Abstract: This work contains an approach to mathematical logical reasoning as a judgment aid in decision-making and the situations in which its use intervenes. Currently technology and the world full of variants have forced the company to make use and development of software to quickly determine the parameters of organizational situations and obtain results closer to reality for making complex decisions.
1. INTRODUCTION
For an individual who is faced with decision-making, he goes through a certain uncertainty, having to choose an alternative within a set of possible actions, which is precise to handle and at the same time can evaluate information about very diverse factors. In this case we are in a constantly changing environment, in such a way that there is no decision that guarantees that the conditions remain the same; although those that are taken without prior analysis, at random, are more exposed than those that follow the appropriate process (Narro, 1996).
Decision making in companies is the essence of administration. Therefore, when it comes to planning, organizing, directing and controlling, managers are based on making a decision, which is one of the most important tasks they have to face. The evolution of the Economy and Business Management towards a great functional complexity and a high technology, have made the decision process require elements that can be reasoned through the construction of a model, which in turn has logical support and much more elaborate methodological, influencing courses of action and results (Rodríguez et al., 1999; Robbins & Coutler, 2005)
On the other hand, companies need to measure and use all statistical and mathematical tools, in order to control inputs, processes, products and effects on the environment, making the system more complex, as a consequence that decisions have greater complexity in the result to be obtained. Coupled with pressure because time disrupts the decision-making of a manager in a company. The data and knowledge that “modern” management makes available to information systems, which propose to measure everything within the company and in turn theoretically satisfy the dream of every rational decision-maker through them (Fiol, 2001; Hernández, 2006).
- DEVELOPING
Logic, models and decisions
The antecedents on rational decision making appear for the first time in ancient Greece (5th century BC) as their decision was based on the use of reasoning and logic. When defining the word "logic" it comes precisely from the Greek lakes and that according to Moro (1978) refers to the word or expression of thought, thus it can also be interpreted as the treatise, reason, expression, reason, intelligence, etc. Later in the arrival of the Renaissance, the concept of scientific decision-making emerged, and it continues to be studied and developed to this day. From the scientific administration, the need was found to create standards, units of measurement or production quantities, which is why a series of models arise whose representation either qualitative or quantitative of a system,show the predominant relationships between its elements; which must be quite detailed if the real problem is to be validly represented. The elements of a model are parameters, variables and functional relationships (Hernández, 2006; Casañ, 2012).
On the other hand, Rodríguez et al. (1999) decision models have two parts: an objective function and a set of one or more constraints. The objective function being an equation that has the following form:
System performance (P) = some relationship (f) between controlled variables (C) and uncontrolled variables (U)
Or P = f (C, U)
The controlled variables in this case are those that the decision maker can manipulate. The uncontrolled variables are those that are not subject to the control of the decision maker (s).
Mathematical model
When speaking of a mathematical model, a development consisting of six stages is taken into account, where, in the first stage, a description of the phenomenon is made, here the variables that intervene are raised, as well as the hypotheses of its behavior. Followed in the second stage that consists of raising the equations that mathematically describe the phenomenon (mathematical model), the boundary conditions and the variability of the solution. The third stage tends to select the method of solving the mathematical model, that is, the choice of the calculation algorithm. Subsequently, the fourth stage consists of programming the calculation algorithm for a computer. For the fifth stage, theCalibration, verification and validation of the model correspond and finally, the sixth stage requires the exploitation of the model, that is, the use of it based on field data, laboratory experiments or assumptions to obtain predictions (Rodríguez et al.., 1999)
In the case of the design of mathematical models for simulation, and in complex problems they can be cheaper, there is also a great variety of this type of models aimed at finding optimal solutions (mathematical programming) in the case of decision making.
Decision making
Currently, decision-making comprises a 7-stage process: defining the problem, identifying the alternatives, determining the criteria, evaluating the alternatives, choosing an option, implementing the decision, and evaluating the results (Casañ, 2012).
Decision-making is a common activity that is present and particularly in business management. Therefore, decision models are simply a means to an end, which will allow through their resolution to help decision-making by generating optimal solutions, or sufficiently close to the optimum, given an established objective. In the same way, they can be used to evaluate the impact of making decisions, before making them, and thus choose the one that best suits the solution (Loy and others, 2009; García & Maheut, 2015).
Commitment risk curve
When analyzing a decision in the company, the manager's preference to assume a risk is inversely proportional to the magnitude of the commitment, which involves the decision, so there is a commitment risk curve as shown in figure 1.
Curve - Risk - Compromise
Figure 1 represents the disposition of some people when making a commitment; on the risky curve, the commitment is much higher, with higher risk than the average individual would like. When the risk is considerably reduced; the curve is represented by those who are risk averse. While the personal curve represents most of us, it tends to accept high risk as long as the commitment is low. However, once the commitment increases to a point where a threat is seen due to its magnitude, it is desired to reduce the risk as much as possible (Rodríguez et al., 1999).
Decision classification
A good administrator has a theory and recognizes within practice that different problems require different solutions, depending on the circumstances, the time and the place. Decisions can be classified into: scheduled and unscheduled.
In particular, we will focus on programmed decisions that in turn are divided into decisions that are routine repetitive and those that are through processes established by the organization. Currently the techniques of the first division are directed to operations research, mathematical analysis and computer simulation models; the technique for the second division is the electronic data processing (Rodríguez et al., 1999).
In accordance with previously agreed rules, policies or procedures; the objective will be to facilitate decision-making, whether in recurring and common situations or vice versa within the business environment.
Complex decisions
According to the complexity of the organization itself, the direction of the decisions becomes more difficult, in this case it is not necessary to need to obtain a calculation based on how the real decision deviates towards the optimal one, but on the measure of the difficulty of determine the optimal behavior when making the decision (Wikipedia, 2015).
Cases of application of quantitative approaches
The reasons why a quantitative approach may be used in the decision-making process are:
- The problem is complex and therefore the manager does not reach a good solution without mathematical reasoning The problems are financial or extremely important in terms of profit, the manager needs a complete quantitative analysis to make the best solution The problem is repetitive and is use mathematical models to save time and effort,
Decisions and the mathematical school
So far we have observed that mathematics is highly recognized in decision-making, in the administrative issue we owe this to the school of quantitative measurement. The development of mathematical theory, Pascal's contributions to probability and calculus, as well as Gauss's bell, as well as the interest expressed by Gilbreth who insisted on the application of statistics to business administration, such as the control of variables, sales, production, staff assistance, quality and how we can observe customer satisfaction to date (Hernández, 2006).
Therefore, the application of mathematical logic and the scientific method to the resolution of administrative problems that can be expressed by mathematical models, in order to deduce, by means of algebraic equations, the questions raised. The division of operations research and decision making is described below.
Operations research
Operations research is defined as the application of the scientific method to the problems that arise in the operations of a system that can be represented, through a mathematical model, and the solution of these problems by solving equations that represent the system (business). Being the main applications of operations research, according to Hernández (2006):
- AlgebraCalculusStatisticsCorrelation and RegressionNOVAHeuristic MethodsNetwork Analysis TechniqueLogisticsMarkov Process ModelsDynamic ProgrammingLinear ProgrammingQueing Theory and Constraints TheoryTheory of ProbabilitiesSimulationAdministrative EconomicsProject Management (PERT / CPM)
The methods reported in the study reported by Forgionne (1983) are the ones that managers have applied most frequently:
Linear programming. It has a wide range of applications and this tool is used for practical problems of operation, project evaluation, cataloging, scheduling and allocation of resources, transportation, among others, in order to obtain a certain level of production with a minimum cost or maximum benefit (Hernández, 2006).
Theory of tails. Valuable tool for reaching decisions that require an optimal balance between the cost of the service and the cost of defections or loss of customers due to long waits for a service (payments, collections, purchases, etc.) (Hernández, 2006).
Simulation. It demonstrates and also proposes to discover the behavior of a system, hypotheses and theories are proposed that try to explain the observed behavior, these theories can be used to predict the future behavior of the system (González, 2007).
Econometrics. Through this model, economic variables are measured with the help of certain basic indicators, such as gross domestic product (GDP), economic growth rate, inflation rate, the price index and stock market quotes, the rate exchange rate and its trend, and the degree of country risk, fundamental data for strategic planning (SP), feasibility studies of companies' investment projects together with market research (Hernández, 2006).
Project management (PERT / CPM). A tool that helps managers fulfill responsibilities for projects that consist of numerous tasks or jobs.
However, the above are models whose linearity of the functions that intervene as well as the relationship that exists is very simple, so that it frequently agrees with the complicated reality. Such a condition is not consistent with frequent decision-making based on uncertainty phenomena (Narro, 1996).
Decision theory in operations research
The degree of complexity of the correct calculation of a risk, for companies or institutions that ensure the probability of an accident, for example, requires actuaries, specialists in mathematics who study calculations, risks and their repercussions on human activity within organizations. Today it has been shown that there have been errors in the calculations and consequences of the results. Based on the theory of probabilities, the decision-making techniqueIt starts from the premise that the more a problem is known, its causes and effects, the knowledge of the level of claims and the costs of its effects increases. This allows companies to calculate their decisions and increase their certainty in them, and, if it is worth it or the risk, start a new business. The businessman, being in an economy of supply and demand and knows that there are always risks (Hernández, 2006).
Multi-criteria paradigm
The complexity includes several objectives, which can be totally or partially conflicting with each other, a method that allows including various criteria to make a decision and at the same time its restrictions are less strict, in order to address the decision problems more Natural and flexible, it is the method of multi-criteria decision making (Casañ, 2012).
For example, you might consider selecting a better site for a plant station. The cost of the land and construction, this implies a series of criteria that lead to the most optimal option, coupled with whether the company wants to consider other criteria such as availability of infrastructure, transportation services, ease of hiring personnel, among others. Represents greater complexity. According to Roche and Vejo (2005) the methods can be applied:
- Scoring method Multicriteria analysis method as a hierarchical analysis process.
Both methods are based on the decision maker who must establish the relative importance of each of the objectives to define alternative preference structures.
3. CONCLUSION
Once the development of the topic is finished, as Masters in administrative engineering, we must consider the following:
The influence of mathematics as an application instrument in decision-making in managers has allowed the assessment of the conditions with respect to the situation of the company.
The logical reasoning, precision, abstraction and formalization of mathematical models seek an optimal solution, currently with the support of technology it is possible to obtain a series of software that allows developing models that bring us as close as possible to reality, it is known that the reasoning time that the situation demands of us these days is very short in relation to the decision-making of a manager. Therefore, disseminating mathematics and the contribution of models whose solution can be obtained in seconds is essential.
On the other hand, with the creation of models we increase the response speed, but let's not forget that the most important thing before the numerical result is the compression of the variables and the logical reasoning to apply it in order to make it the most optimal in relation to the situation of the organization. As well as, the result of the quantification is an auxiliary, in the end the decision that is made is based on the constructive analysis of the previous and post results of the operations and that there is also a small error of significance.
4. BIBLIOGRAPHY
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