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 .

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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.

Many authors have written books on Operations Research. Most of them have mathematical approach rather than decision-making approach. Actually the subject deals with applied decision theory, so I have dealt with the subject with decision-theory approach. The book has fifteen chapters. At the end of the book, objective type questions, which are helpful for competitive examinations are given to help the students to prepare for such examinations. The first five chapters deal with Linear Programming Problems, such as Resource allocation problem, Transportation problem and Assignment problem both maximization and minimization versions. In the first chapter, the historical background of Operations Research O. Typical problems of mathematical orientation and decision making orientation have been solved. In transportation model and in assignment model, problems useful to Production and Operations Management have been solved to make the students to know the application part of the subject. The sixth chapter deals with Sequencing model, where the importance and application of the models is dealt in detail. The problem of Replacement is discussed in Chapter Chapter-9 deals with Waiting line model and its application with certain useful problems and their solutions. Game theory or Competitive theory is discussed in Chapter with certain problems, which have their application in real world situation.

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.

Review and Maintain After implementation, the performance of the model should be carefully and constantly monitored to ensure that it actually does work and fulfill its objectives. The review process should be at regular intervals so that appropriate adjustments can be made to meet changes in conditions which can render the implemented solution inappropriate Lucey, All organizations are subject to change.

Consequently, no solution remains optimal forever. Changes in the system or in the environment of the system make it essential to continually review the models used and the existing solutions to see if adjustments are required. Adjustments should be updated dynamically to ensure that the recommendations are enabling the organization to meet its objectives. The Techniques of Operations Research This section discusses the various techniques of Operations Research that can be used by managers of Nigerian business organizations.

This will provide a broad description of Operations Research techniques and what they can be used for. To achieve this, we classify Operations Research techniques into five categories as shown below: Linear Mathematical Programming Techniques: Inventory Techniques: Linear Programming According to Taha Linear programming is a technique for resolving problems of resource allocation.

It is designed to assist management in its optimization decisions involving the use of competing resources. It offers a simplified technique for specifying how to use limited resources or capacities of a business to obtain a particular objective such as least cost, least time or highest margin when these resources have alternative uses. There are situations where a business organization is faced with the problem of allocating its resources which include money, materials, land, machine time and labour time.

It helps in the process of selecting the most desirable course of action from a number of available courses of action thereby giving management information for making effective decisions about the resources under its control.

Its applicability is however restricted to problems that are entirely linear. The general formulation of a linear programming problem is given as: Linear programming technique has certain distinct advantages such as: Results obtained through linear programming can be easily re-evaluated for changing conditions through sensitivity analysis Ekanem and Iyoha, Transportation Model An important factor in logistics management is the determination of the lowest cost transportation provider from among several alternatives.

In many cases, it is possible to transport items from a plant or www. The major modes of transportation in Nigeria include road, rail, air, water and pipeline. Factors to consider when making a decision include comparative cost of alternative modes, kind of product and transportation time.

A quantitative technique that is used for determining the least cost means of transporting products is the transportation model. It helps to determine the quantity of the item to be transported to each destination on a periodic basis in order to minimize the total cost of transportation or to maximize revenue Levin et al, Apart from transportation problem, the transportation model can be used for machine assignment, plant location and product mix problems Gupta and Hira, There are several methods for solving transportation models.

Assignment Model The assignment model is a special form of a linear mathematical programming model that is similar to the transportation model. However, in the assignment model, the supply at each source and the demand at each destination are each limited to one unit Agbadudu, Assignment problems can be solved using Hungarian method, which involves rapidly reducing the original matrix and finding a set of n independent zeros, one in each row and column, which gives an optimal solution.

This technique can be used to assign salespeople to different territories to maximize sales and profits. Integer Programming An integer programming model is a model that has an algebraic representation that is identical to a linear programming model with the exception that one or more of the structural variables is required to have only integer value Ekoko, In linear programming, the solution of the variables need not necessarily be a whole number.

However, there are situations when it becomes imperative that the solution must be a whole number. There are some situations in business that require whole numbers rather than fractions. Integer programming models are often classified as being either mixed integer programming models or pure integer programming models.

If all the variables must take only integer values, it is pure integer programming. If only some specified variables have to be integers and others may be non-integers, we have a mixed integer programming problem.

Integer programming problems can be solved using Branch and Brand method or Gomory Algorithm Ekoko, Goal Programming This is a type of linear mathematical programming that can be used to analyze decision situations involving multiple goals, which sometimes are complementary or conflicting.

Linear programming model has only one objective function, as such, it is inappropriate for many decision making situations in which a manager is concerned with several potentially conflicting objectives.

Goal programming provides a method for extending linear programming to accommodate models in which there is more than one objective. For example, there are times when management may want to maximize profits and increase wages paid to employees or to upgrade product quality and reduce product cost.

The pervasiveness of multi-objective decisions make goal programming an important tool for managers. Notify me of new posts by email. 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.

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