Çok amaçlı karar verme metodları ve tekstil sanayiinde bir uygulama

Abstract

Klasik Matematik Optimizasyon teknikleri ile karar verme problemi, tek kritere dayanan mak simize veya minimize edilecek bir amaç fonksiyonu ve genellikle birden (azla kısıt denklemi ile ifade edilir. Kısıtları tatmin eden ve amaç fonksiyonunu arzu edilen doğrultuda en iyileyen çözüm "optimum çözüm"dür. Çok amaçlı karar verme bilimi ise, bu problemlerin uygulamaya daha dönük ve gerçekçi yaklaşımı ile ortaya çkıarılmıştır. Bir çok amaçlı karar verme probleminin optimum çözümü ise tüm amaç fonksiyonlarını en iyileyen çözümdür. Bu çalışmada ilk bölümde karar verme teorisi, ikinci bölümde ise çok amaçlı karar verme bili mi ile ilglii genel açıklama ve tanımlamalar verilmiştir. Üçüncü bölümde sonlu sayıda alterna tif kapalı kısıtlar altında kullanılan çok amaçlı karar verme metodlarına örnek olarak ELECTRE metodu anlatılmıştır. Dördüncü bölümde tercih bilgisinin ifade edilmediği metodlar ve Toplu Kriter Metodu anlatılmıştır. Dördüncü bölümde tercih bilgisinin ifade edilmediği metodlar ve Toplu Kriter Metodu anlatılmıştır. Beşinci bölümde Değer Fonksiyonu metodu, Sınırlanmış amaçlar metodu ve hedef rogramlama metodlannı içeren tercih bilgisinin önceden ifade edil mediği metodlara yer verilmiştir. Altıncı bölümde tercih bilgisinin sonradan ifade edildiği me- todlardan Parametrik metod, £ kısıt metodu ve çok kriterli Simpleks metodu anlatılmıştır. Ye dinci bölümde ise günümüzde üzerinde en çok araştırma yapılan Etkileşimli Çok Amaçlı Karar Verme Metodlarından sırası ile, GDF, Etkileşimli Hedef Programlama, STEM, Zıonts ve Walle- nius, Steuer, Yedek değer ikâme ve Etkileşimli Uzlaşım Programlama anlatılmıştır. Sekizinci bölümde yeni geliştirilmiş bir metod olan ISTM (Interactive Step Trade-off Method) ye yer veril miştir. Dokuzuncu bölüm, sadece ISTM metodunun tekstil sanayiine bir uygulaması olmayıp, ülkemiz İçin çok büyük bir önem arzeden Tekstil sanayii ve Tekstil üretim sistemlerinde karşılaşılan problemleri de içermektedir. Diğer sektörlerin yanında ihracat açısından önemli değerlere sahip Türk konfeksiyon endüstrisi ve kota uygulanmayan tek konfeksiyon dalı olması açısından büyük öneme sahip olan deri konfeksiyon dalı da bu bölümde anlatılmıştır. ISTM metodunun uygulanması da bir deri konfeksiyon işletmesinde gerçekleştirilmiştir.

Decision making is the proces of selecting a possible course of action from ali the available al ternatives. In almost all such problems the multiplicity of criteria for judging the alternatives is pervasive. That is, for many such problems the decision maker wants to attain more than one objective; or goal in selecting the course of action while satisfying the constraints dictated by environment, processes and resources. Another characteristic of these problems is that the ob jectives are apparently nancommensurable. Mathematically these problems can be represent ed as; Max[f1(x)/...f|c(x)] Subject to: gi{x)<0, i = 1,2,... m. Where x is a dimensional decision variable vecter. The problem consists of n decision vari ables, m constraints and k objectives. Any or all of the functions may be nonlinear. In litera tür, this problem is often referred to as a Vector Maximum Problem (VMP). There are two approaches for solving the VMP. One of them is to optimize one of the objec tives while appending the other objectives to a constraint set so that the optimal solution would satisfy these objectives at least up to a predetermined level. The problem is given as; Max fj (x) Subject to: gj(x)£0, i - 1,2 -. m f|_ (x) £ aı, L = 1,2... k and L * i Where a\ is any acceptable predetermined level for objective I. The other approach is to optimize a super-objective function created by multipling each objec tive function with a suitable weight and then by adding then together. This aproach leads to the solution of following problem : XI Ic Max Z wi, fi (x) i = l Subject to: gi(x)£0, i=1,... m The weights are usually normalized so that k X wi=l i = l The methods for various Multiple Criteria Decision Making (MCDM) problems are widely di verse. However, even with the diversity, all the methods which are concerned here share the following common characteristics: ( 1 ) A set of eriteria of judgenent (2) A set of decision variables (3) A process of comparing alternatives In the process of decision making, some preference information articulation from the decision maker may be required. If so, then the type of information and when it is given plays a key role in the actual decision making methods. We classify the method for multiple objective de cision making based upon these considerations. The classification has been made in three steps: Step I: The stage at which the preference information is needed. Step li: The type of information needed. Step III: The major methods in any branch formed from Step I and II. There are four fossible stages at which the information is needed from the decision making (Step I). They are: (1) no articulation of preference information is needed from the DM, which is ex plained in Chapter 4. {2} "a priori" articulation of preference information from the DM, which is explained in Chapter 5. XII (3) "a posteriori" articulation of preference information from the DM, which is ex plained in Chapter 6. (4) "progressive" articulation of preference information from the DM, which is ex plained in Chapter 7. In chapter 2, basic concepts of multiple criteria decision making are presented. There are some main terms which have no universal definition used in Multiple Criteria Decision Making literature. They are defined as follows: Attributes: They are the characteristics, qualities, or performance parameters of alternatives. Objectives: They are the directions "to do better" as perceived by the decision maker. Goals: They are things desired by the decision maker expressed in terms of a specific state in space and time. Criteria: They are standards of judgement or rules to test acceptability. This is the dictionary definition of the term. However, as used in the MCDM literature, it indicates attributes and/or objectives. Some other main concepts such as feasible region, optimal solution, the best compromise solu tion, non dominated solution, dominated solution, the preferred solution, etc. have also been explained with examples in this chapter. In chapter 3, the method of ELECTRE is explained, with examples. Measure of scales and weight of importance are determined for each criterion in this method, the pay-off table is es tablished by scoring each alternative for each criterion based on measure of scales deter mined. Then, the matrix of concordance and the matrix of discordance are determined. The best solution is found by considering these two matrices simultaneously. The graph theory is used for finding the best solution in this research. In chapter 4, the methods for solving Multiple Criteria Decision Making (MCDM) problems in which no articulation of preference information is asked from decision maker is presented. This means that this approach doesn't need any interobjective or other subjective preference information from the decision maker once the problem, constraints, and objectives have been defined. Thus, this approach requires that the decision maker be able to accept the solution obtained from the method. The advantage of this route is that in the process of obtaining the solution, the decision maker will not be disturbed by the analyst which is preferable from the point-or-View of the decision maker. However, a major disadvantage, then, is the recessity for the analyst to make many assumptions about the decision maker's preferences. The major method of this category is the method of global criterion which is explained with examples. In chapter 5, the methods in which a priori articulation of preference information is asked from decision making is peresented. In this method, "A Priori" means the preference informa tion is given to the analyst (who is responsible for the solution of the VMP (Vector Maximum XIII Problem) before he/she actually solves the problem. The Decision Maker (DM) provides the information during or after the actual mathematical formulation of the problem. The informa tion may be either: (1 ) Cardinal information, or (2) Mixed (ordinal and cardinal) information. In the case of cardinal information, the DM must give. Some judgement about specific objec tive preference levels or specific trade offs. But, irme information is mixed, the DM must rank the objectives in the order of their importance. Utility function methods and bounded objective methods, under cardinal information category are presented with examples in chapter 5. Lexicographic and Goal programming are presented as the methods for Mixed Ordinal and Cardinal Information given in Chapter 5. Goal programming is one of the widely used methods for Multiple Criteria Decision Making Method. The method requires the Decision Maker (DM) 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 form the set goals. The most common form of Goal Programming formulation requires that the decision maker, in addition to setting the goals for the objectives: also be able to give an ordinal ranking of the objectives. The GP formulation of the VMP for such a case is: min [ P, h] (