Yatırım fizibiliteleri üzerinde hedef programlamasının uygulanması

Abstract

Bu çalışmada çok amaçlı bir karar verme yöntemi olan Hedef Programlaması üzerinde durulmuş, bir yatırım fizibilitesi üzerinde uygulaması gerçekleştirilmiş ve modelin alternatif senaryolara gösterdiği tepkiler incelenmiştir. Birinci bölümde yatırımlar konusuna giriş yapılmış, yatırım kavramı ve çeşitli yatırım türleri açıklanmış ve sabit kıymet yatırımları tanıtılmıştır. İkinci bölümde yatırım fizibiliteleri üzerinde durulmuş, bir yatırım fizibilitesinin hazırlanması, incelenmesi ve değerlendirilmesinde önemli olan noktalar ve izlenecek yollar açıklanmıştır. Üçüncü bölümde karar destek sistemleri ve karar analizlerine giriş yapılmış, çok amaçlı karar verme yöntemlerinden Hedef Programlaması tanıtılmıştır. Bu konuda detaya inilerek grafik yöntem ve Simplex yöntemi örneklerle açıklanmış, hedef programlamada kullanılabilecek teknikler (post optimal duyarlılık analizi, parametrik hedef programlama, belirsizlik altında hedef programlama) anlatılmıştır. Dördüncü bölümde gerçek, ancak anlaşılabilir olması amacıyla nispeten küçük ve basit bir yatırım fizibilitesi seçilmiş, değişkenleri, sapmaları, amaç ve hedefleri belirlenmiş, hedef programlama modeli kurulmuş ve mevcut senaryoda çözümü gerçekleştirilmiştir. Problemin farklı çözümlerini elde etmek ve değişkenlerin hangi yapıda daha hassas hale geldiklerini bulmak amacıyla, farklı önceliklerle farklı amaç ve hedefler geliştirilmiş, bunlar ayrı ayrı modele uygulanmış, çözümler karşılaştırabilir tablolar haline getirilerek sonuçlar yorumlanmıştır.

The usefulness of the mathematical model is well appreciated by the mathematician, engineer, economist, operations researcher and management scientists among others. Such models, and their associated methods for analysis and solution, have found such repeated use in the solution of real world problems that there can be no doubt as to their importance as a decision making aid. Nevertheless, with the recent interest and awareness in the limitations of our natural resources, there has also come a realization of a serious shortcoming in our traditional mathematical models. These models (and their solution methods) are all restricted to the analysis of problems having only a single objective. Unfortunately, real problems almost invariably are characterized by multiple, conflicting objectives. Consequently, if we attempt to describe such multiple objective problems by single objective models, then we should not be surprised when the answers derived from such restricted models fail to yield satisfactory results. Fortunately, recent increased interest in the multiple objective model has led to the development of an effective methodology for both the modelling and solution of virtually all classes of multiple objective problems that one might expect to encounter. This methodology is based on straightforward extensions to a technique known as "goal programming". Goal programming allows one to extend the capabilities of mathematical models so as to encompass decision involving multiple objectives. This is accomplished by assigning, to each objective, a priority (actually, a preemptive priority) that should reflect the priorities of the decision maker. If such preemptive priorities can be established, rather straightforward mathematical techniques are available. Everyone having a familiarity with linear programming can recognize that the basis for many of the problem solving techniques rests on the well-tested simplex method of linear programming. -via- An important property of goal programming is its capability to handle managerial problems that involve multiple incompatible goals according to their importance. If management is capable of establishing ordinal importance of goals in a linear decision system, the goal programming model provides management with the opportunity to analyze the soundness of their goal structure. In general, a goal programming model performs three types of analysis; (1) it determines the input requirements to achieve a set of goals; (2) it determines the degree of attainment of defined goals with given resources; (3) it provides the optimum solution under the varying inputs and goal structures. The goal programming approach to be taken should be carefully examined by the decision maker before he employs the technique. The most important advantage of goal programming in its great flexibility, which allows model simulation with numerous variations of constraints and goal priorities. It can be applied to almost unlimited managerial and administrative decision areas. The following three are the most readily applicable areas of goal programming. 1. Allocation Problems: One of the basic decision problems is the optimum allocation of scarce resources. Let us assume that there are n different input resources that are limited to certain quantities and there are m different types of outputs that result from various combinations of the resources. The decision problem is to analyze the optimum combination of input resources to achieve certain goals set for outputs so that the total goal attainment can be maximized for the organization. Planning and Scheduling Problems: Many decision problems involve some degree of planning and/or scheduling. In order to achieve certain goals in the future, decisions must be made concerning present and future actions to be taken. To accomplish desired outputs, the optimum combination of inputs in certain time periods must be identified. These inputs may include manpower, materials, time, production capacity, technology, etc. Many problems, such as production scheduling, location determination, financial planning, personnel planning, marketing strategy planning, etc., can be analyzed by goal programming. Policy Analysis: For government agencies and nonprofit organizations, the basic decision problem involves the assignment of priorities to various goals and development of programs to achieve these goals. Such decision process constitutes the policy analysis of the organization. Through the application of goal programming the organization is able to -IX- ascertain the soundness of its policies, the input requirements for achievement of set goals, and the degree of goal attainment with the given resources. This review and evaluation process are an integral part of policy analysis. Therefore, goal programming is particularly well suited for decision analysis in public and nonprofit organizations. As with any approach to problem solving, the solution to the problem is only as good as the model used to represent the problem. Thus most errors or anomalities in goal programming are often not the fault of the method, but rather due to the lack of care given in building the model. However, the one major pitfall involved with goal programming is not as much associated with methods and models as it is with philosophy. Unfortunately, in the past, some of the published work in goal programming tended (intentionally or unintentionally) to leave the reader with the impressions that goal programming was simply an interesting, somewhat clever "extension" of linear programming. Such thinking is not only erroneous but it also leads and has led to substantial errors and misunderstandings in goal programming. When one thinks of goal programming as simply an extension of linear programming, he or she is apt to try to apply linear programming terminology and associated results to goal programming without really considering their true implications. To illustrate, a few examples of the unfortunate results of a linear programming based philosophy can be offered. First a linear programming model (as formulated) can be unbounded (for example, profit can increase without limit). Such a problem usually is the result of overlooking one or more "constraints". The simplex method of linear programming signals the occurance of an unbounded problem via en examination of the tableau elements. Some mathematicians have stated then that such an unbounded problem can also exist (and be detected) in linear goal programming. They make such a statement probably because they view linear goal programming as a simple extension of linear programming rather than viewing linear programming as a special subset of linear goal programming. The fact is that a linear goal programming problem cannot be unbounded because right-hand side values are assigned to each objective. A solution then either achieves these values or it does not and thus, even though a right-hand side value could possibly be increased without limit (and the value still achieved), linear goal programming will not signal such a feature (at least not in the same manner as in linear programming). A second problem occurs when the goal programmer uses linear programming terminology such as the inappropriateness of the term "constraint" for absolute objectives and the term "objective" for the -X- achievement function. The extension of such linear programming terminology to goal programming results, at the least, in confusion and, at worst, leads to improper model formulation. Now that we have had a chance to understand the basic differences, it is appropriate to discuss limitations of the technique. It is natural that every quantitative technique has limitations. Some limitations are inherent to all quantitative tools, and some are attributable to the particular characteristics of individual techniques. Here are these limitations: 1. Proportionality: The measure of goal attainment and resources utilization must be proportional to the level of each activity conducted individually. Decision problems that involve some nonlinear relations relationships because of the lack of proportionality are extremely difficult to solve by goal programming at this time. In fact, this is one of the future research needs in goal programming. It is possible to formulate a goal programming model for a nonlinear programming problem by employing the piecewise linear approximation. However, such a case is indeed an infrequent exception. 2. Additivity: The condition that goal attainment and resource utilization be proportional to the level of each activity conducted individually does not ensure linearity. A nonlinearity may occur if there exist joint interactions among some activities of the goal attainment or the total utilization of resources. To ensure linearity, therefore, the activities must be additive in the objective function and constraints. 3. Divisibility: Another limitation of goal programming is that fractions of decision variables must be acceptable in the solution. In other words, the optimum solution of a goal programming often yields noninteger values for the decision variables. For many decision problems this limitation imposes no actual limitation. For example, if the unit used for the decision variables in a product mix problem is number of boxes and a box contains 100 pieces of the product, a fractional solution value is perfectly satisfactory. There are cases, however, where decision variables must be integers to have physical significance. 4. Deterministic: In the normal goal programming model, all of the model coefficients (ay, ty and Pj) must be constants. In other words, the problem requires a solution in a static decision environment. However, in reality the decision environment is usually dynamic rather than static. Therefore, the model coefficients are neither known nor constant. This limitation is a most severe one, as goal programming models are usually formulated for future decision making. The model coefficients are based -XI- on forecasts of future conditions. Information and forecasting methods available are generally inadequate for the precise determination of coefficients. It is also possible that model coefficients are random variables that have unique probability distributions for the value ihey take on when the solution is implemented. Now that the differences have been established, it is appropriate to explain the main purpose of this project. Investments play one of the most important and effective roles in earning money and making profit. Decisions on investments are not made due to feelings and optimistic hopes of the decision maker, who is usually a top manager in his/her organization. Instead, scientific methods and realistic studies are preferred, in order to support the decision maker while making decisions about related investments. Thus, the decision maker has a better chance in evaluating the feasibility studies and choosing between alternatives, since there are now modem decision making techniques, such as linear goal programming, which enable the decision maker choose the optimum investment program. Therefore, in the first two chapters, investment concept and feasibility studies of investments have been established. The third chapter gives a little information about the decision making support systems and decision analysis. The third and fourth sections include the graphical and simplex method of linear goal programming. For any management science technique to be a truly valuable tool for decision analysis, it must accommodate itself to a computer-based solution. In order to apply a technique to practical problems, which is indeed the very purpose of management science training, computer-based analysis is usually required. Man has developed many powerful and mathematically sophisticated techniques ~ nonlinear programming, dynamic programming, game theory, etc. - that have found a disappointingly limited scope to practical applications to real-world problems. Modelling with such techniques is extremely hard for complex problems, and consequently a computer analysis is of little value. In order for goal programming to be a useful management science technique for decision analysis, a computer- based solution is an essential requirement. Thus far, however, there has not been an efficient computer program for goal programming that has been widely circulated. This may well be one of the reasons for Ûm limited application of goal programming in spite of its advantages. The fifth section represents this subject. In the section including advanced topics, three areas where future research is needed in goal programming have been established. These are post optimal sensitivity analysis, parametric goal programming and goal programming under uncertainty. Deriving the optimal solution has been the primary solution procedure of goal programming. However, an analysis of the parameter changes after determining the optimal solution is also a very -XII- important part of any solution process. This procedure is broadly defined as the "post optimal sensitivity analysis'. But sensitivity analysis is limited to determination of the effects of a single change in parameters in the optimal solution. On the other hand, "parametric goal programming" is a systematic analysis of changes in the model parameters. It is a useful tool in determining trade-offs among decision variables and goals. One of the frequent problems in the practical applications of goal programming is the difficulty of determining proper values of modem parameters, especially the right-hand side of the constraints (bi) and technological coefficients (ay). If the values of certain parameters are based on random events that are difficult to predict, the problem becomes "goal programming under the condition of uncertainty". In this section, many of the approaches to linear programming under uncertainty were considered in an effort to determine what parallels, if any, one could draw with respect to goal programming. The scope of possibilities was admittedly narrowed in order to bring into sharper focus the ability of the simplex technique to be retained for goat programming under uncertainty. Other important areas that need a future research, but have not been introduced here are "integer goal programming", "network optimization through goal programming" and "the duality theory of goal programming". In the last chapter a real world problem has been established in which two shipping companies from different nations come together to constitute a joint venture for a period of 7 years. The number of vessels owned by joint venture will be five; three of them are 8.700DWT and two of them are 15.000DWT. The management has got some conflicting objectives such as higher income and lower expenses. The question is how many vessels should begin to be chartered in every year. After this problem has been solved with the given goals and objectives, the parameters have been changed and three more scenarios with different ranking of objectives have been specified. By the combination of each scenario with three different goal adjustments the problem has been solved nine more times. In the end 10 solutions have been scheduled in order to enable to compare all the solutions and see the effects of a single change in parameters in the optimal solution using sensitivity analysis approach.