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Archive for the ‘Operations Research’ Category

Operational Research (OR) is a signpost career for students studying maths or anyone with a wider interest in problem solving. This video is an introduction to OR, gives a flavour of its wide-ranging applications and aims to demonstrate that OR is an interested and varied career. Its just one of the resources available at www.learnaboutor.co.uk

Achieving and Systematizing Operational Efficiency at the 2004 Olympics

The Problem
The Olympics, mother of all international athletic competitions, is also the ultimate challenge in construction planning, execution and event management. The 2004 Olympics, with an $8 billion budget and a workforce of over 130,000 to build some 36 venues and manage 300 athletic competitions, was a tall order for its organizers, the Athens Olympic Organizing Committee (ATHOC). The committee sought not only to ensure operational success of the event itself, but, through “Process Logistics Advanced Technical Optimization” (PLATO), to develop and capture knowledge modeling and resource management tools that could be transferred to future Olympic organizing committees. PLATO’s particular focus was on competition venues, managing the accreditation process for authorized personnel, transporting athletes and spectators, coordinating volunteers, and managing municipal operations around each of the event venues.

The O.R. Solution
Three guiding principles were fundamental to the PLATO process:

1. A holistic view of venue operations was required because of the high level of interdependence among processes, key personnel and geographic locations;
2. A generic, abstract thinking process was required to analyze requirements for each venue, thus avoiding local constraints that might limit the development of universal solutions; and
3. PLATO had to enable stakeholders in the process to visualize the effects of their operational decisions for each venue prior to actual implementation.

Incorporating those principles, the PLATO process featured three interrelated modeling activities:

• Goals modeling: To grasp stakeholders’ goals for the intended systems, facilitating the identification of key choices to be followed and broad perceptions of costs and benefits;
• Business process modeling: To focus analysis and design on customer groups’ value chains and away from narrow functional thinking; and
• Scenarios modeling: To encourage group brainstorming that would let participants focus on alternative solutions and visualize systems behavior.

PLATO models were translated into user-friendly Windows-based computer applications that enabled stakeholders to state assumptions and generate probability distributions for particular outcomes. For example, PLATO’s scenario modeling application for venue services (e.g., ATMs, food service, ticket booths, and bathrooms) allowed users to test different service parameters and project outcomes including attendee traffic patterns. Models were initially constructed using historical patterns and subsequently fine-tuned with data obtained during test events.

The Value
PLATO’s value to the Athens Olympic Organizing Committee included $55 million of estimated savings due to improved resource management and $15 million in savings due to efficiencies achieved in the planning and design process. The portability of the tools generated by PLATO will enable organizers of future Olympic events to achieve similar results. Finally, PLATO demonstrated that small countries like Greece can successfully organize large projects like the Olympics if management takes advantage of sound O.R. and management theories.

TREND ANALYSIS AND TREND ESTIMATION

What Does Trend Analysis Mean?
An aspect of technical analysis that tries to predict the future movement of a stock based on past data. Trend analysis is based on the idea that what has happened in the past gives traders an idea of what will happen in the future. 

There are three main types of trends: short-TERM,intermediate- and long-term.

The term “trend analysis” refers to the concept of collecting information and attempting to spot a pattern, or trend, in the information. In some fields of study, the term “trend analysis” has more formally-defined meanings.

TREND ESTIMATION:

Trend estimation is a statistical technique to aid interpretation of data. When a series of measurements of a process are treated as a time series, then the application of trend estimation can be used to make and justify statements about trends in the data. Using trend estimation, it is possible to construct a model which is independent of anything known about the physics of a process of an incompletely understood physical system. This model can then be used to explain the behaviour of a measurement.

Process may refer to:Biology Process, a projection or outgrowth of tissue from a larger body. Biological processScience and technnology Process ,a computer program or an instance of a program running concurrently with other programs…
is treated as a time series

Time series

In statistics, signal processing, and many other fields, a time series is a sequence of data points, measured typically at successive times, spaced at time intervals trend estimation is the application of statistics Statistics

Statistics is a Mathematics pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It also provides tools for prediction and forecasting based on data techniques to make and justify statements about trend

Trend may refer to:In Business:* Market trends, a prolonged period of time when prices in a financial market are rising or falling faster than their historical average, also known as “bull” and “bear” markets, respectively.

Assuming the underlying process is a physical system that is incompletely understood, one may thereby construct a model, independent of anything known about the physics of the process, to explain the behaviour of the measurement. In particular, one may wish to know if the measurements exhibit an increasing or decreasing trend, that can be statistically distinguished from random behaviour. For example, take daily average temperatures at a given location, from winter to summer; or the global temperature series over the last 100 years.

Particularly in that latter case, issues of homogeneity (statistics).

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The operations management of any organization involves the design, operation, and improvement of the systems that create and deliver the primary products and services of the organization. From an organizational point of view, operations management may be defined as the management of the direct resources that are required to produce and deliver organizational goods and services. Operations management is an area of business that is concerned with the production of goods and services, and involves the responsibility of ensuring that business operations are efficient and effective. It is also the management of resources and the distribution of goods and services to customers. However, people tend to misunderstand operations management with the subject of operations research. 

            During 1940s, scientists of established reputation accepted the challenge of attempting to understand a host of common processes in military operations. Their team effort was called operations research and the focus of their attention was the science of military systems. Hence the world war 11 with its complex problems of logistic control and weapon systems design, provided the impetus for the development of interdisciplinary, mathematically oriented field of operations research.(OR).

            Operations Research, or simply OR is an interdisciplinary science which deploys scientific methods like mathematical modeling, statistics, and algorithms to decision making in complex real-world problems which are concerned with coordination and execution of the operations within an organization. The nature of organization is essentially immaterial. The eventual intention behind using this science is to elicit a best possible solution to a problem scientifically, which improves or optimizes the performance of the organization. Hence, Operations Research brings together practitioner in diverse fields such as mathematics, psychology, and economics etc. Specialists in these fields customarily formed a team to structure and analyze a problem in quantitative terms so that a mathematically optimum solution can be obtained. OR today provides many of the sophisticated quantitative tools in operations management (OM).

            Operations research also closely relates to industrial engineering which takes more of an engineering point of view, and industrial engineers typically consider OR techniques to be a major part of their toolset.

            Some of the primary tools used by operations researchers are statistics, optimization, and simulation. Because of the computational nature of these fields OR also has ties to computer science, and operations researchers regularly use custom-written or off-the-shelf software. Operations research is distinguished by its ability to look at and improve an entire system, rather than concentrating only on specific elements (though this is often done as well). An operations researcher faced with a new problem is expected to determine which techniques are most appropriate given the nature of the system, the goals for improvement, and constraints on time and computing power. For this and other reasons, the human element of OR is vital. Like any other tools, OR techniques cannot solve problems by themselves.

A few examples of applications in which operations research is currently used include designing layout of a factory for efficient flow of materials, constructing a telecommunications network at low cost while still guaranteeing quality service if particular connections become very busy or get damaged, road traffic management and ‘one way’ street allocations, determining the routes of school buses so that as few buses are needed as possible, designing the layout of a computer chip to reduce manufacturing time (therefore reducing cost), managing the flow of raw materials and products in a supply chain based on uncertain demand for the finished products, efficient messaging and customer response tactics, roboticizing or automating human-driven operations processes, globalizing operations processes in order to take advantage of cheaper materials, labor, or other productivity inputs, managing freight transportation and delivery systems, network data traffic: these are known as queuing models or queuing systems, sports events and their television coverage, blending of raw materials in oil refineries, etc, etc.

There was a lack of emphasis on operations management in the post war ii years, for many reasons.

(1) Following World War II, the United States was the obvious world leader in manufacturing. US dominance was the result of several factors including the virtually total destruction of most of the production capabilities of the other leading industrialized nations of the world.

(2) Under foregoing conditions, the lack of foreign competition till for some years resulted in lack of emphasis on operations management since most of the countries were not so serious about global market infiltration, with the collapse of technological power had before the war.

(3) With the demand significantly exceeding capacity during the post war period, emphasis was placed on output, and the operations function typically related to situations only when they occurred. Corporate managers during this period usually told operations managers to focus only on controlling production costs, rather than focusing on other aspects related to operations management.

It is also important to notice the resurgence of interest in OM today, mainly on the reasons as follows;

The ever increasing standard of living in society is a one of major factors that inspires resurgence of interest in operations management today. Operations management enables to increase productivity and better quality goods and service delivery. High productivity is the result of increased efficiency in operations, which in turn translates into lower cost goods and services. Thus higher productivity provides consumers with more discretionary income, which cintr9butes to their higher standard of living. The increased use of automation and robotics also improves the quality of goods.

Most companies today are taking up the challenge to producer environmentally friendly products with environmentally friendly processes all of which falls under the purview of operations management.

Operations management is continuously changing to meet the new and exciting challenges of today’s business world. This ever changing world is characterized by increasing global competition and advances in technology. To survive and prosper in such a global market, companies must excel in more than one competitive dimension. The rise of the global economy and the trend towards globalization has placed emphasis on the issues associated with logistics, quality, productivity and customer satisfaction which operations management made them integral in production sector.

Advances in technology in recent years also have had a significant impact on the operations management function. Information technology (IT) now allows us to collect detail customer data so that we customize products to meet the needs of individual customers..

Operations management provides a systematic way of looking at organizational processes. OM uses analytical thinking to deal with real world problems. It sharpens our understanding of the world around us, whether we are talking about how to compete with competitors or how many lines to add the bank teller’s window.

OM presents interesting career opportunities which can be in direct supervision of operations or in staff positions OM specialties such as quality assurance.

However, the reality is not always the same. Technology has raised the performance bar in both manufacturing and services sector by allowing firms to compete on several dimensions (low cost, quality, speed of delivery, customization etc) simultaneously. For example, firms using technology such as Dell Computer can produce and quickly deliver individually customized products at a very competitive price.

Automation is a result of technology advance that relate to the automatic operation of a production process. Some major developments in manufacturing automation include machining centers, numerically controlled machines, industrial robotics, computer aided design and manufacturing systems, flexible manufacturing systems, computer integrated manufacturing and islands of automation.

Advances in technology, including improved automated equipment, voice recognition systems, high speed data transmission lines like broadband, and faster and more powerful computers also have had a significant impact on services. Contributing to the growing trends in services is the fact that large amounts of data are readily accessible and can be transmitted inexpensively over long distances. Increase in self service, decrease on the importance of the location and the shift from time dependant to non-time dependant transactions and the increase in disintermediation are the results of technological advances in the services sector. Technology also has created the concepts of global and green village for the betterment of the humankind as a reply to its negative impacts such as mechanized human elements in a factory layout for instance.

Under circumstances, the author envisages the future role of the OM function as follows;

             In the new world of e-business, competition takes on a new intensity and a variety of flavors. The unique dynamics of the international online marketplace often requires organizations to pursue multiple, simultaneous, and seemingly contradictory strategies. To identify what is both possible and advantageous, organizations must learn to think smarter and act faster – more so than the toughest competitors they can possibly imagine. This means moving beyond market leadership to another level – one that enables an enterprise to “leapfrog” the competition.

            International e-business success starts with world-class supply chain management and an enabling infrastructure that is a critical component of today’s global enterprise not to be overlooked. E-business is obviously the future, and the Business-to-Business (B2B) component is taking the lead in defining what success will look like in this future. Additionally, in this emerging world of business, adaptation to constant change will prove an important ingredient for success. The future role of operations management should taker the above factors into serious consideration if any firm seeks to secure and sustain in competitive edge.

            Future opportunities are hard to estimate, and many change programs are therefore built on limited information. Case decisions are often made on the basis of previous internal successes and failures rather than a fact-based market review.

Companies often set targets for change without having the full picture of the current environment, which means that either the outcome of the change is not considered optimal or the costs of the change are deemed too high to generate a net benefit.

Too many Business Process Re-engineering projects have been launched with great expectations and end with disappointing results.

            Strategy should be based on a concrete understanding of market capabilities, practices and processes, to allow specific operational targets to be clearly articulated and demonstrated. A framework needs to be put in place to accurately describe current and future operational performance, in order to increase confidence and credibility in the change and improvement process.

            Operations management as a field deals with the production of goods and services that we come in everyday contact in domestic life. Without effective management of operations, a modern industrialized society can not exist. Operations are the engine that creates wealth for the enterprise and underpins the global economy.

            Operations managers however have important responsibilities in the service sector as well (80% is in the service sector in USA) such as in hotels, banks airlines retail stores etc. In each of these organizations, operations mangers are responsible for providing the supply of services much like their counterparts in manufacturing product the supply of goods.

Managing the transformation process in an efficient and effective manner is the tasks of the operations manager in any type of organization. Wealth is created in the global economy through excellent operations management. Wealth creation occurs when the value of outputs in goods and services exceeds the cost of the inputs used. It is reflected in the standard of living of the people and is a function of constantly increasing productivity.

Raising productivity of operations, the ratio of output to input, is therefore the primary basis for creating wealth. A company can not prosper in ling run unless they have higher productivity than their domestic and foreign competitors. The tasks of the future operations manager can not be withdrawn from wealth creation. The future operations manager must be more sensitive and challengeable than today in creating wealth by improving productivity.

Product Description
The update to the second edition of Management Science: The Art of Modeling with Spreadsheets by Steve Powell and Ken Baker is revised to be compatible with Microsoft Excel 2007. Like the original second edition, the text expands upon the essential skills needed to develop real expertise in business modeling.  In principle, two students could work side by side in a course, one using the Second Edition and relying on Excel 2003, the other using the Update E… More >>

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Lecture Series on Fundamentals of Operations Research by Prof.G.Srinivasan, Department of Management Studies, IIT Madras. For more details on NPTEL visit nptel.iitm.ac.in

The fact that simulation technology is one of the best technologies ever developed is easily evident when we look at its widespread use in almost all types of industries, including both manufacturing and service sector business entities.
The effectiveness of simulation tools and techniques however, is proven when we look at how well and how easily they have integrated with Six Sigma, which is considered as the best available quality management tool by most industry experts.
For better understanding, let’s look at exactly how simulation technology is aiding Six Sigma project executions and consequently allowing businesses to improve quality, reduce costs and streamline their business processes.
Verifying the Applicability of New Business Processes
Businesses constantly need to rework their business processes in order to suit changing customer needs and requirements, which is exactly where Six Sigma concepts and simulation tools are combined to get the best possible results. Simulation tools are most commonly used during Six Sigma DMAIC process (Define, Measure, Analyze, Implement, and Control) and the DMADV process (Define, Measure, Analyze, Design, and Verify).
They are basically used for verifying the applicability of all new business processes as might have been suggested during the DMAIC and DMADV project implementations. The simulation technique is quite useful because it accurately predicts which processes will deliver the desired results and those that will do just the opposite (i.e. lead to potential losses or inefficiency).
Based on these predictions, businesses can then decide whether or not to give their final approval for the suggested business process. All this certainly helps because it allows businesses to ensure that only those processes get selected for final implementations, which hold the most potential.
Making Accurate Business Forecasts
Six Sigma simulation tools are used for making accurate business forecasts, something that provides enough time to businesses for making the necessary changes or alterations. For example, businesses can benefit by getting accurate information about their future manpower requirements.
They will then be able to select the most appropriate time of recruitment and also the exact number of individuals that need to be recruited. This eventually will help in saving costs since businesses will no longer have to invest huge amounts in maintaining the bench strength. Another good example is the use of simulation tools for predicting future market demand, related to the goods or services offered by a business organization.
Such predictions certainly help a lot because they allow businesses to alter their existing production levels in line with the changing market trends.
IT (Information Technology) has been a major contributor to the development of Six Sigma simulation tools and techniques and since new technological breakthroughs are constantly happening in the IT sector, we too can predict that such tools will become even more advanced in the days to come. However, certainly no prizes for predicting the most likely beneficiaries, since it will obviously be businesses.

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Industrial engineering has expanded from its origins in manufacturing to transportation, health care, logistics, services, and more. A common denominator among all these industries, and one of the biggest challenges facing decision-makers, is the unpredictability of systems. Probability Models in Operations Research provides a comprehensive overview of the probabilistic and stochastic modeling approaches commonly used to capture the randomness in industrial a… More >>

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Mathematics for Operations Research

Although it may not be a very popular form of employment, operations research analysts play a vital role in laying down systems according to the requirements. Operations analysts are employed in almost all leading sectors like the armed forces, telecommunications, traffic management, banking and finance, insurance, research organizations and consulting firms.

Operations Research Analyst – Job Description

There are several critical tasks that these analysts need to handle as a part of their routine work. Some of the major functions are as follows:

1. If working for traffic management, operations research analysts carefully study the traffic flow at a certain junction and then accordingly set the traffic signal. They need to ensure that traffic flows smoothly and there are no traffic jams.

2. Operations analysts also need to set up new traffic management systems in areas with no existing system at all.

3. Their services are also required for public management in large shopping centers and cafeterias. The analysts must bear in mind the layout of the area and create a system wherein there would be no major blockages and people can move around freely.

4. Also, they also provide recommendations to the management staff about the number of personnel required to handle the public. Also, they help in choosing the vital points where personnel must be particularly deployed.

5. The oldest sector wherein operations analysts have been pressed into service is the armed forces. During wars, the analysts are responsible for deploying forces and supplied where needed and closely monitor enemy movements like enemy submarines.

6. In large corporate houses and multinational corporations, the analysts play a key role in designing systems so as to effectively manage the man-power, finances and equipments.

7. Their job also involves finalizing business strategies, planning and forecasting along with allocating resources, managing supply chain, improve on the distribution network and analyze the large database of the company.

8. Yet another key function of operations analysts is to use mathematical and statistical models, linear programming and computer modeling to analyze the data to create reports based on which major policy decisions can be taken. To derive any concrete solutions, they must first drilldown the data and divide it into different components. Every component is then given a mathematical value and the mathematical relationship between these components is studied to derive actionable insights. Every part that is broken down must be analyzed minutely as often more than one part can be problematic.

9. Often it is possible that analysts may not be able to devise any concrete structure for a specific problem. Thus, in such cases they also need to devise test plans and measure its success rate before actually finalizing the plan.

Salary

The average salary for operations research analysts is $64,000. However, fresh candidates with no experience start with much lower packages of $40,000. To get a higher package or an entry into a larger firm, freshers must get their resumes done from professional agencies. Another alternative is to scan sample resumes and draft their CVs accordingly.

With an increase in experience, the salary would also increase and can reach up to $85,000.

An operations analyst job is specialized and fundamental and requires the candidates to be able to formulate efficient systems and processes.

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Pfizer Taps Sage Bionetworks to Build Cancer Models for Drug Discovery, Development
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Schaum’s Outline of Operations Research

1. INTRODUCTION

There are many alternatives to represent classifiers. The decision tree is probably the most widely used approach for this purpose. Originally it has been studied in the fields of decision theory and statistics. However, it was found to be effective in other disciplines such as data mining, machine learning, and pattern recognition. Decision trees are also implemented in many real-world applications. Given the long history and the intense interest in this approach, it is not surprising that several surveys on decision trees are available in the literature. Nevertheless, this survey proposes a profound but concise description of issues related specifically to top-down construction of decision trees, which is considered the most popular construction approach. This paper aims to organize all significant methods developed into a coherent and unified reference.

2. DECISION TREES

A decision tree (or tree diagram) is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. Decision trees are commonly used in operations research, specifically in decision analysis, to help identify a strategy most likely to reach a goal. Another use of decision trees is as a descriptive means for calculating conditional probabilities. In data mining and machine learning, a decision tree is a predictive model; that is, a mapping from observations about an item to conclusions about its target value. More descriptive names for such tree models are classification tree (discrete outcome) or regression tree (continuous outcome). In these tree structures, leaves represent classifications and branches represent conjunctions of features that lead to those classifications. The machine learning technique for inducing a decision tree from data is called decision tree learning, or (colloquially) decision trees.

3. DECISION TREE REPRESNTATION

The decision tree induction algorithm has been used broadly for several years. It is an approximation discrete function method and can yield lots of useful expressions. It is one of the most important methods for classification. This algorithm’s terms follow the “tree” metaphor. It has a root, which is the first split point of the data attribute for building a decision tree. It also has leaves, so that every path from root to leaf will form a rule that is easily understood. Since the decision tree is built by given data, the data value and character will be more important. For example, the amount of data will affect the result of the tree building procedure. The type of attribute value will also affect the tree model. Decision trees need two kinds of data: Training and Testing.

Training data, which are usually the bigger part of data, are used for constructing trees. The more training data collected, the higher the accuracy of the results. The other group of data, testing, is used to get the accuracy rate and misclassification rate of the decision tree. Many decision-tree algorithms have been developed. One of the most famous is ID3 (Quinlan 1986, 1983), whose choice of split attribute is based on information entropy. C4.5 is an extension of ID3 (Prather et al. 1997). It improves computing efficiency, deals with continuous values, handles attributes with missing values, avoids over fitting, and performs other functions.

CART (Classification and Regression tree) is a data-exploration and prediction algorithm similar to C4.5, which is a tree construction algorithm. Breiman et al. (1984) summarized the classification and regression tree. Instead of information entropy, it introduces measures of node impurity. It is used on a variety of different problems, such as the detection of chlorine from the data contained in a mass spectrum). Although decision trees may not be the best method for classification accuracy, even people who are not familiar with them find them easy to use and understand. Figure 1 shows a binary decision tree. It gives us an impression of a decision. It uses a circle as the decision node and a square as the terminal node. Each decision node has a condition that is represented by a function F, and the parameter is the split point of the split attribute. Each terminal node has a class label C, the value of which represents a class. It is apparent that it is easy to use decision trees to interpret the tree to rules, from which we can do analysis, and easy to interpret the representation of a nonlinear input-output mapping (Jang 1994).

Figure 1: A Typical binary Decision tree

Figure 1. A typical binary decision tree Lots of works address the splitting node choosing method and optimization of tree size, but less attention has been given to the weight of the data attributes. In this study, we use a system-reconstruction analysis method to get the weight of each attribute, which we use to reform raw data. After that, we use the decision-tree algorithm mentioned above to build a decision tree, from which we can find the decision-accuracy and misclassification rates.

4. ID3 ALGORITHM

The ID3 algorithm can be summarized as follows:

Take all unused attributes and count their entropy concerning test samples

Choose attribute for which entropy is maximum Make node containing that attribute

The algorithm is as follows:

According to Gestwicki, Itemized Dichotomozer 3 algorithm, or better known as ID3 algorithm was first introduced by J.R Quinlan in the late 1970’s. The algorithm ‘learned’ from relatively small training set of data to organize and process very large data sets. Ballard stated that ID3 algorithm is a greedy algorithm that selects the next attributes based on the information gain associated with the attributes. The information gain is measured by entropy, where Claude Shannon first introduced the idea in 1948.

ID3 algorithm prefers that the generated tree is shorter and the attributes with lower entropies are put near the top of the tree. These techniques satisfy the idea of Occam’s Razor. Occam’s Razor stated that, “one should not increase, beyond what is necessary, the number of entities required to explain anything”, which means that one should not make more assumptions than minimum needed. Hild described the basic technique on the implementation of ID3 algorithm and it is shown below.

For each uncategorized attribute, its entropy would be calculated with respect to the categorized attribute or conclusion. The attribute with lowest entropy would be selected. The data would be divided into sets according to the attribute’s value. For example, if the   attribute ‘Size’ was chosen, and the values for ‘Size’ were ‘big’, ‘medium’ and ‘small, therefore three sets would be created, divided by these values. A tree with branches that represent the sets would be constructed. For the above example, three branches would be created where first branch would be ‘big’, second branch would be ‘medium’ and third branch would be ‘small’. Step 1 would be repeated for each branch, but the already selected attribute would be removed and the data used was only the data that exists in the sets. The process stopped when there were no more attribute to be considered or the data in the set had the same conclusion, for example, all data had the ‘Result’ = yes.

ID3 algorithm had been used and implemented in many fields. One of the earliest implementation of ID3 algorithm is on a chess game. Ivan Bratko, the artificial intelligence researcher was the one implemented this chess game. According to Gestwicki, Bratko supplied the ID3 program with several pages of textbook recommendations for playing the chess endgame of white king and rook versus black king and knight. He made the rules around the idea of ‘knight’s side lost in at most n moves’. The result shows that ID3 algorithm is efficient in both time and space considerations, where the feature vector of the games and the decision tree size is small, compared to the training instances.

In a study by Gestwicki, one experiment had been conducted to predict the greyhound race. The experiment was to compare between the net profit gained by the ID3 algorithm and by three greyhound-racing experts. In this experiment, the system had been trained with 200 training races and 1600 dogs. The result shows that there are 26 races that the ID3 did not make any bet. This showed that the system was restricted from making any illogical choices, which is unlike human that were to gamble without logic in order to gain more winning.

5. C4.5 ALGORITHM

At each node of the tree, C4.5 chooses one attribute of the data that most effectively splits its set of samples into subsets enriched in one class or the other. Its criterion is the normalized information gain (difference in entropy) that results from choosing an attribute for splitting the data. The attribute with the highest normalized information gain is chosen to make the decision. The C4.5 algorithm then recurses on the smaller sublists. This algorithm has a few base cases.

All the samples in the list belong to the same class. When this happens, it simply creates a leaf node for the decision tree saying to choose that class. None of the features provide any information gain. In this case, C4.5 creates a decision node higher up the tree using the expected value of the class. Instance of previously-unseen class encountered. Again, C4.5 creates a decision node higher up the tree using the expected value.

In pseudo code the algorithm is

Check for base cases For each attribute a Find the normalized information gain Let a_best be the attribute with the highest normalized information gain Create a decision node that splits on a_best Recurse on the sublists obtained by splitting on a_best, and add those nodes as children of node Improvements from ID3 algorithm

C4.5 made a number of improvements to ID3. Some of these are:

Handling both continuous and discrete attributes – In order to handle continuous attributes, C4.5 creates a threshold and then splits the list into those whose attribute value is above the threshold and those that are less than or equal to it. Handling training data with missing attribute values – C4.5 allows attribute values to be marked for missing. Missing attribute values are simply not used in gain and entropy calculations. Handling attributes with differing costs. Pruning trees after creation – C4.5 goes back through the tree once it’s been created and attempts to remove branches that do not help by replacing them with leaf nodes.

6. CART ALGORITHM

Classification and regression trees (CART) is a non-parametric technique that produces either classification or regression trees, depending on whether the dependent variable is categorical or numeric, respectively. Trees are formed by a collection of rules based on values of certain variables in the modeling data set.

Rules are selected based on how well splits based on variables’ values can differentiate observations based on the dependent variable Once a rule is selected and splits a node into two, the same logic is applied to each “child” node (i.e. it is a recursive procedure) Splitting stops when CART detects no further gain can be made, or some pre-set stopping rules are met

Each branch of the tree ends in a terminal node

Each observation falls into one and exactly one terminal node Each terminal node is uniquely defined by a set of rules

The basic idea of tree growing is to choose a split among all the possible splits at each node so that the resulting child nodes are the “purest”. In this algorithm, only univariate splits are considered. That is, each split depends on the value of only one predictor variable. All possible splits consist of possible splits of each predictor.

7. COMPARISON OF ID3, C4.5 and CART

Algorithm designers have had much success with greedy, divide-and-conquer approaches to building class descriptions. It is chosen decision tree learners made popular by ID3, C4.5 (Quinlan1986) and CART (Breiman, Friedman, Olshen, and Stone 1984) for this survey, because they are relatively fast and typically they produce competitive classifiers. In fact, the decision tree generator C4.5, a successor to ID3, has become a standard factor for comparison in machine learning research, because it produces good classifiers quickly. For non numeric datasets, the growth of the run time of ID3 (and C4.5) is linear in all examples.

The practical run time complexity of C4.5 has been determined empirically to be worse than O (e2) on some datasets. One possible explanation is based on the observation of Oates and Jensen (1998) that the size of C4.5 trees increases linearly with the number of examples. One of the factors of a in C4.5’s run-time complexity corresponds to the tree depth, which cannot be larger than the number of attributes. Tree depth is related to tree size, and thereby to the number of examples. When compared with C4.5, the run time complexity of CART is satisfactory.

8. CONCLUSION

The decision-tree algorithm is one of the most effective classification methods. The data will judge the efficiency and correction rate of the algorithm. The survey is made on the decision tree algorithms ID3, C4.5 and CART towards their steps of processing data and Complexity of running data. The inductive learning algorithms had successfully recognized and generalized the rules contains in the training data given. The accuracies for the algorithms were also very high, which means the system produced a reliable result. This result also showed that inductive learning can be successfully implemented in a complex problem domain, and therefore it is very useful to be implemented in the real world problems. The second conclusion is that the algorithms had the ability to learn new rules and therefore had the ability to adapt to changes. Finally it can be concluded that between the three algorithms, the CART algorithm performs better in performance of rules generated and accuracy. CART algorithm produced less rules yet was more accurate than the other two algorithms. This showed that the CART algorithm is better in induction and rules generalization compared to ID3 algorithm and C4.5 algorithm.

ACKNOWLEDGEMENT

First, I would like to thank Almighty for His blessings towards the successful completion of this survey paper. I would like to extend my thanks to my Research Guide                            Dr. (Mrs.) M. Punithavalli, Director, Dept. of Computer Science, Sri Rama Krishna College for Women, Coimbatore for her valuable assistance, help and guidance during the research process. I also would like to extend my gratitude to my Husband                      Mr. M. S. Raja Sekaran for his moral support and co-operation.

REFERENCES

[1] S. R. Safavin and D. Landgrebe. A survey of decision tree classifier methodology. IEEE Trans. on Systems, Man and Cybernetics, 21(3):660-674, 1991.

[2] S. K. Murthy, Automatic Construction of Decision Trees from Data: A  MultiDisciplinary Survey. Data Mining and Knowledge Discovery, 2(4):345-389, 1998.

[3] R. Kohavi and J. R. Quinlan. Decision-tree discovery. In Will Klosgen and Jan M. Zytkow, editors, Handbook of Data Mining and Knowledge Discovery, chapter 16.1.3, pages 267-276. Oxford University Press, 2002.

[4] S. Grumbach and T. Milo: Towards Tractable Algebras for Bags. Journal of Computer and System Sciences 52(3): 570-588, 1996. IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS: PART C, VOL. 1, NO. 11, NOVEMBER 2002 11

[5] L. Breiman, J. Friedman, R. Olshen, and C. Stone. Classification and Regression Trees. Wadsworth Int. Group, 1984.

[6] J.R. Quinlan, Simplifying decision trees, International Journal of Man-Machine Studies, 27, 221-234, 1987.

[7] T. R. Hancock, T. Jiang, M. Li, J. Tromp: Lower Bounds on Learning Decision Lists and Trees. Information and Computation 126(2): 114-122, 1996.

[8] L. Hyafil and R.L. Rivest. Constructing optimal binary decision trees is NP-complete. Information Processing Letters, 5(1):15-17, 1976

[9] H. Zantema and H. L. Bodlaender, Finding Small Equivalent Decision Trees is Hard, International Journal of Foundations of Computer Science, 11(2):343-354, 2000.

[10] G.E. Naumov. NP-completeness of problems of construction of optimal decision trees. Soviet Physics: Doklady, 36(4):270-271, 1991.

[11] J.R. Quinlan, Induction of decision trees, Machine Learning 1, 81-106, 1986.

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