# What is the goal of surgical research

## Operations Research (OR)

Operations Research (OR) is the application of mathematical methods to prepare optimal decisions. If the decisions to be prepared are of an operational nature, OR is also called corporate research. OR originated in England and the USA during the Second World War and was initially used in the military field; today the business application dominates.

Linear programming (LP) is the most important and best developed OR method. LP is used to determine the greatest profit, the lowest costs, the highest advertising success, the shortest route, the cheapest feed mixture, the minimization of waste, etc.

Operations Research (often abbreviated to OR) is a branch of business administration and management that uses mathematical models and processes to map decision problems and to derive recommendations for action.

Operations research is used with increasing success to determine optimal business decisions.

Operations Research consists of scientific methods and procedures with the aim of providing the entrepreneur and other decision makers with quantitative documents for the solution of planning and coordination problems, which present themselves as mathematically calculable selection problems with several alternatives.

Operations Research relates variables of a technical-social system to one another in such a way that a functional model can be created with which (behavior) predictions are possible.

German terms for operations research are: business research, decision research, planning, process, process research, etc.

Operations Research is mainly used to solve the following problems: storage problems, allocation and distribution problems, problems of waiting times and congestion, replacement problems, competition problems.

To solve a problem with OR, the following steps are necessary:

1. Verbal formulation of a problem

2. Development of a suitable mathematical model

3. Deriving a solution from the model (with the help of algorithms)

4. Checking of model and solution for consistency

5. Continuous monitoring of the solution during its application.

Such a solution can often only be achieved through the interaction of different disciplines: business administration, engineering knowledge, statistics and mathematics, possibly physics, sociology, psychology etc ...

1. Mathematical tools from statistics and probability theory: probability laws, distribution types, random variables, addition theorems, Monte Carlo method, queuing theory, Markov processes

2. Mathematical tools from equation theory: linear and non-linear equations, numerical calculation of function values, - simulation as a step-by-step calculation method.

3. Mathematical tools from optimization theory: extreme value methods from differential calculus, linear and non-linear optimization, dynamic optimization, game theory, etc.

Limits to the applicability of operations research:

Some operations research procedures require data that cannot be obtained in practice, e.g. in game theory, gains and losses that are not available in practice.

In addition, the factors involved in the operations research model must be quantifiable and measurable. Limitations of the mathematical models presuppose that there are strictly functional relationships between the individual variables.

In the OR model, many operational processes can only be recorded in a very simplified manner, so that the accuracy and reliability of such results is greatly reduced. There are restrictions due to the existing solution methods (algorithms), since the known solution methods, for example, are not sufficient to clearly determine optimal combinations for non-linear programs.

Furthermore, there are limitations due to the economy. The sometimes quite considerable costs make it necessary to consider whether the savings to be achieved justify the use of operations research. The use of operations research places considerable demands on cost accounting, since most optimization problems cannot be solved without recourse to cost information.

Operations Research cost data can be found in the cost accounting. Since the optimization approaches mostly work with limit values, the development of cost accounting to calculate with - marginal costs accommodates the increased use of operations research.

Operations Research was developed in Great Britain and the USA during the World War to obtain and analyze documents for making decisions about military measures and operations.

Operations research or corporate research is a research area that, due to constant new and further developments, can hardly be precisely delimited. The aim of Operations Research is to find an optimal solution for the structure and mode of operation of a system under consideration using quantitative scientific methods. Such systems are e.g. B. Warehousing, production, queuing systems, transport systems. Looking at problems with the whole system in mind does not mean that they have to be solved in a single investigation. Since this approach is too extensive, in practice sub-problems are solved one after the other and sometimes also recursively. The characteristic of Operations Research (OR) R. as a scientific discipline is that it is not a better solution compared to the existing one, but an optimal solution that should be found. However, this does not rule out the fact that, for reasons of cost, heuristic methods are used in addition to exact methods. In all operations research optimization processes, it must not be overlooked that the results are only meaningful to the extent that the model used corresponds to reality. The optimization results should not be a guideline for action, but a recommendation for action. Although the research area Operations Research is still very young, the first research activities began during the Second World War, a large number of model structures with associated solution processes already exist. The most important model type from a theoretical and practical point of view is the linear program (linear programming). Starting from linear programming, integer programming and non-linear programming were developed. Network planning technology, like transport optimization, is a special form of linear programming. For this, solution algorithms could be created that work much faster than z. B. the simplex method. The backpack problem can be seen as a special form of integer programming. Model structures that do not emerge from linear programming are queue models, competition models (game theory) and dynamic programming. The models shown can essentially be solved with four methods, the graph-theoretical method, the mathematical programming method, the simulation and the heuristic method. The problem of operations research today does not lie in the theoretical model and method development, but in the application. The knowledge about Operations Research (OR) R. is still relatively little widespread in practice, the costs for a practical model development and the associated data acquisition are usually very high. In some cases, there is still a lack of suitable, user-friendly software packages. The findings of operations research have so far found the greatest dissemination in the military sector, in economic planning (e.g. transport policy, energy industry) and in large companies.

Scientific methods and procedures with the task of providing the entrepreneur and other decision makers with quantitative documents for the solution of planning and coordination problems, which present themselves as mathematically calculable selection problems with several alternatives. Developed during the war in Great Britain and the USA for the acquisition and evaluation of documents for the decisions about military measures and operations, OR is used with increasing success to determine optimal business decisions. German terms that could not be generally accepted: business research, decision research, planning, process, process research etc. OR is mainly used to solve the following problems: storage problems, allocation and distribution problems, problems with waiting times and congestion, replacement problems, competition problems. To solve a problem with OR, the following steps are required:

1. Verbal formulation of the problem

2. Development of a mathematical model

3. Deriving a solution from the model with the help of algorithms

4. Examination of the model and solution

5. Continuous monitoring of the solution during its application.

Such a solution can usually only be created through cooperation between different disciplines: business economists, statisticians, mathematicians, physicists, engineers, sociologists, psychologists, etc.

1. Mathematical tools from statistics and probability theory: probability laws, distribution types, random variables, addition theorems, Monte Carlo method, queuing theory, Markov processes

2. Mathematical aids from equation theory: linear and non-linear equations, numerical calculation of function values, simulation as a step-by-step calculation method.

3. Mathematical tools from optimization theory: extreme value methods from differential calculus, linear and non-linear optimization, dynamic optimization, game theory, etc.

Limitations of application: Some OR procedures require data that cannot be obtained in practice, e.g. in game theory, profits and losses that are not available in practice. In addition, the factors that go into the OR model must be quantifiable and measurable. Limitations of the mathematical models presuppose that there are strictly functional relationships between the individual variables. In the OR model, many operational processes can only be recorded in a very simplified manner, so that the accuracy and reliability of such results is greatly reduced. There are restrictions due to the existing solution methods (algorithms), since the known solution methods, for example, are not sufficient to clearly determine optimal combinations for non-linear programs. There are also economic limitations. The sometimes quite considerable costs make it necessary to consider whether the savings to be achieved justify the use of OR. The use of OR places considerable demands on cost accounting, as most optimization problems cannot be solved without recourse to cost information. Operations Research cost data can be found in the cost accounting. Since the optimization approaches mostly work with limit values, the development of cost accounting to calculate with marginal costs accommodates the increased use of OR.

There are different ideas about the term operations research in German-language literature. In general, it is understood to mean operational research, corporate research or planning research. Operations research is the application of scientific knowledge to solving a problem using mathematical models. The following features are decisive:

1. A goal is determined. As a rule, a size is to be maximized or minimized provided that certain secondary conditions (restrictions) are fulfilled.

2. A mathematical model is used to solve the optimization problem.

Operations Research's approach to solving problems can generally be described as follows:

1. Formulation of the problem, analysis of the problem structure and recording of the existing restrictions,

2. Development of a mathematical model,

3. Calculation of the optimal solution,

4. Examination of the result for economic reality,

5. Control of the solution when it is implemented in practice.

(OR) (corporate research, optimal planning, mathematical decision-making preparation) model-based preparation of decisions for the design and control of socio-technical systems (e.g. companies), in short: model-based planning or model-based decision-making preparation. Model support means working with mathematical planning models. Preparing for a decision also means looking at the decision-making situation from as many relevant perspectives as possible. For this reason, the interdisciplinary nature of the OR plays a central role. The OR tries to use a wide range of expertise to create such decision proposals or decision documents in which all relevant dependencies and effects are processed as far as possible. The mathematical planning models therefore also often represent economic as well as technical, scientific, legal and sociological categories of knowledge. OR was created during World War II, in England and the USA, in connection with the preparation of military decisions. After the end of the war, OR found increasing interest in private companies, with England and the USA continuing to lead. Since the 1960s, public administration (transport planning, health planning, training planning, financial and budget planning, etc.) has been added as a third area of ​​application for OR, again with England and the USA as pioneers. The ideas of the OR penetrated to Germany since the mid-1950s, where they were continued from a business, mathematical and engineering point of view. The development is systematically promoted by the professional association "German Society for Operations Research" (DGOR). Behind the OR companies in the USA, Great Britain and Japan, it is the fourth largest OR company in the world, closely followed by the OR companies in other industrialized nations. The DGOR is the German member of the international umbrella organization "International Federation of Operational Research Societies" (IFORS), to which around 40 national OR societies belong. Three sub-areas are characteristic of the OR knowledge area, planning models, planning mathematics and planning methodology. (1) Planning models: The (mathematical) planning models are the central tool of the OR, which distinguishes it from conventional planning activities. For numerous characteristic problems from different functional areas of companies (and other socio-technical systems), standard types of planning models are available today (sales planning models, procurement planning models, financial planning models, investment planning models, warehouse planning models, personnel planning models, production planning models, project planning models, etc.). (2) Planning mathematics: The planning models serve the purpose of providing the model user with a variety of insights into the socio-technical system under consideration. So you need to be able to answer questions from users. Suitable mathematical procedures are required for this. On the one hand, all conventional mathematical methods can be used in the OR. On the other hand, a variety of new calculation methods have been developed within the OR, each with reference to novel mathematical model structures. (3) Planning methodology: the focus of the practical OR work is the planning methodology with system approach and model construction and with planning management. It encompasses the entire planning process from problem analysis to implementation of the planning results. Literature: Churchman, CWIAckoff, R. LJArnoff, EL, Operations Research, 5th edition, Munich Vienna 1971. Müller-Merbach, H., Operations Research, 3rd edition, Munich 1973. Hanssmann, F., Quantitative Betriebswirtschaftslehre , Munich, Vienna 1982.

1. Characterization Operations Research is an interdisciplinary branch of knowledge that deals with the analysis and solution of real, complex decision problems. The main subject of the application is the preparation of the decision; which should enable optimal decisions in the best case. For this purpose, the real decision problem is mapped using a mathematical planning model that is solved by applying quantitative analysis methods. Ultimately, recommendations for action should result from this, which optimize the given evaluation criteria for assessing the consequences of entrepreneurial action. Instead of the term Operations Research, other, mainly Synonymous terms such as optimal planning, quantitative corporate planning, corporate research, decision research, process and planning research, mathematical planning calculation, operational research and optimization calculation are used, but these have not become generally accepted.
2. Historical development of operations research Apart from a few forerunners of operations research (e.g. queue models, lot size formula 1915), its development is dated from 1940 onwards.During this time, mathematical methods were mainly used in the USA and Great Britain to analyze and prepare military strategic decisions. After the end of the Second World War, the methods of operations research began to be gradually applied in the private sector. Companies were founded, for example ORSA (Operations Research Society of America, USA, 1952), ORS (OperationalResearch Society, Great Britain, 1954), SOFRO (Societe Fran9aise de Recherche Operelle, France, 1956), AKOR (Working Group OperationalResearch, Germany, 1957), DGU (German Society for Corporate Research, Germany, 1961). The latter merged in 1971 to form DGOR (German Society for Operations Research). The GMÖOR (Society for Mathematics, Economics and Operations Research) existed at the same time. The DGOR had mainly dealt with the application aspect of Operations Research, while the GMÖOR had essentially devoted itself to the further development of the mathematical theories of Operations Research. In 1998 DGOR and GMÖOR merged to form GOR (Society for Operations Research). In the meantime there are national associations of this kind in almost all industrialized countries, which merged in 1958 to form IFORS (International Federation of Operational Research Societies).
3. Modeling and solution methods in Operations Research Based on a real problem with a need for decision-making and action, realistic objectives and alternative courses of action must first be determined. A mathematical planning model is then formulated through abstraction and structure-preserving images with the help of (random) variables, functions, equations, inequalities, etc., which generally represents a simplified image of the real system. After collecting problem-relevant data, the model is analyzed and solved. In addition to exact algorithms that lead to an exact model solution, approximate methods that generate approximate solutions with assessable deviations from the optimal solution, heuristics that represent systematic search methods for generating not necessarily optimal, but mostly satisfactory model solutions, as well as simulation methods that are more experimental Have character, be distinguished. With the assessment of the results obtained, a decision aid for the real initial problem is finally given, whereby here the aspects neglected in the model formation may also have to be analyzed in more detail.
4. Subareas of Operations Research In the relevant literature there are a number of systematization approaches for the area of ​​Operations Research. Essentially, the systematizations according to the model type and the areas of application are to be mentioned in this context. From the point of view of the underlying model type, the following sub-areas of operations research result in particular: linear, non-linear, integer and dynamic optimization, graph theory and network planning, stochastics (storage models, queue models, simulation, etc.). If, on the other hand, the application areas of (quantitative) corporate planning are in the foreground, the following sub-areas of operations research can be distinguished: decision theory, game theory, queuing theory, reliability theory, project management, storage problems, transport problems, assignment problems and sequence problems.
5. Business applications of operations research Methods of operations research are used to a greater or lesser extent in almost all operational functional areas. In the procurement area, the main focus is on determining the optimal order quantities and warehouse disposition. One of the main fields of application of methods in operations research is certainly the production area. In addition to the determination of optimal production programs, particular mention should be made of mixing and blending problems, the determination of optimal solution sizes, layout planning and internal transport, machine occupancy problems as well as the area of ​​servicing and maintenance. In the sales area, for example, the determination of the optimal sales program as well as transport and route planning problems can be solved using methods of operations research. Further applications in the personnel area are, for example, personnel deployment problems or timetable optimization, and in the investment and financing area, for example, investment program decisions or simultaneous investment and financial planning problems. Note For the related areas of knowledge, see analysis methods, business management, procurement management, decision-making, business management, financial mathematics, logistics, utility analysis, econometrics, optimization, optimization models, mathematical, portfolio management, production management, project management, process management, statistics, corporate planning, business mathematics.

Literature: Domschke, W., Drexl, A .: Introduction to Operations Research, 6th edition, Springer Berlin Heidelberg New York 2005; Domschke, W., Scholl, A .: Fundamentals of business administration: an introduction from a decision-oriented point of view, 3rd edition, Springer Berlin Heidelberg 2005; Gal, T., Gehring, H .: Business planning and decision-making techniques, De Gruyter-Verlag Berlin New York 1981; Hauke, W., Opitz,
0.: Mathematical business planning, 2nd edition, Books on Demand GmbH 2003; Klein, R., Scholl, A .: Planning and decision: Concepts, models and methods of a modern business decision analysis, Vahlen Munich 2004; Müller-Merbach, H .: Operations Research, Methods and Models of Optimal Planning, 3rd edition, Verlag Franz Vahlen Munich, 10th reprint 1992; Neumami, K., Morlock, M .: Operations Research, 2nd edition, Carl Hanser Verlag Munich Vienna 2002; Nieswandt, A .: Operations Research, 3rd edition, Verlag Neue Wirtschaftsbriefe Herne Berlin 1994; Runzheimer, B .: Operations Research, linear planning calculation, network planning technology, simulation and queuing theory, 8th edition, Betriebswirtschaftlicher Verlag Dr. Th. Gabler GmbH Wiesbaden 2005; Sclmeeweiss, Ch .: planning 2, concepts of process and model design, Springer Berlin Heidelberg New York 1998; Zimmermann, W., Stache, U .: Operations Research, Quantitative Methods for Decision Preparation, 10th Edition, Oldenbourg Verlag Munich Vienna 2001. Internet addresses: http://gor-ev.de (Society for Operations Research), http: // www.oegor.at (Austrian Society for Operations Research), http://www.svor.ch (Swiss Association for Operations Research), http: //www.vvs-or.n1 (Vereniging voor Statistiek en Operationele Research / Netherlands Society for Statistics and Operations Research), http://www.euro-online.org (The Association of European Operational Research Societies), http://www.ifors.org. (International Federation of OperationalResearch Societies), http://vwww10.hrz.tu-darrnstadt.de/bw13/0R-Lexikon.pdf (Prof. Domschke, TU-Darmstadt: wisu-Lexikon Operations Research), http: // carbon .cudenver.edu / —hgreenbe / glossary / index.php (Greenberg: Mathematical Programming Glossary), http://www.fh-augsburg.de/informatik/projekte/mebib/fai/informatik/or.html (Augusburg University of Applied Sciences: Learning programs on Operations Research), http://www.ruhr-uni-bochum.de/or/index.htin?main_service_unilinks.htm; na-vi_lehrstuhl.htm (Ruhr-Uni Bochum: overview and addresses for operations research at universities).

(Corporate research): The development of formal and quantitative decision models for corporate management using mathematical methods, with the help of which the optimal decision can be found with regard to a specific objective.

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