The operations research It is a method that is dedicated to the application of advanced analytical disciplines to help in problem solving and decision making, being useful in the management of organizations. That is, it is devoted to establishing the supreme values of some real-world goal: the maximum of profit, performance or return, or the minimum of loss, cost or risk..
In this discipline, problems are divided into their basic components and then solved with defined steps, through mathematical analysis. Analytical methods used include mathematical logic, simulation, network analysis, queuing theory, and game theory.
Using these techniques from the mathematical sciences, operations research achieves optimal or feasible solutions to complicated decision-making problems. His techniques have solved problems of interest in a variety of industries.
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Due to the statistical and computational nature of most of these methods, operations research also has strong links with analysis and informatics..
Operations researchers facing a problem must stipulate which of these methods are the most appropriate, based on improvement objectives, nature of the system, computational power, and time constraints..
Mathematical programming is one of the most powerful techniques used in operations research, to such an extent that sometimes both terms are used interchangeably.
This programming has nothing to do with computer programming, but it means optimization. Discrete programming or optimization addresses problems where variables can only assume discrete values, for example, integer values.
Due to its emphasis on human-technology interaction and its focus on practical applications, operations research has been interpolated with other disciplines, especially industrial engineering and operations management, also relying on psychology and organizational science..
In the 17th century, mathematicians like Pascal and Huygens tried to solve problems that involved complex decisions. These types of problems were solved during the 18th and 19th centuries using the combinatorics.
In the 20th century, the study of inventory management could be considered the beginning of modern operations research, with the inexpensive batch quantity developed in 1913.
During 1937, operations research was initially applied in Great Britain, in the research carried out to integrate radar technology in air combat operations, thus differentiating itself from research carried out in laboratories.
The term operations research was coined in early 1941 during World War II, when British military management convened a group of scientists to apply a scientific approach to the study of military operations..
The main objective was to effectively allocate scarce resources to the various military operations and activities within each operation..
As in Great Britain, radar stimulated developments in the US Air Force. In October 1942 all commands were urged to include operations research groups in their personnel..
Operations research grew in many areas other than the military, as scientists learned to apply its principles to the civilian sector. Its effectiveness in the military sphere extended its interest to other industrial and governmental areas..
Partnerships were organized, beginning in 1948 with the Operations Research Club of Great Britain, which in 1954 became the Operations Research Society.
In 1952 the Operations Research Society was formed in the USA. Many other national societies also appeared.
In 1957 the first international conference on operations research was held at the University of Oxford. By 1959 the International Federation of Operations Research Societies was formed.
In 1967, Stafford Beer described the field of management science as the business use of operations research..
With the development of computers over the next three decades, operations research can now solve problems with hundreds of thousands of variables and constraints..
Every day, operations research professionals solve real-life problems that save money and time. These problems are very diverse and almost always seem unrelated. However, its essence is always the same, making decisions to achieve a goal in the most efficient way..
The central objective of operations research is optimization, that is, doing things in the best possible way, depending on the given circumstances.
This general concept has many applications, for example, in data analysis, allocation of goods and resources, control of production processes, risk management, traffic control, etc..
Operations research focuses on the development of mathematical models that can be used to analyze and optimize complex systems. It has become an area of academic and industrial research. The process is divided into three steps.
- A set of possible solutions to a problem is developed.
- The alternatives obtained are analyzed and reduced to a small set of solutions that are likely to be viable.
- The alternate solutions produced undergo a simulated implementation. If possible, they are tested in real world situations.
Following the optimization paradigm when applying operations research, the decision maker selects the key variables that will influence the quality of the decisions. This quality is expressed by means of an objective function to be maximized (profit, speed of service, etc.), or to be minimized (cost, loss, etc.).
In addition to the objective function, a set of constraints is also considered, be they physical, technical, economic, environmental, etc. Then, by systematically adjusting the values of all the decision variables, an optimal or feasible solution is selected.
It is an algorithm to program a set of activities in a project. The critical path is determined by identifying the longest stretch of dependent activities and measuring the time required to complete them from start to finish..
It is a basic combinatorial optimization problem. In this problem there are multiple agents and multiple tasks. Any agent can be assigned to perform any task.
Depending on the task assigned to the agent, a cost is incurred which can vary. Therefore, it is required to perform all the tasks, properly assigning an agent to each task and a task to each agent, to minimize the total cost of the assignment..
A model is of great help to facilitate the investigation of operations, since the problems are expressed by means of models that show the relationship of the variables.
As it is a simplified representation of the real world, only those variables relevant to the problem are included. For example, a model of free-falling bodies does not describe the color or texture of the body involved..
The models represent the relationship between controlled and uncontrolled variables and system performance. Therefore, they must be explanatory, not merely descriptive..
Many of the simplifications used cause some error in the predictions derived from the model, but this error is quite small compared to the magnitude of the operational improvement that can be obtained from the model..
The first models were physical representations, such as model ships or airplanes. Physical models are usually quite easy to build, but only for relatively simple objects or systems, being generally difficult to change.
The next step after the physical model is the graph, which is simpler to build and handle, but more abstract. As a graphical representation of more than three variables is difficult, symbolic models are used.
There is no limit to the number of variables that can be included in a symbolic model. These models are easier to build and operate than physical models.
Despite the obvious advantages of symbolic models, there are many cases where physical models are still useful, such as when testing physical structures and mechanisms. The same is true for graphic models.
Most operations research models are symbolic models, because symbols better represent the properties of the system.
The symbolic model is in the form of a matrix or an equation. These models provide solutions in a quantitative way (cost, weight, etc.), depending on the problem.
Symbolic models are completely abstract. When symbols are defined in the model, meaning is given to it.
Symbolic models of systems with different content often show similar structures. Therefore, the problems that arise in the systems can be classified in terms of few structures.
As the methods for extracting solutions from the models depend only on their structure, few methods can be used to solve a wide variety of problems from a contextual point of view..
The applications of operations research are abundant, such as in manufacturing companies, service organizations, military branches and governments. The range of problems you have contributed solutions to is huge:
- Airline, train or bus scheduling.
- Assigning employees to projects.
- Development of strategies adopted by companies (game theory).
- Management of water flow from reservoirs.
The processes of a complex project that affect the total duration of the project are identified.
Design the blueprint for the equipment in a factory or the components on a computer chip, to reduce manufacturing time and therefore reduce costs.
Configure telecommunications or energy system networks to safeguard quality of service during interruptions.
To minimize transportation costs, while considering factors such as avoiding placing hazardous materials near homes.
Performed on many types of networks, including circuit-switched networks, such as the public telephone network, and computer networks, such as the Internet.
Management of the flow of operational activities in a project, as a consequence of the versatility of the system, through operations research techniques, to reduce this variability and allocate spaces using a combination of time, inventory and capacity allocations.
It is the management of the flow of components and raw materials derived from an unstable demand for finished products.
Freight management of delivery and transportation systems. Examples: intermodal freight or the traveling salesman problem.
Globalize operational processes in order to take advantage of more economical labor, land, materials or other productive inputs.
Refers to cutting a material in stock, such as paper rolls or metal sheets, into pieces of specific sizes, seeking to minimize material waste.
An analysis of the cars that stopped at urban service stations located at the intersection of two streets revealed that almost all came from just four of the 16 possible routes at the intersection (four ways of entering, four ways of exiting).
When examining the percentage of cars that stopped in the service for each route, it was observed that this percentage was related to the amount of time lost when stopping..
However, this relationship was not linear. That is, the increase in one was not proportional to the increase in the other..
It was later found that the perceived lost time exceeded the actual lost time. The relationship between the percentage of stopped cars and the perceived lost time was linear..
Therefore, a model was built that related the number of cars that stopped at the service stations with the amount of traffic on each route of the intersection, which affected the time required to obtain the service..
It consists of assigning workers to tasks, trucks to delivery routes, or classes to classrooms. A typical transportation problem involves the allocation of empty rail cars where they are needed.
It is also used to determine which machines should be used to manufacture a particular product, or which set of products should be manufactured in a plant during a particular period..
This technique is routinely used for problems such as mixing oil and chemicals in refineries, selecting suppliers for large manufacturing corporations, determining shipping routes and schedules, and managing and maintaining truck fleets..
Bayesian statistics are applied to search for lost items. It has been used several times to find lost vessels:
Played a key role in recovering flight records in the 2009 Air France Flight 447 disaster.
It has also been used in attempts to locate the wreckage of Malaysia Airlines Flight 370..
Inventory issues arise, for example, to determine the quantities of goods to be purchased or produced, how many people to hire or train, how large a new production facility or retail store should be.
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