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Çok amaçlı karar verme metodları ve tekstil sanayiinde bir uygulama

Multiple criteria decision making methods and an application to the textile industry

  1. Tez No: 22049
  2. Yazar: H.EDA ÖZTÜRK
  3. Danışmanlar: PROF. DR. RAMAZAN EVREN
  4. Tez Türü: Yüksek Lisans
  5. Konular: Endüstri ve Endüstri Mühendisliği, Industrial and Industrial Engineering
  6. Anahtar Kelimeler: Karar verme, Tekstil endüstrisi, Çok amaçlı karar verme, Decision making, Textile industry, Multiobjective decision making
  7. Yıl: 1992
  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: Belirtilmemiş.

Özet

ÖZET ÇOK AMAÇU KARAR VERME METODLARI ve TEKSTİL SANAYİİNDE BİR UYGULAMA 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.

Özet (Çeviri)

SUMMARY MULTIPLE CRITERIA DECISION MAKING METHODS AND AN APPLICATION TO THE TEXTILE INDUSTRY 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 : XIIc 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 XIIIProblem) 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] (<T, d+), P2 h2 (d“, d+)... P, h! (<T, d+) ] Subject to: gj(x)£o, j » 1,2,... m fi(x) + dr-di+-bi, İ=l,2,...k d^di+^OVi, dr,di+ = OVi Where hi (d~, d+), i = 1,2,...L are linear functions of the deviational variables, and are called achievement functions di”is colled as“the under-achievement”while di+ is called as“the over-achievement'' of the ith goal. The Pi's are preemptive weights that is, Pi >» Pi + 1. The solution is that hi (d”, d+) is minimized first; let min hj = hi *. Next iWd“, d+) is mini mized, but İn no circumstances con hi be greater then h] *. Thus, a lower ranking achieve ment function cannot be satisfied to the detriment of a higher ranking achievement function. This process confines until h. (d~, d*) is minimized. Advantages of Goal Programming are that the decision maker does not need to give the nu merical weights for the objectives. He/she is forced to give only one ordinal ranking of them. There are mainly three methods for the solution of linear goal programming: XIV(1) Graphical solution method (2) Iterative solution method (3) The modified Simplex method. These methods, together with some examples are explained in Chapter 5. If any of fi (x) and gi (x) functions are nonlinear, the problem becomes a nonlinear goal pro gramming problem which is also mentioned in Chapter 5. The following methods could be used for solving nonlinear goal programming problems: (1) Iterative solurino method (2) Method of Griffith and Stewart (3) Pattern Search method. The methods of Griffith and Stewart, is basedon the linear approximation of nonlinear func tions then the nonlinear goal programming problem can be solved by linear goal program ming. The pattern search method is based on an extension of the search method of Hooke and Jeeves and it is particularly easy method to program. In Chapter 6, Methods for ”A Posteriori“ articulation of preference information given are pre sented. The methods of this class determine a subset of the complete set of nondominated so lutions to the VMP. From this subset the DM chooses the most satisfactory soluton, making im plicit trade-offs between objectives based upon some previously unindicated or nun quantifiable criteria. In any case, the trade-off information (which remains implicit) is received from the DM after the method has terminated and the subset of nondominated solutions has This class of methods does not require any assumption or information regarding the DM's util ity function. One disadvantage which has severely limited these methods practical applicabili ty is that they usually generate a brge number or nondominated solutions; it becomes almost impossible for the DM to choose one which is most satisfactory. Therefore, the methods are generally incorporated into some of the interactive methods such as Zionts-Wallenius (see sec. 7.8), the Method of Steuer (see sec. 7.9). Parametric Method, The e Constraint Method and multicriteria Simplex method are mentioned in Chapter 6. XVIn Chapter 7, the interactive methods are introduced. Interactive methods rely on the progres sive definition of the decision maker's preferences along with the exploration of the criterion space. Much work has been done recently on this class of methods. The progressive defini tion takes place through a DM-Anafyst or DM-Machine dialogue at each iteration. At each such dialogue, the DM is asked about some trade-off or preference informatino based upon the current solution (or the set of current solutions) in order to determine a new solution. Some methods require explicit information regarding the trade-off between attainment levels of ob jectives at each stage; others require the implicit trade-off information in the form allowing the DM to indicate acceptability of the current achievement level. The advantages of the methods are: (1 ) there is no need for ”a priori" preference information; (2) it is a learning process for the DM to understand the behaviour of the system; (3) only local preference information is needed; (4) since the DM is part of prospect of being implemented; (5) there are less restrictive assumptions as compared to methods described previously. The disadvantages are: (1 ) solutions depend upon the accuracy of the local preference the DM can indicate; (2) for many methods there is no guarantee that the preferred solution can be obtained. Within a finite number of interactive cycles; and (3) much more effort is required of the DM then is so with metinods presented previously. The method proposed by Geoffrion, Oyer and feinberg is presented in Section 7.5. This method demonstrates that a large step gradient algorithm can be used for solving the rector maximum problem if the decision maker is able to specify an overall utility function defined on the values of the objectives. However, the method never actually requires this function to be indentified explicitly. Instead, it asks only for such local information as is needed to perform the computations. The procedure is described in the context of the Frank-Wolfe algorithm which is a specific nonlineer programming method. The problem is formulated as follows: MaxUtf1(x),f2(x)/...fk{x)] Subject to: xe x The objective functions fi (x) and the feasible set x, x = { x I 9 (x) £ 0 ), are assumed to be ex plicitly known, but the utility function U (f) is assumed to be only implicitly known. Interactive Goal Programming (IGPj is a method which is another mathematical expression of the concept of the Geoffrion method, and the computational procedures are the same. The STEP-meihod (STEM) the progressive orientation procedure, and the method of constraints are for solution of multiple objective linear programming problems. STEM allows the Decision Maker (DM) to leam to recognize good solutions and the relative significance of the objectives. In the methdo, phases or computation alternate (interactively) with phases of decision. XVIIn this method a subset of nondominated extreme points is presented to the decision maker. If the subset constraints an acceptable solution, the procedure is terminated; otherwise the deci sion maker chooses the best subset of solutions, which is then used to determine a new set of nondominated extreme points, and the process is repeated. On the other hand, The Method of Zionts-Wallenius is assumed that all the objective functions are Concave (to be maximized) and the constraints form a convex set; nonlinear functions are linearized, me overall utility function is assumed to be unknown explicitly to the DM, but is implicity a linear function and, more generally, a concave function of the objective functions. The method makes use of such an impiici function on an interactive basis. The first step of the method is to choose an arbitrary set of positive multipliers or weights and generate a composite objective function or utility function is then optimized to produce a non- dominated solution to the problem. From the set of nonbasic variables, a subset of efficcient variables is selected. For eacn efficient variable a set of trade-offs is defined by which some objectives are increased and others reduced. A number of such trade-offs are resented to the DM, who is requested to state whether the trade-offs are desirable, undesirable or neither. From his/her answers a new set of consistent multipliers is constructed and the associated non-dominated solution is fonud. The process is then repeated, and a new set of trade-offs is presented to the DM at the current solution; convergence to an overall optimal solution with re spect to the DM's (implicitutility function is assured. The Interval Criterion Method, proposed by Steuer, is an extensison of the multiple objective linear programming method. Multiple objective linear programming problems, even moder ately sized ones, often have an unwork ably large number of nondominated extreme points. Steuer's interactive multiple objective linear porgramming method presents to the DM 2k+l nondominated extreme points at each iteration (k is the number or objectives); the decision maker has only to indicate the most preferable solution from this set. Once this solution is identified, the nondominated extreme point in the neighborhood are explored and a new set of nondominated solutions are identifie and presented to the DM. The method of surrogate worth trade-off İs proposed by Heimes, Hall and Freedman (trecag- nizes-that given any current set of objective levels attained, it is much easier for the decision maker to assess the relative value of the trade-off of marginal increases and decreases between any two objectives than their absulavalues. The method consists of two phases 1 -Identifation and generation of nondominated solutions which form the trade off functions in the objective space, 2-The searchsord preferred solution in the non olominated solutions. The preferred decision is located by interaction with the deci sion maker to assess the indifference band by the use of the newly introduced surrogat worth function. The last method which is presented in Chapter 7 is the Interactive Compromise Programming (ICP). The method attempts to reduce the complexity of Information required from the Decision Maker (DM). No prior information is required from the DM. The information required from the DM at each iteration is also simple to provide. The solutions in terms of the degrez of closeness to the Ideal solution are presented to the DM and he is just asked his mast preferred and/or least preferred solution. The method does not require significantly more data then XVIIpure linear programing is done. It may nor be recessary to generate all of the nondominated after each iteration; the efficiency and feasibility of the compromise solutions are also guaranted. It is hoped that convergence with this method would be fast, because the new solution presented to the DM among others, even at the first iteration, is the most probable solution found in the minimax sense. In Chapter 8, A new method to solue multiobjective optimization problems (MOP's), called the Interactive Step Trade-off Method (ISTM) is proposed. With the help of an auxiliary problem AP (e ), the preferred solutions of MOP's will be found on their efficient solution faces in ISTM. Using local trade-off information presented by the analyst, the Decision Maker (DM) makes decisions step by step, which hearisticolly directs the analyst to look for efficient solu tions of MOP's, along preference directions, in proper setp sizes until the preferred solutions are found. The interaction in the method is practical, clear, and easy to understand. The method may be used in the design of decision support systems in such frek's as the production management of industrial enterprises. The proposed algorithm of ISTM is programmed for the computer (see. appendix) and used to solue a real problem mentioned in Chapter 9 In Chapter 9, an application of MCDM problems, in the Textile production systems is present ed. Firstly, Textile Production systems and the problems in this field are presented. The differ ent problems of sequencing production operations in parallel processor shops of the textile company are considered. The complexity of these problems depends on: (1 ) the machine change over times which occur when the change overs cannot be realized in parallel during processing times, and (2) the operation due dates which have to be at best re spected when the workshops do not constitute stocks. The objective is to minimize mean com- pletino time and mean tardiness. Section 9.1 models these different scheduling problems and presents some tools to solue these problems. Textile Industry in general and Turkish Clothing Industry together with leather clething technol ogy are also mentioned in Chapter 9. Clothing Industry Because of the cheap labour which is easily found in such areas likeclothing Industry, this field is very attractive for new investors. However there are some quotas applied by developed countries cuhich set the implication of exports in Textile Clothing Industry. Hence, because of it's freedom of quotas, Leather Cloth ing Industry, in Turkey, if some precautions in this field such as making new investments in Leather Tecnology or getting jointed together some small business which are directly dealt with this Industry, are taken into consideration. XVIII

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