7 49% Complexity and Local Search Approaches for the Stable Marriage Problem with Ties, Algorithmica, 6. ACKNOWLEDGEMENT 58(1), 170–187. This study was started as part of a quality VITAE improvement project in TuAFA and accomplished by senior cadets. The Authors express their gratitude Okay Iù IK to officials at Human Resources Evaluation and Col.Iù IK(Ph.D.) is the chief of Financial Accounting Admission Center in TuAFA, for their close support. and Statistics Office in Turkish Air Force Hq. He has B.S. in Electronics Engineering and received his M.S. “Open Access: This article is distributed under the and Ph.D. in Industrial Engineering and Engineering terms of the Creative Commons Attribution License Management from Middle East Technical University (CC-BY 4.0) which permits any use, distribution, and reproduction in any medium, provided the original and Old Dominion University in 2001 and 2009 author(s) and the source are credited.” respectively. His research interest is in statistical Iù IK, Bø LGE, KILIÇARSLAN 12 Program Allocation Process Improvement By An Assignment Model quality control, design for six sigma, QFD, multiple response surface optimization methodology, decision theory and mathematical modeling. Muhammet BøLGE Lt. Bø LGE had his B.S. degree in Industrial Engineering from Turkish Air Force Academy, in 2013. Recently he is following advance pilot training nd program as a pilot candidate in 2 Main Jet Base Com., ø zmir, Turkey. YÕ ldÕ rÕ m KILIÇARSLAN Lt. KILIÇARSLAN had his B.S. degree in Industrial Engineering from Turkish Air Force Academy, in 2013. Recently he is following advance pilot training nd program as a pilot candidate in 2 Main Jet Base Com., ø zmir, Turkey. Iù IK, Bø LGE, KILIÇARSLAN

Journal

Journal of Aeronautics and Space Technologies (Havacilik ve Uzay Teknolojileri Dergisi)Springer Journals

Published: Sep 19, 2015

References