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Çok amaçlı karar vermede yeni bir yöntem ve uygulaması

Application working on trade banking of a new multiple objective decision making method

  1. Tez No: 46304
  2. Yazar: A.COŞKUN DÜNDAR
  3. Danışmanlar: PROF.DR. RAMAZAN EVREN
  4. Tez Türü: Doktora
  5. Konular: Endüstri ve Endüstri Mühendisliği, Industrial and Industrial Engineering
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 1995
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 226

Özet

ÖZET ÇAKV Yöntemlerinin İncelenmesi ve Yeni bir ÇAKV Yönteminin Ticari Bankalara Uygulama Çalışması Bu çalışma 5 bölümden oluşmaktadır. Birinci bölümde, Karar Verme Teorisinden kısaca bahsedilmiş ve karar vermeye sistem yaklaşımı yapılmaya çalışılmıştır. Daha sonra karar verme sürecindeki temel unsurlar sıralanmış, amaç sayısı ve bilgi düzeyine göre karar verme türleri tablo halinde ifade edilmiştir. ikinci bölümde ÇAKVnin kısa tarihçesi ve terminolojisine değinilmiştir. Aynı bölümün gereği ÇAKV yöntemleri sınıflandırılmış ve özetlenmiştir. Üçüncü bölümde, yeni yöntemin geliştirilmesinde yararlanılan temel bazı ÇAKV yöntemleri örnek çözümleri ile birlikte ele alınmıştır. Dördüncü Bölümde yeni yöntem; formülasyonu, algoritması, temel prensipleri, Lineer ve Non-Lineer sayısal örnekleri, fayda ve sakıncaları ile birlikte genişçe ele alınmıştır. Beşinci bölümde ise; yeni yöntem sermaye yeterliliği, risk faktörü ve karlılıktan oluşan üç amaçlı, 12 kısıtlı ve 16 karar değişkenli gerçek bir finansal probleme uygulanmış ve bu yeni çalışmanın genel bir değerlendirilmesi yapılmıştır. xııı

Özet (Çeviri)

SUMMARY APLICATION WORKING ON TRADE BANKING OF A NEW MULTIPLE OBJECTIVE DECISION MAKING METHOD Decision making is the process of selecting a possible course of action from all the available alternatives. In almost all such problems the multiplic ity of criteria forjudging the alternatives is pervasive. That is, for many such problemls, the decision maker wants to attain more than one objective or goal in selecting the course of action while satisfying the constrains dictated by environment, processes, and resources. Another characteristic of these pro blems is that the objectives are apparently noncommensurable mathemati cally, these problems can be represented as: Max Lfi (x), f2 (x),..., fk(x)j Subject to: gi(x)ifi(x) i=l Subject to: gi(x) In the Weighting method, all the objectives are weighted to generate a non dominated set and so that, it's possible to express the opposite objective values in the same unit. £ constraint method supposes that a profit which is upon the maximum level defined associated to the objectives by decision maker, is harmful. The aim of another method which is called Multiple objective linear programming is to optimise the objectives under definite accepts by associat ing the best combinations of the qualities. Finally, when a decision maker is only related to inferrior values in the solution of the problem, adjusting searching method can be used. In third chapter, some basic multiple objective decision making meth ods have been mentioned with their examples, and Interactive compromise Goal Programming which is the subject matter of this thesis and which has been told in fourth chapter made use of this theory. One of the widely used methods for multiple Criteria Decision making method, Goal programming is presented. The method requires the decision maker to set goals for each objective that he/she wishes to attain. A preferred solution is then defined as the one which minimizes the deviations from the set goals. XVlllThe most common form of Goal programming formulation requires that the decision maker, in addition to setting the goals for the objectives, is also able to give on ordinal ranking of the objectives. The Goal programming for mulation of the Vector maximum problem for such case is: Min [pihiCd-, d+), p2h2(d-, d+),...., pLhL(dr, d+)] Subject to: gj(x) 0, Vi di-.dj^O.Vi Where bj, j= l, 2,..., k are the goals set by the decision maker for the ob jectives; dj“ and d+ are respectively the under- achievement and over- achievement of the jth goal, h^d”, d+), are linear functions of the devational variables and are called achievement functions. The pj's are preemptive weights; that is, Pj » pi+1. The solution is that h1(d“, d+) is minimized first; let min h1=h1*. Next h2(d”, d+) is minimized, but in no circumstances can hj be grater then. l^*. Thus a lower ranking achievement function. This process continues until hi(d", d+) is minimized. Goal programming method is quite similar to lexico graphic method; the difference is that Goal programming requires goals for the objectives which are set by the decision maker and achievement func tions to be minimized in the order they are formed. Advante ges of Goal Progranrming are that the decision maker does not need to give the numerical weights for the objectives. He/She is obliged to give only an ordinal ranking of them. There are mainly three methods for the solution of linear goal program ming: * Graphical solution method. * Iterative solution method * The modified simplex method. xixSome special computer programs for linear models are available. The modified simplex algorithm approach for a moderate size problem is time consuming, and it needs a large capacity computer. The same problem can be solved iteratively by the basic simplex algorithm. If any of f j(x) and gj(x) functions are nonlinear, the problem becomes a nonlinear goal programming problem. The following methods could be used for solving nonlinear goal programming problems: * Iterative solution method * Method of Griffith and stewart * Pattern search method. Other important and interactive method is method of Geoffrion-Dyer- Feinberg; Interactive methods rely on the progressive definition of the deci sion maker's preferences along with the exploration of the criteria space. Much work has been done recently on these methods. The progressive defini tion takes place through a decision maker-analyst or decision maker-ma chine dialogue at each iteration. At each such dialogue, the decision maker is asked about some trade-off or preference information based upon the current solution (or the set of cur rent solutions) in order to determine a new solution. The method proposed by Geoffrion, Dyer and Feinberg demonstrates that a large-step gradient algorithm can be used for solving the vector maxi mum problem if the decision maker is able to specify an overall utility func tion defined on the values of the objlectives. However, the method never actu ally requires this funciton to be identified explicitly. Instead, it asks only for such local information as is needed to perform the computations. The proce dure is described in the context of the Frank- Wolfe algorithm Which is a spe cific nonlinear programming method. The problem is formulated as follows: MaxUtfiCx),^)...,^!)) Subject to: xe X The objective functions f^x) and the set X, X= (x I g(x) f°r these objectives ideal values are avaliable in order to make the function of xe X. DM for each objective function can do sensitivity analysis in order to be in the way f(x), xe X by putting added constraint. Added constraint is set by reducing Af value from ideal value. This Af value is changed constantly by DM. These changings are in equal parts. When the number of these parts in crease, they get away from ideal value. The value which is reduced as monotonous value from ideal value of ob jective function can not be smaller than anti-ideal value (minimum) Thus, the more sensitivity analysis is done, further it gets away from ideal value. This operation can be until the last f(x) value becomes equal to anti-ideal value. - DM and DM's can be easily directed by computer if they are prepared by persons who know objective and constraint equations. Thus, even only the DM which can turn on and off the computer, the method will operate the com puter program and can get result. - If DM can weight the objective functions as verbal and numerical, ob jective equation number will be reduced from. Multiple objectives to single objective. So with the constraint set which is given to equated objective func tion, solution can be found with the condition of xe X. These solutions can be renewed by changing their order or weighting ratio. - If DM prefers the solution set in any process, or determines as compro mise solution, the operation ends. If this condition is not provided, termina tion criterion can determine how much iteration will continue. - Criterion depends on the condition of operation ending when it reach es the value of oc determined by DM beforehand. Absolute value of ideal value of i. objective is calculated, i. iteration val ue is substracted from the gotten value. Then the gotten value is diveded to absolute value of ideal value. The gotten result is substracted from one. - By converting objective funtions to single objective, all the solutions produced by optimizations with the condition of xe X are non dominated. But while objective function values between two points are determined with the increases of At, and if the begining point is not a non dominated point, the prefered compromise solution can be non dominated solution ei ther. In this point the method can provide a dominance in favour of objective reference that DM will choose. But this is possible by adding the above men tioned reference objective to constraint equation. When in minimization problems, it is > and in maximization problems, it is

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