Hedef programlama ve çok amaçlı transportasyon tekniği

Abstract

Klasik lineer programlama teknikleri çak amaçlı problemlerin çözümünde yetersiz kalır. Bu tip problemlerin analizinde çok amaçlı programlama tekniği kullanılır. Bu programlamanın esas amacı ideal çözüme en yakın mümkün çözümü seçmektir. Çok amaçlı karar verme problemleri sadece mikro dü zeyde değil, makroekonomik karar vermede de kullanılır. Enflasyon, ekonomik gelişme, işsizlik v.s. gibi ekonomik problemlerdeki en önemli sorun amaçlar arasındaki çatış madır. Bu tip problemlerin analizinde kullanılan çok amaçlı program tekniği, problemin çözümünü kolaylaştırır. Firma içindeki bütün faaliyet alanlarında çok amaç lı problemlere rastlamak mümkündür. Örneğin: Satmalına bölümünde bazı çok amaçlı problemler, satın alınan ma lın toplam maliyeti, şirket gereksinimleri, üçüncü şahıs tarafından tedarik edilen max-min satınalma düzeyi ola bilir. Pazar araştırmasında ise yatırımın dönüş hızı, promosyon için yapılan harcamalar, pazardaki büyüme, rek lam hacmi, özel kampanyalar çok amaçlı problemler olarak düşünülebilir. Benzer şekilde işgücü planlama problemin de, iş eğitim programlarında ve diğer alanlarda birçok amaç düşünülebilir. Klasik Transportasyon probleminede çok amaçlı yak laşmak mümkündür. Bu tip problemler e taşıma maliyeti minimizasyonu dışında taşıma zamanı, karşılanmamış talep, kullanılmayan kapasite gibi amaçlar eklenebilir. Sonuç olarak, çok amaçlı karar verme teknikleri fir manın her birimde uygulanabilecek bir yapıya sahiptir.

Decision making is nüt only the province of opera tions research, management science and decision science. It is an activitiy that everyone is interested in. While making decision about alter natives, multiple cri teria programming techniques are used in the solutions to the problem. The main purpose of them is to select a possible solution which is as closely as the ideal solution. Criteria or choice can be defined and quantitatively measurable or they can be mostly qualitative, poorly measurable, and laden with uncertainty. In the first case, the alternatives of choice are well described, their consequences are measurable. In the second case, the alternatives are only characterized by the criteria, their outcomes are uncertain and the cause-effect rela tionships are unclear. The decision maker's tasks of deciding can be clas sified into four basic groups: 1)- Clearly defined, certain alternatives, which are evaluated in terms of a single criterion. 2)- Poorly defined, uncertain alternatives, which are evaluated in terms of a single criterion. 3)- Clearly defined, certain alternatives, which are evaluated in terms of multiple criteria. IX 4)- Poorly defined, uncertain alternatives, which are evaluated in terms of multiple criteria. These four modes of decision making may be charac terized as computation, judgment, compromise and inspi ration, as in the table below; Criteria of choice Description of alternatives Certain Uncertain Single Computation Judgment Multiple Compromise Inspiration Computation is a typical mode of operations research and decision analysis. A QJell-def ined and quantitati vely measurable criterion is used to assign each alterna tive a single number and then the alternative with the best value is computed ox searched. For example: What is the shorttest route from a given production facility to a given ware house? Judgment: The objective is usually single-dimensi onal, clearly stated, but poorly measurable. Because of the objective's poor measurability, these approaches resort to observations and evaluation of a large number of decision situations. Compromise involves multiple criteria. Well-defined competing ob jectives-f or example: In choosing a produc tion mix with respect to both cost and production time. Attainment of shorter time is possible only at higher cost. The decision about these problems having conflict ing objectives, can be solved only by soma forms of com promise. Inspiration as. a mode Df decision making is receiv ing a great deal of attention within the field of MCDM The most complex strategic decisions involve a mix ture Df. quantitative and qualitative multiple criteria as well as uncertain. Under such conditions it may be diffucult to recognize even whether a compromise solu tion has been reached. Political issues emphasis on human factors and their management is self evident. The decision maker must invent a new alternative, create a neiii vision. Such creative problem solving requires rat her heavy reliance upon inspiration. Multiple objectives appear not only on the microle- vel of business and management decision making, groups» firms and corporations but also at the level of macro- economic policy making. The most important subject in economic problems which are employment, economic growth, inflation, international harmony etc, is conflict between objectives. Relation between decision maker and multiple crite ria programming techniques used in the economic problem makes the solution of the problem easier. Multiple and conflic ting objectives, for example, "minimize cost" and "maximize the quality of services" are real stuff of decision maker. Such problems are more complicated than the convenient assumptions of economic indicate. Improving achievement with respect to one objective can be accomplished only at the expense of another. Decision making can be defined as a struggle to resolve dilemma of conflicting objectives. Multiplicity of criteria occurs in almost every area of business decision making and operations. They appear in accounting, finance, operations management, man power planning, personel selection etc. A breakeven analysis usually deals with one particu lar product but that product is typically part of a port folia of products. A multiproduct breakeven analysis would lead naturally to decision making within the frame work of conflicting breakeven points. For example in budgeting the multiple criteria may include profits, sa les revenues, number Df worker hours, number of people hired, departmental budgets and etc. Working capital management involves profit, cash balances, current ratio, bank deposit balances etc. Capital budgeting models rep resent one of the richest sources of multiple criteria: Budget allocation targets, net present value, income growth, cash inflow, total cost purchased items, company requirements, minimum and maximum purchases placed with any supplier, unit requirements per supplier etc. Media planning concerns budget over expense, exposure limits, population groups, economic segments. XI Marketing planning deals with the rate Df return of investment, wages and salaries, promotional expenditure, annual market growth, volume of advertising, special campaigns etc. In manufacturing function, There are many different types of manufacturing firms that use different sets of criteria to judge their performance. A steady state manuf acturer, facing constant and reliable demand, is concerned about low cost and rapid delivery. The market creating firm would typically emphasize reliab le delivery and product flexibility. Innovative firms are most likely concerned about high quality, reliable delivery and the learning capacity of their employees. Additional criteria are taken into account by different firms at different times: Consistent quality, low in vestment, volume flexibility, good working conditions, low pollution, product classification, and some others. Using one or another combination of criteria could affect the success dt failure of a firm. Using Dne criteria or too many criteria are both undesirable extremes and usually signal bad management similarly problems of man power planning, training programs, project assignment, sales effort allocation and others are characterized by multiplicity of criteria. It is similar in business decision making. Especi ally in financial planning, there are many indicators of company performance which should be neither too high or too low as strategic or tactical devices, they should be on target or as close as possible to it. Typical examples include dividend cover, amount of liquidity, dept equity ratio. Organization of This Thesis; Chapter 2 provides the language and basic concepts of multiple criteria decision making. Concepts of cri teria, goals, objectives and attributes are explained and carefully defined. In this chapter technological versus economic problems and objectives of the firm, the role of profit are described. After discussing the role Df the profit among the multiplicity of business objectives and criteria of per formance, an example of multiob jective conflict is analy zed quantatively. Xll Chapter 3 cavers goal programming methods used in different problems such as integer, nonlinear, linear, 0-1 etc. and linear multiob jective programming. Decision alternatives which are discrete are often dealt with. They could be listed separately one by one, forming countably small sets of "points" in the multidi mensional space of attributes or criteria. There are many types of problems in which not only every discrete points but also every feasible combination of them iden tifies a decision alternative. Thus there could be an infinite number of possible courses of action. Their analysis by simple enumeration, as we usually can do with discretely defined alternatives, would be prohibitively time consuming, costly, or plain impossible. One needs more efficient method. A suitable methodology for handl ing such problems is called linear multiob jective program ming (LMP). While linear multiob jective programming deals with minimization or maximization of various objectives func tions, goal programming is concerned with conditions of achieving prespecied targets or goals. The setting of goals is a tactical device which often complements the pursuit of objectives. Depending on the situation, for example, an athlete's objective might be torun as fast possible, Dr to be the fastest in a given group of runner, as or to run 1DD meters in no more than 1D.2 seconds, or to finish at least third in the field. The tactics emplo yed will be different in every instance. Once individual goals have been stated, the purpose of goal programming is to achieve the goal portfolio as closely as possible, to minimize the set of deviations from goals. All goals can be considered simultaneously or they can be taken one by one. Solution techniques of integer, D-1j nonlinear goal programming are described in this chapter in addition some problems related with these methods are solved iteratively, Chapter k: One of the most applications of linear programming is in solving transportation problems. üJhile solving this problem by linear program, there is only an objective which is related with minimization of cost. It's possible to increase the number of criteria adding delivery time, quantity of goods delivered, unfulfilled Xlll demand, under capacity, reliability of delivery, safety of delivery and many others. Therefore problem can easily be transformed into multiple criteria transpor tation problem. Moreover chapter 4 provides the solu tion technique of multiple criteria transportation prob lem. In appendix A, There is a problem whose data, sour ces,, demands, cost values, values that are related with procurement of the order on time, were provided from Uni lever Company. Two conflicting criterias, one of which is cost minimization and the other is procurement öf the order on time are analyzed by the help of computer programs (BASIC-QSB). When the last solution to this complex problem having ten sources and thirty nine demands is examined. The proximity of compromise solution to ideal solution can be easily seen.