The decisions we make at this time will have a future consequence, starting from this, and moving to the organizational field, this maintains a very close relationship with the ability to make decisions in complex situations and they have to do with the business exercise of all the organizations.
These decisions are very important as they require special skills and abilities on the part of those responsible for making them, since it has to be done quickly and effectively, and above all with the certainty that the best decision is being made.
During the investigation of this topic, we will be able to observe the importance of mathematical models that serve as the basis for complex decision-making processes in organizations.
Keywords:
- Logic Mathematics Decision Making Organizations Businesses Mathematical Models
LOGIC OF SIMPLE MATHEMATICAL MODELING AS A BASE ELEMENT IN COMPLEX DECISION MAKING
Development of logical thinking
Frequently, it is heard that logic represents a fundamental basis for the development of mathematics since we affirm that, in turn, mathematics allows a development of the logic of thought or of logical thinking, depending on the type of logic talked about.
If a formal logic is proposed, as it is traditionally known, where compliance with forms and rules give validity to conclusions, paths built through mathematics.
On the contrary, if a logic that supports mathematics is considered as a process of learning development, it is a dialectical logic, where the concepts seem contradictory and contradictory as well.
(Peñalva, 2010)
Development of logical thinking and problem solving
Some theories and schools have tried to explain how logical thinking works in problem solving application, this is how cognitive logic is found, historically it has provided certain useful results for these purposes, with two basic approaches such as: the theory of an associationist thought which emphasizes an element of the resolution chain and the gestalt theory, being one that is based on a structural understanding of a specific situation to be resolved.
Mathematics, essential in decision-making
The researcher known as Onesimo Hdez. Lerma, is the founder of the Stochastic Control Theory, in Mexico; has indicated that mathematics is essential for the decision-making process in our country.
He argued that a large part of economic decisions are based on forecasts, on analyzing statistical data and the most used tool for them is mathematics.
In a congress, of which he was part, he clearly said that everything that surrounds us is practically mathematical.
This theory proposed by the (Stochastic Control Theory) deals with a decision-making process, which precisely tries to control and create strategies to be able to influence a certain system.
By stochastic control, it means that you work with probabilistic problems also known as stochastic or random. Its main areas of application are: economy, engineering, finance, technology, population control, management of renewable and non-renewable resources, among others.
(El Universal, 2013)
Decisions based on mathematical models: the contribution of operations research
(González Martín, nd) Making decisions not only in companies, is one of the most defining characteristics of what human beings understand by what is called life. In a way, living is synonymous with being able to decide.
A undoubtedly important number of decisions, made by certain people, have a degree of transcendence since they not only affect the family or individual environment, but also have the ability to decisively influence collectivities in the environment, natural resources and society enjoys.
Many decisions, where different organizations and individuals are involved, acquire adequate guarantee indices when these are supported by objective training, which are normally expressed in quantitative data.
Quantitative decision support: the methods
Monochrome paradigm
In the original approach to a decision problem, it is assumed that the decision maker's preferences can be represented mathematically by a single function (objective function) which allows ordering the possible decisions, assigned to each one, a certain index of desirability, based on certain hypotheses on rationality expected by the decision maker.
Mathematical programming is the set of techniques with which Mathematics approaches the general study of optimization problems in a single-objective, static and single-decision-making framework.
Linear Programming has also proven to have an enormous variety of applications in economics and organizations, especially in the choice of techniques or production factors that allow obtaining a certain level of production with a minimum cost or maximum benefit. Together with input-output analysis and Game Theory, it could be considered among the antecedents of the so-called Linear Economy.
Game Theory or the analysis of conflict problems or strategy games constitute the methodological support of decision problems with more than one actor.
Group decision, voting, and social choice problems have this structure. They have been used in market situations where the behavior of each participant will depend on the actions of all the others.
Multi-criteria paradigm
It is normal and in a certain habitual way for human beings to make decisions about problems of a certain complexity that include several objectives, which may be totally or partially in conflict with each other, so that improvement in any of these could worsen the value of the other objectives that are evaluated according to multiple criteria and where the best or optimal alternative is not evident.
Too many problems of an economic nature are characterized by the fact that in choosing the best decision, several criteria have to be taken into account and, therefore, it is desired to achieve more than one objective.
Multiobjective programming and multi-criteria decision theory are responsible for solving problems of this type and therefore, there are many works in which this theory is applied to problems of an economic nature.
(Rodríguez-Uría, Bilbao Terol, Arenas Parra, & Pérez Gladish, sf)
Mathematical models
Based on what has already been developed, it is established that each problem requires its own solution either from one or different mathematical methods.
However, it is possible to appreciate trends between the methods, which allow to give an added value according to the problem they face. Some busier math models are:
Mathematical modeling techniques
There is an extensive amount of mathematical modeling resources and each of them are based on what you want to analyze.
Each model has its own characteristics and based on this, it also has specific factors immersed in the process.
Therefore, four levels of decision-making can be considered:
- Strategic Programming Planning Execution
Visualization technique
They consider those graphically based models by means of computers, they are prioritized in display models. Thus, they are designed correctly and adjusted to the needs for the decision-making process.
Mathematical optimization
It is commonly based on the algorithms for mathematical programming. Each of them are designed to meet the requirements, while the algebraic or differential can use some other type of programming based on specific needs.
Heuristics
Used for optimization and when the structure of the models is not appropriate, despite their restrictions, they can offer solutions that are useful when the mathematical algorithms are not known or known.
Expert systems
These systems seek to mount an existing system on top of another, based on advanced human knowledge. They require a large investment in time and money, since training is needed.
Analytics and data mining
The purpose of this is to obtain historical data for the creation of some models that support decision-making.
(López Ramos, 2015)
Use of mathematical models for decision making
Mathematical models and the decision-making process are not so far apart from each other after all, since both react accordingly to eventualities of organizations and companies to evaluate their performance.
It is very important that all organizations encourage from the decision-making process, regardless of the organization level, people who have a responsibility within the company for the use of mathematical modeling, allowing them to have the expected results.
Decision making is therefore a process that must be incorporated as an extra function in the management positions of an organization and must also be carried out with caution in order to determine the best and optimal decisions that will affect the entire organization.
conclusion
Companies, regardless of their turn or size, have a common factor for managers to carry out: make decisions, and although it seems to be a very common and even common issue, it must be taken seriously since that is everything. a process that requires attention and investment.
A small decision can set the direction of organizations, which is why an effective tool to apply it in these processes is mathematics through some specific fields such as linear programming or statistics.
In this way, the study of decision-making arises from the implementation of mathematical models, which provide a quantitative panorama of the current and real situation of the company, based on which, managers have the option of choose or make the decision that they consider most opportune or optimal.
Thesis topic proposal
Implementation of a mathematical logic model to improve the decision-making process of an organization.
General objective
Implement a mathematical logic model to improve the decision-making process within an organization in the Orizaba region.
A g r adequacy
To the National Technological Institute of Mexico for being my alma mater and to Dr. Fernando Aguirre y Hernández for their support and motivation to carry out these articles on the subject of Fundamentals of Administrative Engineering.
References
- The universal. (August 8, 2013). Retrieved on May 2, 2016, from: http://archivo.eluniversal.com.mx/ciencia/2013/matematicas-indispensables-toma-decisiones-79561.html González Martín, C. (sf). Decisions based on mathematical models: the contribution of operations research López Ramos, LA (November 12, 2015). Gestiopolis. Retrieved May 2, 2016, from: https://www.gestiopolis.com/modelacion-matematica-simple-para-la-toma-de-decisiones/Peñalva, L. (January 2010). Scielo.org. Retrieved May 2, 2016, from: http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S0188-77422010000100008Rodríguez-Uría, MV, Bilbao Terol, A., Arenas Parra, M., & Pérez Gladish, B. (sf). Mathematics as a support for decisions in economics and business.
