In Germany, the most effective way of allocating study places in subjects for which admission is restricted, such as medicine or pharmacy, is through the Central Office for the Allocation of Study Places (Zentralstelle für die Vergabe von Studienplätzen, ZVS) in Dortmund.
The centralized ZVS procedure offers several advantages over the direct application procedure and has the potential for significant improvement, meaning that the number of disappointed applicants not receiving a place at their chosen university or close to home could be cut in half. These are the results outlined in a study by PD Dr Johannes Josef Schneider of Johannes Gutenberg University Mainz, which he undertook together with colleagues at the University of Regensburg. Their analysis and proposals for optimization of the system were published in the specialist journal Physica A.
In most cases, students with university admission qualifications have to apply directly to universities for their subject of choice. Around one third of places for students starting university are allocated by the ZVS. "Both procedures pose certain problems," states Schneider, who works at the Center for Computational Research Methods in Natural Sciences at Mainz University. "A relatively large number of candidates are frustrated and feel let down by the ZVS because they don't get a place at their chosen university. Or they have no university place at all at the start of the semester because the allocation process is still underway." As Schneider and his colleagues Christian Hirtreiter and Ingo Morgenstern at the University of Regensburg determined with the help of computer simulations, the allocation of study places in restricted subjects through the ZVS is nevertheless the more effective solution compared with the direct application process, which has now been in place for a couple of years.
It is relatively frequently the case that candidates who use the decentralized procedure and apply directly to their chosen universities have no study place at semester commencement. "As far as the politicians are concerned, it would be ideal if universities could pick and choose their own students and decide for themselves which applicants are best suited to which subject at their university. But the reality is completely different," explains Schneider. It is true that universities do, to a large extent, make their decisions on the basis of the examination grades achieved by a candidate. This means that because each candidate applies to several universities at once to increase the chances of getting a place, the applicants with the best exam results are offered places first, while the candidates with lower marks are rejected and have to apply again. However, the computer simulations show that the situation worsens the more applications each school leaver submits. "In the ideal scenario, where each candidate only applies to one university, the number of subsequent application rounds would be reduced and the university places would be allocated on time for the start of semester." According to the computer model, however, if applicants each try their luck at three universities, some applicants could need up to 30 application rounds before they are successful - which would mean a waiting time of two and a half years before they can begin studying.
The ZVS system, on the other hand, means that more students can begin their studies on time and fewer places are free at universities at the start of semester, which is beneficial for both the individuals and society as a whole. But the ZVS allocation system is not without problems. "For example, it is quite possible that an applicant from Cologne who lists Heidelberg as his first choice, Munich as his second choice, and Cologne as his third might not be offered a place at any of these chosen universities, as the ZVS processes each university choice individually, one after the other. As one major decisive factor is proximity to the university, the applicant has no chance of getting a place in either Heidelberg or Munich. By the third round, the places at Cologne University will have already been allocated to applicants who listed Cologne as their first or second choice." Schneider and his co-authors have thus decided to propose a system which looks at university choices not individually but together at the same time. In their computer simulations, they were able to reduce the number of students who fail to get a place at one of their selected universities or close to home by more than 50 percent in comparison with the corresponding figure for the current ZVS selection procedure.
The researchers found that the best results can be achieved using optimization algorithms that are also used in solution-finding in other areas. The US news magazine "Time", for example, recently listed one of Schneider's computer algorithms for the optimization of packing problems among the top 50 most important inventions of 2009. And the academics have adopted a similar approach to the problem of study place allocations. Random events are simulated on the computer using so-called Monte Carlo simulations. "Just like in a casino where chance decides that the ball lands on number 12 on a roulette wheel, the computer also generates random configurations," explains Schneider. In the case of university applications, the computer first allocates each prospective university student to a random university. Then two applicants randomly swap their university places. The new solution is compared with the previous one. The quality of the solution is evaluated on the basis of how many students are assigned to one of their chosen universities or are given a study place close to home. If this exchange between applicants results in a major deterioration in outcome, the applicants are re-assigned their original university places - otherwise the new solution is retained. "Using this method it is possible to implement a step-by-step system of allocation of university places until the end result is achieved and the applicants have all been appropriately assigned study places."
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