Üniversite bütçelerinin uzun dönemli planlaması için şebeke analizi

Abstract

Üniversitelerde uzun dönemli planlama çalışmaları özellikle Türkiye gibi gelişmekte olan ülkelerde üzerinde ciddiyetle durulması gereken bir sorundur. Zira kısıtlı olan kaynakların en verimli şekilde kullanılması önemlidir. Bir başka husus ise, bir bilim yuvası olan üniversitelerde bilimsel çalışmaların artırılması ve bu çalışmaların sonuçlarının hızla ülkenin kalkınması için kullanılmasının gerektiğidir. Ayrıca, bu kurumlardan yetişecek daha nitelikli elemanların katkısı da gözardı edilemez. Yöneylem Araştırması alanında üniversite planlaması üzerine yapılmış çeşitli çalışmalar mevcuttur. Ancak bu çalışmalar bir üniversitenin çok az bileşenini kapsar. Zira bir üniversitenin bütün yönlerini kapsayan modeller oldukça büyüktürler ve çözümleri zor olmaktadır. Bu çalışmada üniversite planlamasına Ek Kısıtlı Genelleştirilmiş Şebeke Analizi (Embedded Generalized Networks) tekniği uygulanmıştır. Şebeke analizi tekniği daha hızlı sonuç veren ve büyük kapsamlı problemlerin çözümüne imkan tanıyan bir tekniktir. Ancak üniversite gibi geniş kapsamlı bir kurumun modellenmesi için Salt Şebeke Modelleri (Pure Networks) ve Genelleştirilmiş Şebeke Modelleri (Generalized Networks) yeterli olmamaktadır. Çünkü gözönüne alman bileşenler arasındaki ilişkiler sadece akışların korunumu ve dağıtılması ile sınırlı değildir. Bir bileşenin başka bir bileşenle ilişkisi olabilir. Bu durumda bağlardaki akışların birbirleriyle olan oransal ilişkilerini ifade etmeye yarayan ek kısıtların da tanımlanması gerekir. Ayrıca burada verilen şebeke modelleri akış şebekeleridir (Flow Networks). Zira literatürde faaliyet şebeke modelleri içerisinde mütalaa edilen ve yine genelleştirilmiş şebeke modelleri olarak adlandırılan modeller de vardır. Bu tez çerçevesinde incelenen şebeke modellerinde bağlar akışları, diğer şebeke modellerinde ise bağlar faaliyetleri ifade eder. Üniversite planlaması için kurulan model devlet üniversitelerini esas almış olup sayısal uygulama için İstanbul Teknik Üniversitesi 'nin değerleri kullanılmıştır. Geliştirilen modelde, üniversitenin, 5 tanesi kişilerle, 1 7 tanesi harcama kalemleriyle ve 5 tanesi de gelir kalemleriyle ilgili olmak üzere toplam 27 bileşeni gözönüne alınmıştır. Amaç öğrenci/araştırma görevlisi, öğrenci/öğretim üyesi gibi oranlar ile araştırma faaliyetlerine ayrılan paylan yükseltmek ve hazine yardımı miktarını en küçüklemektir. Bununla ilgili çeşitli senaryolar model aracılığıyla denenmiş ve sonuçları irdelenmiştir.

Today, planning problems are solved by using several methods of Operations Research. Apart from this, recent developments in operations research, algorithms and computer technology provide the solutions for more and more complex problems. Mathematical modelling is the process of expressing and interpreting the real life events by several mathematical symbols. The use of the mathematical models increases rapidly. This is the result of the system analysis, the computer technology and the algorithms. The steps of expressing an event by using mathematics are as follows: i) Definition of the problem ii) Mathematical formulation iii) Mathematical analysis iv) Interpretation of the analysis to obtain the solution Of course, the most important step is the first one. Because, any mistake made at this step will cause the miss-expression of the real event. Thus, the solution will be wrong. The optimization is the process of finding the best solution for the problem. Mathematically, to find the maxima or minima of the function f(xl,x2,....,xn) with n variables according to the objective. This function can be subject to some constraints such as g;(x,,,x,,...., x") = ö;,/ = 1,2,..., m. Although, the optimization is used by statistics and applied mathematics, it is also an important topic of operations research. But this difference must be emphasized. Operations research asks what to do. Namely, there is a decision making function. Network analysis depends on the graph theory. The beginning of the graph theory is Euler's famous paper titled "Bridges of Koenigsburg" which was published in 1736. Euler proved that it was impossible a tour among the bridges of Koenigsburg by visiting a bridge only once. But, after the paper, there was no more research made until the 1 st World War. A graph consists of the set of nodes, and the set of arcs which connect them. If the -iX- directions for the arcs are defined, then the graph is cailed a "directed" or an "oriented graph". Furthermore, if some functions are defined on the arcs, then this graph becomes a network. The network problems are divided into three categories as follows: 1) Distance networks: The distances between nodes are important. For example, the distances between the cities of a country. 2) Activity networks: In the activity network, jobs to be made and the sequence of them are important. For example, project planning networks so what CPM. 3) Flow networks: The flows within arcs and the costs of flows are important. For example, the distribution of goods for consumer demand. In network analysis, it is very easy to understand the relations between events. Because it is a very powerful visual tool to express the relations. Many events in real life can be imagined as flow networks. For example, the flow of water in pipes, the flow of traffic in roads, the flow of electricity in wires, or the flow of the money in time and events. The elements of a network are: 1) Flow: The quantity of the elements which flow in the arcs. This is the decision variable. 2) Upper bound: The maximum quantity that an arc can carry. 3) Lower bound: The minimum flow quantity that is allowed for an arc. 4) Cost: The carrying cost per unit flow. The optimization is performed according to this cost. 5) External flows: The flow entering to (or exiting from) the network at nodes. This means the extra flows. 6) The conservation of flow at nodes: The main philosophy of the network analysis is the conservation of flow at nodes. All constraints, except those for bounds, are written according to this law. Flow networks are classified in three groups: 1) Pure networks: In pure a network there is no arc gain or loss. Namely, a flow at the beginning of an arc is equal to the flow at the end of that arc. 2) Generalized networks: In generalized networks, arc gains or losses are defined. Flows at the beginning and the end of arcs are not equal. For example, the pressure loss of water in a pipe. 3)Embedded generalized networks: If some side constraint are defined for a generalized network, it becomes embedded generalized network. The main approach for this Ph.D. thesis is the last one. The mathematical formulation of the embedded generalized network is as follows: min c'x subject to Ax0 There are many applications of network models in operations research literature. For example, allocation land for sectors, air-traffic control, building evacuation problem, project selection, manpower planning, operations planning in air cargo transportation, and so on. The input or the output of money to or from a system or an event is called cash flow. Engineering Economics is interested in cash flows. According to engineering economics, the time value of money is important. The time value of the money is defined as the equivalence of money at the one moment in time and at another moment in time. The relation between these two time points is the equivalence. This equilavence is examined by the techniques such as present (or future) value analysis and internal rate of return analysis. But the money has a special importance. Thus, the researchers in the field of operations research study for the planning of financial problems. Many succesful research studies have been done. Cash flow problems can be modeled by network analysis as well as other techniques. Especially, Generalized Network Models quite fit to the cash flow models. But sometimes, financial events do not occur within only one arc. More than one arc is required to express the event. For example, to loan with periodic instalments requires more than one arc, i.e. one is for the money input and others for the repayments. And some ratios must be defined on the arcs depending on the first arc. This is accomplished by using the side contraints within the network structure. The network formulation with side constraints is called ''Embedded Generalized Networks". In formulation of financial problems by network modelling, the events and the time points are expressed by nodes and the transfer of money is represented by the arcs connecting these nodes. Furthermore, other network elements such as upper or lower bound can be added to the model. The planning of the universities' cash flow is an interesting research area. The results -xi- 2) Academic staff sub-network: the proffessors and the research assistants are pianned within this sub-network. 3) Lecturer sub-network: Lecturers are for lessons other than professionai ones. The number of the lecturers are computed in this sub-network. 4) Managerial staff sub-network: The managerial people of a university is planned in this sub-network. 5) Cash flow network: The financial side of ali components are planned in this sub network according to the incomes. This model is solved for three periods of planning horizon. The results are discussed in Chapter 6. And suggestions for further research are given in Chapter. 7. -Xlll- 2) Academic staff sub-network: the proffessors and the research assistants are pianned within this sub-network. 3) Lecturer sub-network: Lecturers are for lessons other than professionai ones. The number of the lecturers are computed in this sub-network. 4) Managerial staff sub-network: The managerial people of a university is planned in this sub-network. 5) Cash flow network: The financial side of ali components are planned in this sub network according to the incomes. This model is solved for three periods of planning horizon. The results are discussed in Chapter 6. And suggestions for further research are given in Chapter. 7. -Xlll