𝗣𝗗𝗙 | This is an introductory text for Operations Research with focus on methods used to solve Linear Programming Problems (LPP). Albright, Winston & Zappe, Data Analysis and Decision Making. Albright, VBA for Modelers: Developing Decision Support Systems with Microsoft Excel. help the students with a book on Operations research. OPERATIONS RESEARCH, with other chapters to students, with a hope that it will.
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The British/Europeans refer to "operational research", the Americans to Therefore, to give a formal definition of the term Operations Research is a difficult task. Introduction to. Operations Research. Deterministic Models. JURAJ STACHO. Department of Industrial Engineering and Operations Research. PDF Drive is your search engine for PDF files. As of today we have 78,, eBooks for you to download for free. No annoying ads, no download limits, enjoy .
Skip to main content. Log In Sign Up. IOSR Journals. Volume 7, Issue 4 Jan. Operations Research is a problem solving and decision-making science. It is a kit of scientific and programmable rules that provide managers at all levels with a quantitative basis for decision-making. However, research has indicated that majority of managers in Nigerian business organizations do not make use of operations research techniques.
It assists managers in making effective decisions in order to achieve efficiency, increase productivity and overall corporate performance INFORMS, According to Akingbade et al it is a problem-solving science-based activity using analysis and modelling as a basis for aiding decision-makers in organizations to improve the performance of the operations under their control. It is concerned with analyzing complex problems and assisting decision-makers work out the best means of achieving objectives.
It can be said to have been in existence since the beginning of mankind Agbadudu, However, the concept emerged in during world war ll, when a team of scientist was called upon by the military management in England to develop ways to make the most effective use of limited military resources Anderson et al, and Taha, Their mission was to formulate specific proposals and plans for aiding the military commands to arrive at decisions on optimal utilization of scarce military resources and also to implement the decisions effectively.
The United States military management took a leaf from the British military management and started the use of Operations Research.
Due to the successful utilization of Operations Research by military management in Britain and United States, managers of business organizations became interested in using the techniques to solve organizational problems.
Today, Operations Research is a dominant and indispensable decision making tool and is widely used in business organizations in western countries. Despite the fact that Operations Research has been a compulsory course for all business students in Nigerian universities and there is a professional body, the Institute For Operations Research of Nigeria INFORN Foster , Akingbade et al , Agbadudu, ; and Ighomereho have noted that the use of Operations Research in Nigerian business organizations is still limited because not much of it is practiced at the moment.
The objectives of this paper therefore are to examine the nature of Operations Research, the development of Operations Research, the steps in Operations Research, the various Operations Research techniques available for managers of Nigerian business organizations and the areas of operation where they can be applied.
The Concept and Nature of Operations Research Operations Research has been defined in various ways by different authors. Right from its formal inception in , there has not been a consensus about its definition. The reason usually given is that it is too www. Churchman and Arnoff defined Operations Research as a systematic study of the basic structures, characteristics, functions and relationships of an organization to provide executives with a sound, scientific and quantitative basis for decision making.
Saaty in his opinion defined it as the art of giving bad answers to problems to which otherwise worse answer are given. In another view, Ekoko defined it as the application of scientific method by interdisciplinary teams to problems involving the control of organized systems so as to provide solutions which best serve the purpose of the organization as a whole while Lucey defined it as the attack of modern science on complex problems arising in the direction and management of large systems of men, machines, materials and money in industry, business, government and defence.
For the purpose of this paper, the definition by Kalavathy will be adopted. Indeed, Operations Research is a scientific approach for analyzing problems and making decisions in organizations. It aims at providing rational bases for decision making by seeking to understand and structure complex situations and to use this understanding to predict system behaviour and improve performance.
The distinctive approach is to develop a scientific model of the system incorporating measurements of factors such as change and risk with which to predict and compare the outcomes of alternative decisions and strategies. The purpose is to help management determine its policy and actions scientifically.
Development of Operations Research Over the years, Operations Research has evolved through different stages. Magee reviewed the phases through which it has developed. According to him, it has gone through three phases of growth; the primitive phase, the academic phase and the maturing phase. In this paper, the matured phase is included. The Primitive Phase This phase is between and At this stage, the problem solvers were interested in practical operational problems.
These problems were well defined and capable of being handled by the smaller, less sophisticated computers available then. Also, it was in the process of developing into a separate professional field and the theoretical foundations of the discipline developed rapidly.
However, only very few Universities offered formal training in Operations Research. The Academic Phase In the early s, the number of Universities offering programmes in Operations Research grew over percent.
Magee pointed out that in this phase, people with some Operations Research experience began to be found at the higher corporate levels in private enterprises.
The increasing speed and availability of computers were of great help during this time. Magee noted that research during this phase tended to be academic, that is, it was more concerned with developing theory than with finding workable applications. Also, it was during this time that the limitations of Operations Research became evident. Maturing Phase Magee described the maturing phase as a time when balance between theory and practice was obtained.
He argued that even though evidence of such concerns was noted years ago, the real thrust towards practice and applications did not come until the s. In this phase, it has become a compulsory course for undergraduate students especially those in management sciences and engineering. It is also offered as a course of study at the Masters and Ph. D levels in most universities.
This phase has also featured the use of software packages that have removed the burden of computation IV. The Importance and Limitations of Operations Research Decisions, especially business decisions, can be characterized by many interrelated factors.
The combined impact of the interrelated factors is rarely obvious, so that intuition and common sense alone do not necessarily lead to good decision-making. This is not to suggest that common sense, intuition, executive www. If the manager has had experience with similar problems or if the problem is relatively simple, heavy emphasis may be placed on qualitative analysis.
It is an undeniable fact that we are living in a changing world. As old problems are solved, new problems arise with new structures and relations and this has effect on decision-making. A quantitative analysis is important when: When management is faced with more decision factors than they feel they can cope with, Operations Research can be used to analyze complex real-world systems with the goal of improving or optimizing performance.
For example, a great deal of money is involved and the manager desires a thorough analysis before attempting to make a decision. Assessing the risk of a new project or contract can be tricky. Operations Research can help to quantify risk, which is a key to controlling it and help to plan how best to balance risk against the gains an organization can expect.
Most organizations probably track information about many aspects of their operations and have huge amounts of data they do not use for decision-making. Operations Research specializes in working with data, extracting the most valuable information from what is currently collected and indicating the additional data that could be collected to increase the value even further.
Agbadudu stated two reasons for using Operations Research to solve real world problems. They are: The results of a mathematical debate are precise and depend only on the initial assumptions. For a given set of assumptions, the mathematical conclusions are accurately expressed and their results cannot be argued.
Despite the relevance of Operations Research to organizations, Griffen argued that quantitative techniques cannot fully account for intangible or qualitative factors in decision-making. Qualitative or intangible factors are factors that are difficult to measure numerically. For example, individual behaviour and attitudes, employee morale, image of the organization are major factors in managerial decisions but they cannot be quantified. Another weakness of quantitative aids is that they may not always adequately reflect reality.
Mathematical models may require a set of assumptions that may not be realistic. In addition, for most techniques, the manager must identify and characterize all variables to be considered.
When the solution is subsequently implemented, a variable that has gone unaccounted for may influence it in some way. According to Agbadudu the limitations of Operations Research are: As a result of these limitations, when using Operations Research, the decision maker should concentrate on the quantitative facts or data associated with the problem and develop mathematical expressions that describe the objectives, constraints and other relationships that exist in the problem.
It should be noted that Operations Research may be useful in some situations but not in others that may call for a more intuitive approach. Although the best decisions are based on sound information Nickels et al, , managers deciding rationally must have a clear understanding of the alternative courses by which a goal can be achieved under existing circumstances and limitations.
They must also have the information and the ability to analyze and evaluate alternatives and also be eager to choose the best solution by selecting the alternative that most effectively satisfies goal achievement Weihrich and Koontz, However, due to the limitations of www.
This involves choosing a course of action that is satisfactory or good enough under the circumstances. Operations Research does not result in decisions, but it generates enough quantified data to direct the decision maker to the most plausible decision. This suggests that common sense, intuition, executive judgement and experience are also relevant in decision-making but purely subjective decision-making might not be sufficient.
The Steps in Operations Research Operations Research encompasses a logical and systematic approach to problem solving. This approach follows a generally recognized and ordered set of steps as shown in the figure below: The Operations Research Approach Source: Adapted from Taylor and Bernard Problems are not always the result of a crisis that must be reacted to, they can also be anticipated.
Once it has been determined that a problem exists, the problem must be clearly and concisely defined. In many cases, defining the problem is the most important and the most difficult step. It is important to go beyond the symptoms of the problem and identify the true causes. One problem may be related to other problems, solving one problem without regard to other related problems can make the entire situation worse.
It is important to analyze how the solution to one problem affects other problems or the situation in general. In the view of Ekoko the existence of a problem implies that the objectives of the firm are not being met and so the objectives of the organization must be clearly defined. A stated objective helps to focus attention on what the problem actually is. Model Construction After formulating the problem, the next step is to develop a model that attempts to capture the essential features of the problem under consideration.
Taylor and Bernard defined a model as a simplified representation of an existing problem situation. Operations Research models usually consist of mental models, verbal models, diagrams and mathematical models Akingbade et al, However, the most widely used Operations Research models are the mathematical models which comprise a set of mathematical relationships. The objective of a model is to identify significant factors and interrelationships. The reliability of the solution obtained from a model depends on the validity of the model representing the real system.
In discussing model formulation, Wayne suggested that models should be developed carefully. They should be solvable, realistic, easy to understand and modify and the required input data should be obtainable and that in complex situations were analytic models cannot be formulated, the analysts should develop a simulation model, which enables a computer to approximate the behaviour of the actual system.
These estimates are used to develop the model. According to Barry and Stair obtaining accurate data for the model is essential because even if the model is a perfect representation of reality, improper data will result in misleading results.
Model Solution Developing a solution involves manipulating the model to arrive at the best optimal solution to the problem. In some cases, this requires that an equation be solved for the best decision.
In other cases, a trial and error method is used, trying various approaches and picking the one that result in the best decision. The accuracy of the solution depends on the accuracy of the input data and the model. It should produce a solution which works technically, which meets the constraints and which operates in the problem environment.
It should work consistently under the conditions for which it was designed. It should produce value for the organization in excess of what it costs. It should be viable in its organizational setting and it should have the support of management. It will also be necessary to carry out sensitivity analysis of the optimal solution for some changes in the uncontrollable variables.
These analyses are necessary because some of the variables change overtime. For example, the prices of raw materials fluctuate, cheaper when in season and costly when out of season. Validating the Model Model validation concerns the efforts that are made to demonstrate that the model and the solution are sufficiently realistic to serve as a solid foundation for subsequent management action.
The validation process includes careful consideration of assumptions, a review of data that were used in the model and checks to detect mathematical or arithmetic errors. To determine how well the model fits reality, one determines how valid the model is for the current situation. Ekoko defined a validated model as one that has been proven to be reasonable abstraction of the real problem it is intended to represent.
Implementation This is the application of the information generated from the Operations Research model.
After careful interpretation of the results and the final solution approved by the decision maker, it is then implemented or incorporated into the organization.
It is the effectiveness of Operations Research in solving the problem it is expected to solve that determines its integration into the organization. Sometimes, the solution may not be implemented because although technically valid, management may consider that it should not be implemented. In implementing the results of Operations Research, managers must consider both qualitative and quantitative factors as stated earlier. That is why Lucey pointed out that Operations Research is an aid to the decision-making process.
In otherwords, the results of Operations Research should be combined with qualitative information in making decisions.
The Operations Research techniques provide information that can aid the manager in making effective decisions. The original problem can then be modified to test different conditions and decisions the manager thinks might occur in the future. As such, the Operations Research process is continuous rather than simply providing one solution to one problem hence the feedback loop.
The experiences gained from implementation provide feedback to different stages in the Operations Research modelling process. Content in this Article. Natarajan, P.
Balasubramani, A. J K Sharma. Gupta and D. Tech Elective. Related Topics. Optimization in Operations Research: Rardin Pearson Prentice Hall Paperback: Operations Research: An Introduction Hamdy A. Taha Pearson Edition no. Carter, Camille C. Applications and Algorithms Wayne L. Winston Duxbury Resource Center Edition no. Leave A Reply. Kindly share this post with your friends to make this exclusive release more useful.
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