Çok amaçlı karar verme metodları ve bir bilgisayar programı
Multiple criteria decision making methods and a computer programme
- Tez No: 22042
- Danışmanlar: PROF. DR. RAMAZAN EVREN
- Tez Türü: Yüksek Lisans
- Konular: Endüstri ve Endüstri Mühendisliği, Industrial and Industrial Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1992
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 156
Özet
Bu çalışma ana olarak üç bölümde toplanabilir. îlk bölümde temel olarak karar verme olayı incelenmiş, karar verme süreci içinde bir problemin gözlenmesi ve saptanması daha sonrada amaçların saptanması ve uygulanması anlatılmıştır. Verilen kararın uygulanmasından sonra da çalışmaların devam ettiği vurgulanmış ve geri beslemelerle birlikte model kurmanın önemi üstünde durulmuştur. İkinci bölümde ise çok amaçlı karar verme metodları anlatılmıştır. İlk olarak temel kabuller içersinde tanımladığımız, bileşenler, amaçlar, hedefler ve ölçütler açıklanmış sonrada optimal çözüm, baskın çözüm, tercih edilen çözüm ve tatmin edici çözüm gibi ifadelere yer verilmiştir. Bundan sonra mevcut metodların sınıflandırılmasına geçilmiş ve tercihsel bilginin verilmesine bağlı olarak mevcut metodlar sınıflandırılmıştır. Buna göre ilk olarak hiç bir tercih bilgisinin verilmediği metodlardan toplu kriter metodu incelenmiş, daha sonra tercihsel bilginin başlangıçta verildiği metodlara geçilmiştir.; Tercihsel bilginin ilerleyen safhalarda verildiği etkileşimli metodları ele almadan evvel etkileşimli yaklaşımın avantaj ve dezavantajları üstünde durulmuş, bu tip metodların yapısı incelenmiş ve kendi aralarında sınıflandırılmıştır. Buna göre ilk olarak 1. grup etkileşimli metodlardan Geoffrion (GDF) metodu ele alınmış, bu metodda kullanılan Frank-Wolfe algoritması üzerinde durulmuş ve bir eleştiri getirilmiştir. 2. grup etkileşimli metodlardan ise Zionts-Wallenius ve Steuer metodları incelenmiştir. 3. grup metodlar ise kendi aralarında da üçe ayrılmıştır ve 3A grubu adı altında STEM metodu, 3B grubunda Delft ve Ni jkamp' in zincirleme optimizasyon modeli incelenmiş ve zincirleme olarak çok amaçlı problem çözme tekniğinin avantaj ve dezavantajları üstünde durulmuştur. 3C grubundan uzlaşık programlama (Compromise programming) ve etkileşimli uzlaşık programları ayrıntılarıyla incelenmiştir. Oçüncü bölümde ise tercih bilgisinin ilerleyen safhalarda verildiği 2. grup etkileşimli metodlardan Zionts- Wallenius metodunun bir bilgisayar programı yazılmış, bu yöntemle bir vaka problemi çözülmüş ve diğer yöntemlere göre karşılaştırması yapılmıştır.
Özet (Çeviri)
Today, multiple criteria decision making is perhaps one of the most important researc topics in the field of decision science. The essential activity of a manager is decision making. This activity is becoming more complex because managers (decision-makers) try to integrate in to their own decisions many different factors. In addition, over the last 20 years, the place allotted to multiple criteria problems in conferances, in academic publications and in practice has increased in importance. In these forums, we have seen many models claimed to be true decision aids. Chapter 1, covers the definition of the decision making and a general points of view about the decision making. Provides the language and basic concepts at Multiple Criteria Decision Making, concepts of criteria, goals, objectives and attributes are explained and carefully defined in this chapter. Many algorithms have been developed for multiple criteria decision making problems. The general multiple criteri decision making problem may be formulated as follows; Max F (x) i 1=1,2,...,m Subject to, 9 (x) » P i i+1 xih - Linear function of the deviation variables + d = The over-achievement of the it's goal d = The under-achievement of the it's goal Advantages of goal programming are that decision maker does not need to give the numerical weights for the objectives. He is forced to give only ordinal ranking of them. In this section of chapter 5, the interactive methods are presented which are introduced by the progressive definition of the decision maker's preferences. The progresive definition takes place through a decision maker & analyst or decision maker & machine dialogue at each iteration. The advantages of the interactive methods are ; there is no need for a priori preference information, it is a learning process for the decision maker to understand the behaviour of the system, only local preference information is needed and there are less restrictive assumptions as compared to methods presented previously. And the disadvantages are ; solutions depend upon the accuracy of the local preference the decision maker can indicate, there is no guarantee that the prefered solution can be optained within a finite number of cycles, much more effort is required of the decision maker. The method of Geoffrion, Dyer and Feinberg in its various forms begins with a feasible solution x' and has the decision maker provide information from which the partial derivates can be estimated. Then using the vector of partials as weights, a composite objectives optimized over the feasible solution space to obtain a solution x' '. A single dimensional search is carried out by the decision maker to determine the best solution on straight line segment connecting x' and x". The new solution becomes solution x1 and the process is repeated until solution x' does not change from one iteration to next. The multiple criteria decision making problem is formulated as follows; Max U (f (x)) i xnSubject to, x e X Where, U = Utility function f = Objective function X = Feasible set The Step method (STEM) which is Benayoun developed as an iterative tecnique that should converge to the best compromise solution in no more than k iterations, where k is the number of objectives. The method based on a geometric notion of best, i.e., the minimum distance from an ideal solution, with modifications of this criterion derived from a decision makers reactions to a generated solution. In that case that a clear trade-off is not given a method which can be used, is the stem method. This method is a solution tecniques for multiple objective linear programming problems. In this method a subset of non-dominated extreme points is presented to the decision maker. If the subset constraints an acceptable solution, the process is terminated, otherwise the decision maker chooses the best subset of solutions, and procedure is repeated. The method of Zionts-Wallenius is assumed that all the objective functions are concave and the constraintsform a convex set. The first step of the method is to choose weights and generate a composite objective function. For each efficient varieble a set of trade-off is defined by which some objectives are increased and others reduced. They are presented to the decision maker and from answers of decision maker a new set is constructed. The method of Steuer is somewhat different from the other methods. It assumes a linear utility function; the methods described so far assume nonlinear utility functions. It generates a sequence of sets of efficient solutions and ask the decision maker to choose the most-prefered solution of each set. The set of vectors of weights used to generate the solutions are generators of a convex cone. The method then shrinks the cone about the most-prefered solution and the process is repeated. Though the procedure is not guaranteed to xmfind the optimal solution. It generates good solutions, and has been applied to several practical problems. In this section covers, compromise programming approach, in which the distance to an ideal solution is minimized, no goals have to be chosen a priori. The information required from the decision maker at each iteration is also simple to provide. It may not be necessary to generate all of the non-dominated solutions after each iteration; the effiency and feasibility of the compromise solutions are also guaranteed. The biggest special of this method is that there is not necessary the analyst. Preference information is given every iteration and the solution of the problem with interactive compromise programming takes a short time. In Chapter 6, When a posteriori articulation of preference information given, this class of methods does not require any information regarding the decision maker's utility function. One disadvantage which has severely limited these methods practical applicability is that they usually generate a large number of non-dominated solutions, it becomes almost impossible for the decision maker to choose one which is most satisfactory. The methods of this category which are explained with examples are Parametric Method and The e Constraint Method. In Chapter 7, A computer-based information system is essential for effective managerial decision making. During past several years, the development and dissemination of microcomputer software have had a profound impact on decision making. A wide variety of software packages for such areas as accounting, finance, marketting, business planning, decision support system and business simulation are available. Thus, A computer programme which is written by basic and using Zionts- Wallenius Method is presented. In order to put the computer programme in perspective, it may be useful to solve a sample muliple criteria decision making problem and compare it with several other methods. xiv
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