Operations research

Operations research, or operational research in British usage, is a discipline that deals with the application of advanced analytical methods to help make better decisions.[1] It is often considered to be a sub-field of mathematics.[2] The terms management science and decision science are sometimes used as synonyms.[3] Employing techniques from other mathematical sciences, such as mathematical modeling, statistical analysis, and mathematical optimization, operations research arrives at optimal or near-optimal solutions to complex decision-making problems. Because of its emphasis on human-technology interaction and because of its focus on practical applications, operations research has overlap with other disciplines, notably industrial engineering and operations management, and draws on psychology and organization science. Overview The major subdisciplines in modern operational research, as identified by the journal Operations Research,[6] are: History Historical origins Related:  Research DesignLearn to code

Decision-making Sample flowchart representing the decision process to add a new article to Wikipedia. Decision-making can be regarded as the cognitive process resulting in the selection of a belief or a course of action among several alternative possibilities. Every decision-making process produces a final choice that may or may not prompt action. Decision-making is the study of identifying and choosing alternatives based on the values and preferences of the decision maker. Decision-making is one of the central activities of management and is a huge part of any process of implementation. Overview Edit human performance with regard to decisions has been the subject of active research from several perspectives: Decision-making can also be regarded as a problem-solving activity terminated by a solution deemed to be satisfactory. Some have argued that most decisions are made unconsciously. In regards to management and decision-making, each level of management is responsible for different things.

Constraint satisfaction problem Examples of simple problems that can be modeled as a constraint satisfaction problem Examples demonstrating the above are often provided with tutorials of ASP, boolean SAT and SMT solvers. In the general case, constraint problems can be much harder, and may not be expressible in some of these simpler systems. "Real life" examples include planning and resource allocation. Formal definition Formally, a constraint satisfaction problem is defined as a triple , where [1] is a set of variables, is a set of the respect domains of values, and is a set of constraints. Each variable can take on the values in the nonempty domain . is in turn a pair , where is a subset of variables and is an . . satisfies a constraint if the values assigned to the variables satisfies the relation An evaluation is consistent if it does not violate any of the constraints. Resolution of CSPs Constraint satisfaction problems on finite domains are typically solved using a form of search. Theoretical aspects of CSPs

Explanation This description may establish rules or laws, and may clarify the existing ones in relation to any objects, or phenomena examined. The components of an explanation can be implicit, and be interwoven with one another. In scientific research, explanation is one of several "purposes" for empirical research.[1] [2] Explanation is a way to uncover new knowledge, and to report relationships among different aspects of studied phenomena. Explanation attempts to answer the "why" question. Arguments In this sense, arguments aim to contribute knowledge, whereas explanations aim to contribute understanding. Arguments and explanations largely resemble each other in rhetorical use. Justification Justification is the reason why someone properly holds a belief, the explanation as to why the belief is a true one, or an account of how one knows what one knows. It is important to be aware when an explanation is not a justification. Types  See also Further reading Notes

Merging data in PowerPivot | Javier Guillén Update 9/23/13: Check an example using Power Query to deal with the same issue described on this article: One of the most common requests I have seen from data analysts working with PowerPivot is how to merge two or more datasets. For example, you are given the following two sales extracts and are asked then to generate a YTD report based on their composite data Extract 1 (Table 1): Extract 2 data (Table 2): If we want to report on total amount for the year, we must combine these two files. Somebody new to PowerPivot may be tempted to add a relationship between those two tables on the common key column (Product ID). PowerPivot complains that there are duplicate values, which indeed there are (on both tables, Product ID has multiple values that are the same). Notice how there was a sales amount for 1/1/2012 for the city of Bogota. Let’s go back to our example. Worksheet only example

Theoretical computer science An artistic representation of a Turing machine. Turing machines are used to model general computing devices. Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on more mathematical topics of computing and includes the theory of computation. It is difficult to circumscribe the theoretical areas precisely. TCS covers a wide variety of topics including algorithms, data structures, computational complexity, parallel and distributed computation, probabilistic computation, quantum computation, automata theory, information theory, cryptography, program semantics and verification, machine learning, computational biology, computational economics, computational geometry, and computational number theory and algebra. History While logical inference and mathematical proof had existed previously, in 1931 Kurt Gödel proved with his incompleteness theorem that there are fundamental limitations on what statements could be proved or disproved.

Descriptive research Descriptive research is used to describe characteristics of a population or phenomenon being studied. It does not answer questions about how/when/why the characteristics occurred. Rather it addresses the "what" question (what are the characteristics of the population or situation being studied?) [1] The characteristics used to describe the situation or population are usually some kind of categorical scheme also known as descriptive categories. Hence, research cannot describe what caused a situation. Social science research In addition, the conceptualizing of descriptive research (categorization or taxonomy) precedes the hypotheses of explanatory research.[2] For a discussion of how the underlying conceptualization of Exploratory research, Descriptive research and explanatory research fit together see Conceptual framework. References Jump up ^ Shields, Patricia and Rangarjan, N. 2013. External links Descriptive Research from BYU linguistics department

Constraint optimization General form A general constrained minimization problem may be written as follows: where and Solution methods Many unconstrained optimization algorithms can be adapted to the constrained case, often via the use of a penalty method. Equality constraints If the constrained problem has only equality constraints, the method of Lagrange multipliers can be used to convert it into an unconstrained problem whose number of variables is the original number of variables plus the original number of equality constraints. Inequality constraints With inequality constraints, the problem can be characterized in terms of the Karush–Kuhn–Tucker conditions, in which simple problems may be solvable. Linear programming If the objective function and all of the hard constraints are linear, then the problem is a linear programming problem. Quadratic programming Constraint optimization problems Branch and bound First-choice bounding functions Russian doll search

Prediction A prediction (Latin præ-, "before," and dicere, "to say") or forecast is a statement about the way things will happen in the future, often but not always based on experience or knowledge. While there is much overlap between prediction and forecast, a prediction may be a statement that some outcome is expected, while a forecast is more specific, and may cover a range of possible outcomes.[clarification needed][citation needed] A "prediction" may be contrasted with a "projection", which is explicitly dependent on stated assumptions. Although guaranteed accurate information about the future is in many cases impossible, prediction can be useful to assist in making plans about possible developments; Howard H. Informal prediction Outside the rigorous context of science, the term "prediction" is often used to refer to an informed guess or opinion. Statistics More formal and systematic predictions can be made by the testing of formal hypotheses using statistical methods. Finance

SQLBI - Marco Russo : Many-to-Many relationships in PowerPivot UPDATE: This blog post is still good for learning DAX principles, but a better description of many-to-many patterns is available on The Many-to-Many Revolution whitepaper that is available here: - please download it and use the pattern described there to write faster DAX formulas! PowerPivot doesn’t have the capability of really understand a many-to-many (M2M) relationship between two tables. In a relational world, a many-to-many relationship is materialized using a bridge table that split this relationship in two separate one-to-many relationships between the two original tables and the bridge table. Apparently, we can do the same in PowerPivot, but the behavior is not the expected one. Some workaround is possible using DAX, but there are some undesirable side effects if we only use calculated column. As we will see, it is necessary to use calculated measures to get the best results. Consider two tables, Customers and Accounts. Customers Table

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