MATHEMATICAL SCHOOL OF ADMINISTRATION: ORIGIN, CHARACTERISTICS - DUDAS - 2025

The mathematical school of administration is a theory framed in the administrative sciences that seeks to respond to certain organizational problems through the use of mathematical models. It offers objective solutions using mathematical sciences as a way to avoid the influence of human subjectivity.

The main objective of the mathematical school of administration is to reduce uncertainty and provide solid support that is decisive in decision-making. Emphasis is placed on the rationality of the arguments and on a logical and quantitative basis.

The objective of the mathematical school of administration is to generate solutions to organizational problems through mathematics. Source: pixabay.com

The development of the mathematical school represented a great contribution to administrative sciences, since it allows the use of novel planning and management techniques in the field of organizational resources, be they human, material or financial.

Origin

The mathematical school of administration has its origins in the time of World War II. At that time, the problems within the administration of resources in the English armies arose out of control, and the need to optimize them was prevalent in order to achieve the objectives set.

To this end, scientists from different disciplines met with the aim of seeking solutions, always taking the scientific framework as a reference. From this context, the quantitative technique called operations research was created.

Due to the good acceptance of the method used for the administration of the resources, the United States decided to use it in the military administration. At the end of the war, the Anglo-Saxon country decided to apply this system in the industrial sector.

characteristics

The use of operations research can vary, as it can be expressed through the use of mathematical methods or the scientific method only. However, these two approaches have some common characteristics:

- The problem is faced from a systemic perspective; that is, breaking down and identifying the problem in the parts that comprise it, in order to be able to deal with all related aspects.

- The use of the scientific method is the main basis for approaching the resolution of the problem.

- Use of specific techniques of probability, statistics and mathematical models. Probability is used when making decisions that involve uncertainty or risk, and statistics are used when it is necessary to systematize the data.

- The organization is considered as a whole, not as just some department or section. Thanks to this, importance is given to all the parts together and not to any one in particular.

- Mainly seeks the optimization and improvement of operations in order to give solidity and security to the organization in the short, medium and long term.

- It is constantly updated, constantly incorporating new methods and techniques.

- It is based on the use of quantitative analysis.

- As its name implies, its main focus is directed towards the execution of tasks, including human and technological resources.

Phases of operations investigation

Operations investigation has the following defined steps:

Problem formulation

In this step, a review is made of the systems, the objectives set and the courses of action.

Construction of a mathematical model adjusted to the reality of the system under study

This model seeks to identify which are the variables related to the problem, and at least one is taken as an independent variable and subject to modification.

Determination of the model solution

The objective of this phase is to decide whether the solution of the model conforms to a numerical or analytical process.

Test of the selected model and presentation of the solution

Once the ideal model has been chosen, it is put into practice to generate possible solutions to the problem.

Control of the solution found

This control phase seeks to verify that the variables that could not be controlled within the model maintain their values. It is also checked that the relationship between the identified variables remains constant.

Implementation of the solution

It seeks to translate the solution obtained into concrete actions that can be formulated in the form of processes, which are easily understood and applicable by the personnel who will carry out the implementation.

Application areas

Mathematical theory can be applied in various areas of the organization. In the beginning it was conceived especially for the areas of logistics and material resources, but currently it is not limited to these scenarios.

Within the areas of application, we can highlight finance, labor relations, quality control, occupational safety, process optimization, market research, transportation, material handling, communication and distribution, among others..

Theories used in operations research

Probability and statistics

It makes it easy to obtain as much information as possible using existing data. It allows obtaining information similar to that provided by other methods, but with the use of little data. It is commonly used in situations where the data cannot be easily identified.

The use of statistics within the field of management, specifically in the area of ​​quality control in industry, is due to the physicist Walter A. Shewhart, who worked at Bell Telephone Laboratories during World War II.

Thanks to their contribution, William Edwards Deming and Joseph M. Juran laid the foundations for the study of quality, not only in products but in all areas of the organization through the use of statistical methods.

Graph theory

This theory has various applications, and is used to improve algorithms related to searches, processes and other flows that may be part of the dynamics of an organization.

As a consequence of this theory, network planning and programming techniques arose, which are widely used in civil construction.

Said techniques are based on the use of arrow diagrams that identify the critical path, directly relating costs and the time factor. As a result, the so-called "economic optimum" of the project is generated.

The optimal economic value is achieved through the execution of certain operational sequences, determining the best use of the available resources in an optimal period of time.

Theory of waiting queues

This theory applies directly to high flow and waiting conditions. He takes special care in the time factor, the service and the relationship with the client. The intention is to minimize service delays and use different mathematical models to solve these delays.

Queuing theory generally focuses on telephone communication problems, machinery damage, or high traffic flow.

Dynamic scheduling

When problems arise that have different phases that are interrelated, dynamic programming can be used. With this, an equal degree of importance is given to each of these phases.

Dynamic programming can be used when different alternatives appear, such as performing corrective maintenance (repairing), replacing (buying or manufacturing) some machine or equipment, or buying or renting some real estate.

Linear programming

The use of linear programming is mainly used when it is required to minimize costs and maximize profits.

Usually the projects that are managed through linear programming have a series of limitations that must be overcome in order to achieve the objectives that have been set.

Games theory

It was proposed by the mathematician Johan von Neumann in 1947. It consists of the use of some mathematical formulation to analyze problems that have been generated by the conflict of interest that arises between two or more people.

For this theory to be applied, one of these scenarios must be generated:

- There must not be an infinite number of participants, all must be identifiable.

- Those involved can only have a finite number of possible solutions.

- All the existing possibilities and actions must be within the reach of the participants.

- The "game" is clearly competitive.

- If one participant wins, another must automatically lose.

When all participants have selected their course of action, the game alone will determine the gains and losses that have arisen. Thus, all the results resulting from the chosen action routes will be calculable.

Authors

Among the most prominent authors of the mathematical school of administration are the following:

Herbert Alexander Simon

He was a political scientist, economist, and student of the social sciences. Simon's most representative contribution was to contribute significantly to the optimization of decision-making processes.

For him, economics is a science closely linked to elections; This was the reason why he devoted his studies mainly to decision making. In 1947 he wrote his most important work, entitled Administrative behavior: a study of decision-making processes in administrative organization.

Igor H. Ansoff

This economist and mathematician is known as the leading representative of strategic management. During his life he advised large companies such as General Electric, IBM and Philips, and also taught at various universities in Europe and the United States.

The field of study that he developed the most was that of strategic management, especially in real time, emphasizing the recognition and management of the environment in which a particular organization finds itself.

West Churchman

Churchman managed to link philosophy with science by focusing your work on the systems approach. For him, the objective of systems is to allow human beings to function in the most optimal way possible.

Systems, according to Churchman, are a group of tasks arranged in a certain way in order to meet certain goals. Some of his most prominent publications are Prediction and optimal decision and The systems approach.

Advantage

- Proposes the best techniques and tools for solving problems related to the executive area of ​​the organization.

- Provides another way of visualizing the reality of the problem through the use of mathematical language. In this way, it provides much more specific data than can be obtained from oral description alone.

- It facilitates the approach to problems in a systemic way, since it allows to identify all the related variables

- Allows the separation of problems into stages and phases.

- It uses logic and mathematical models, which allows obtaining objective results.

- Computers are used to process the information provided by mathematical models, which facilitates any type of calculation and speeds up the selection of the solution to the existing problem.

Disadvantages

- It is restricted only to use in execution and operation levels.

- There may be problems within the administration that cannot be solved by the theories proposed by operations research. It will not always be possible to reduce problems to quantitative numerical expressions.

- Mathematical theories are perfectly applicable to the specific problems of the organization; however, they do not have scalability towards general or global problems. This is mainly due to the impossibility of relating all the variables in a single set.

References

1. Morris Tanenbaum, Morris. "Operations Research" In Encyclopedia Britannica. Retrieved on August 1, 2019 in Encyclopedia Britannica: britannica.com
2. Sarmiento, Ignacio. "Administrative Thought" (2011) At the Autonomous University of the State of Hidalgo. Retrieved on August 1, 2019 at the Autonomous University of the State of Hidalgo: uaeh.edu.mx
3. Thomas, William. "History of OR: Useful history of operations research" In Informs. Retrieved on August 1, 2019 in Informs: informs.org
4. Guillen, Julio "Operations research, what it is, history and methodology" (2013) In GestioPolis. Retrieved on August 1, 2019 in GestioPolis: gestiopolis.com
5. Trejo, Saúl. «Mathematical theory of administration. Operations research »(2008) In GestioPolis. Retrieved on August 1, 2019 in GestioPolis: gestiopolis.com
6. Carro, Roberto. "Investigation of operations in administration" (2009) At the National University of Mar del Plata. Retrieved on August 1, 2019 at the National University of Mar del Plata: nulan.mdp.edu.ar
7. Millán, Ana. "The application of mathematics to management and organization problems: historical antecedents" (2003) In Dialnet. Retrieved on August 1, 2019 in Dialnet: dialnet.unirioja.es