Online Course Operations Research – Introduction to Operations Research: 7/E by Hillier and Lieberman (available online) Reference Books Operations Research: An Introduction, 8/E Hamdi a. By Taha Operations Research: Applications and Algorithms Wayne L. By Winston
“Research on Operations” includes – How to manage and coordinate operations/activities? or implemented in almost every organization with the advent of the Industrial Revolution. Available resources for various activities in a manner that is most effective for the organization as a whole. These types of problems and the need to find better ways to solve them have provided the environment for the emergence of operations research (commonly known as OR). Effectively manage the various military operations and activities within each operation. So, the British and then the US. Army management called upon a large number of scientists to adopt a scientific approach to tackle these and other strategic and tactical problems. In effect, they were asked to conduct research on (military) operations. These teams of scientists were the first OR teams.
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4 or scientific method research is used to investigate the problem of concern or involves a ‘team approach’
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Much of this course will be based on the mathematical methods of Operations Research (OR) however, this does not mean that the practicals or studies are primarily mathematical exercises.
7 What is a model? The objective of the model is to identify significant factors and to identify the variables as a set of mathematical symbols to represent the components of the actual system. Reference: 201/OR%20Lecture1.pdf Validation of a model representing a real system.
Mathematical equations describing models of genetic structure, physical laws of motion or chemical reactions, graphs, organizational charts, and industrial accounting systems. Mathematical models are also ideal representations, but they are expressed in terms of mathematical symbols and expressions. Such laws of physics as F ma and E mc2
A model in OR is a simplified representation of operations. Mathematical models are expressed in terms of mathematical symbols and expressions to allocate available resources to various activities in a way that is most effective for the organization as a whole. An OR study seeks solutions that are optimal Attempts to find an optimal solution for the problem under consideration (referred to as an optimal solution) The “search for optimality” is an important theme in OR or currently one of the fastest growing career fields. The US College Graduates (U.S. Bureau of Labor Statistics) We say optimal rather than optimal because there may be multiple solutions that combine to be optimal.) Physics laws such as F = ma and E = mc2 are familiar examples of mathematical models.
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Consists of a system of equations and related mathematical expressions that describe the essence of the problem. If there are ‘n’ quantifiable decisions to be made, they are represented as decision variables (say, x1, x2, , xn – unknown to be determined) performance or A measure of the objective function (eg, profit) is then expressed as a mathematical function of these decision variables (eg, P = 3×1 + 2X2 ……….5Xn) Any restrictions or constraints on the values that can be assigned to these decision variables mathematically Also expressed, usually by inequalities or equations (for example, x1 +3x1x2 + 2×2 < 10). The constants (coefficients and right-hand sides) in the constraints and objective function are called parameters of the model.
To select values of decision variables to maximize the objective function, subject to specified constraints.
15 Sensitivity Analysis Determining appropriate values to assign to model parameters is both an important and challenging part.Collecting ‘relevant data’ is often necessary, as it is difficult to collect accurate data. , only a rough approximation, because of the uncertainty about the true value of the parameter, it is important to analyze how the solution obtained from the model will change if the value assigned to the parameter is changed to other plausible values. The process is called sensitivity analysis (one value per parameter) Unlike textbook problems where you are given numbers, real problems require collecting relevant data to determine parameter values.
16 OR TEAM ROLE YOUR ROLE IS THAT OF A CONSULTANT !!!! Not as a decision maker!!!! Identifying the “right” problem from a management point of view Identify a number of alternatives under different assumptions or over a different range of values of some policy parameter (the trade-off between cost and benefit). Collect relevant data about the problem. Data decision makers make final decisions based on their judgment Working in a consultative capacity the team performs a detailed technical analysis of the problem and then presents recommendations to management. Decision maker: It is necessary to install a new computer-based management information system for managers to collect the necessary data on a continuous basis and in the required form. A large amount of data is usually required to obtain a precise understanding of the problem and to provide the necessary input for the mathematical model to be formulated in the next phase of the study. Precision: Sometimes data are quite ‘soft’ i.e. rough estimates based on educated guesses.
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In real life, most practical problems are not as simply defined as in your course work. Often these are described vaguely and imprecisely so it is important to first define the problem statement well which includes setting things like appropriate objectives. , limitations on what can be done, interrelationships between the area of study and other areas of the organization, possible alternative courses, time limits for decision making, etc. The process of problem definition is critical in that it is difficult to extract the “right” answer from the “wrong” problem! Vaguely and imprecisely described to OR teams. Well defined: It requires first understanding the system concerned.
Reformulating the problem definition into a form suitable for analysis
A common theme in OR is the search for an optimal (optimal) solution A number of software packages are readily available for developing a process (usually a computer-based process) for deriving problem solutions from an OR model because the model is essentially one. An ideal rather than an accurate representation of a real problem, there can be no utopian guarantee that the best solution for the model will prove to be the best possible solution implemented for the real problem.
22 Model Testing Real problems usually do not have only one “right” model Experiments conducted to test the hypothesis that the model is a sufficiently accurate representation of the essential features of the situation that the conclusions (solutions) derived from the model are also valid. Modify it as needed for the actual problem Testing a model usually leads to a successor model that provides a better and better representation of the problem.It is also possible to develop two or more completely different types of models to help analyze the same problem. come The process of testing and improving a model to increase its validity is commonly referred to as model validation.
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23 Implementation The last phase of the OR study is to implement this system as determined by the management which is very important and requires model solutions to accurately translate into the operating process.
The most important scientific advance of the mid-20th century Since the 1950s, its impact has been extraordinary. Today it is a standard tool that has saved thousands or millions of dollars for most companies. Linear programming. Dozens of textbooks have been written about linear programming, and articles have been published describing important applications that now number in the hundreds.
Mathematical functions in both the objective function and the constraints are all linear functions Briefly, the most common type of LP application involves the general problem of allocating limited resources among competing activities in the best possible (i.e., optimal) way.
26 Examples The various situations to which the previously mentioned description applies are diverse, ranging from profit-maximizing product mix, allocation of national resources to local needs, choice of shipping patterns, agricultural planning – allocating acreage to crops that maximize. Total net return, combining pollution abatement methods that achieve air quality standards at minimal cost, designing radiation therapy that effectively attacks the tumor while minimizing damage.
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