Business decision making with multiple criteria

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* Introduction

* Theoretical and conceptual references

* Operations Research

* Main tools of Operations Research

* Making business decisions

* Decision making with multiple criteria

* Conclusions

* Bibliography


Companies are worried constantly make choices that enable them to optimize their performance so as to get the most benefit. This is why operations research is an important tool for management when taking any decision. It is necessary then the application of tools that support decision making in order to remove the strong degree of empiricism that present management. This article aims to apply the method of weighted average weights for responding to existing problems in a company, which facilitate and improve decision making. With the application of this tool multiattribute decide a proposed solution to a detected failure.

Keywords: decision making, operations research, multiple criteria.


In the current socioeconomic environment highly competitive and complex, traditional methods of decision making have become relatively ineffective and that those responsible for directing the activities of companies and institutions face complex and dynamic situations that require creative and practical solutions supported by a solid quantitative basis.

Companies are worried constantly make decisions that allow them to optimize their performance so as to get the most benefit. The evident difficulty of making these decisions has made the man to lead the search for a tool or method that allows you to make the best decisions based on available resources and the objectives

Tools for business decisions such as mathematical models have been applied to a wide range of situations in making decisions in various areas of management. At present it has increased the use of mathematical models to interpret and predict the dynamics and control in making management decisions. These applications include multi-criteria decisions, sales forecasts, predictions of the impact, effects of advertising campaigns, strategies to protect inventory shortage, to determine optimal investment strategies, portfolio, etc.

The objectives of any company should always be taking the lead in their field, controlling the efficiency and effectiveness of all its components using methods to find the best relationships that best operate the system, given a specific objective.

Given the rapid progress that has occurred in almost all the sciences in recent decades, is no longer feasible want to know a little of everything, but specialize in some branch of science. The problems that arise in organizations can not easily be resolved by a single specialist. On the contrary are disciplinary problems, the analysis and solution require the participation of several specialists. These interdisciplinary groups necessarily require a common language to understand and communicate, where operations research has to be that bridge of communication.

The focus of operations research is the same scientific method. In particular, the process begins with careful observation and the formulation of the problem and continues with the construction of a scientific model (usually mathematical) that attempts to abstract the essence of the real problem. At this point we propose the hypothesis that the model is sufficiently accurate representation of the essential characteristics of the situation so that the conclusions (solutions) obtained are also valid for the real problem. This hypothesis is verified and modified by appropriate tests.

So in a sense, Operations Research includes creative scientific research of the fundamental properties of operations. However, there is more than that. In particular, operations research also deals with the practical administration of the organization. Thus, to succeed, you must also provide positive and clear conclusions that can use the decision maker when needed.Cuban organizations, in particular, because of the urgent economic revival which is bound the country face new goals: to resist, survive and be competitive in the new environment. They must raise their levels of productivity, efficiency and profitability by what its members are questioning whether their companies are prepared to meet these goals under the new conditions, reflection that leads to the analysis and review of the same. Hence the importance of applying mathematical methods to make decisions in any area of the company.

The company under study is no exception as it has a high degree of empiricism in making decisions by its managers and employees leading to shortfalls in the performance of business functions, so it was considered appropriate to apply a model facilitate and improve decision making in the organization under study.

Theoretical and conceptual references

Between the theoretical aspects considered relevant for this work, highlighting the analysis of operations research, models and tools for implementation, as well as business decisions especially multiple criteria. These will be discussed below.

Operations Research

There are many definitions offered on operations research, the following referenced in Delgado Landa (2008), are a useful basis for an initial understanding of the nature of OR [1]

Mores-Kimball (1943): Scientific method by which executive management has a quantitative basis for decisions on operations under their control.

Ackoff, Sasieni (1968): The application of scientific method by interdisciplinary teams to problems involving the control of organized systems (man and machine) to provide solutions that best meet the purpose of the organization as a whole.

Wagner (1969): Scientific approach to the solution of problems in executive management.)

Hiller, Lieberman (1974): Making optimal decisions, and modeling, deterministic and probabilistic systems that originate in real life. These applications in government, business, engineering, economics and natural and social sciences are characterized mainly by the need to distribute limited resources. In these situations, scientific analysis, such as provided by the IO, can provide important information.

Gross (1979). Branch of applied mathematics to the process of decision making.

Hillier, Lieberman, Shamblin, Stevens, Taha, Tierauf, Grosse, Sasieni, to mention some of the great specialists in operations research (OR), give a series of definitions that might be summarized as:

It is a scientific approach to decision making. You could say that the IO using a planned approach (scientific method) and an interdisciplinary group to represent, by symbolic models, the functional relationships that exist in reality, which provides a quantitative basis for decision making. Applies tools that seek to obtain the optimal result of the use of scarce resources.

Generalizing Operations Research is the application of scientific method by a multidisciplinary group of people with a problem, mainly related to the efficient distribution of limited resources (money, raw materials, labor, energy), which is based on the approach systems (this approach is that in which a group of people with different areas of knowledge, discuss how to solve a problem in group). Can be considered both an art and a science. As art reflects the efficient and limited concepts of a mathematical model defined for a given situation. As science understands the deduction calculation methods to solve the models.

Features which denote actions that can perform this science can be summarized as:

* Operations Research uses the scientific method to investigate the problem at hand. In particular, the process begins with careful observation and the formulation of the problem including the collection of relevant data.

* Operations Research takes an organizational standpoint. In this way attempts to resolve conflicts of interest among members of the organization so that the result is the best for the entire organization.

* Operations Research tries to find a better solution (so-called optimal solution), for the problem under consideration. Instead of being content with improving the state of things, the goal is to identify the best course of action.

* The Operations Research is necessary to use the team approach. This team should include staff with strong backgrounds in mathematics, statistics and probability theory, economics, business administration, computer science, engineering, etc. The team also needs to have the experience and skills to enable proper consideration of all the ramifications of the problem.

* Operations Research has developed a series of techniques and models useful to engineering systems. These include: linear programming, queuing theory, integer programming, dynamic programming.

* Operations Research tends to represent the problem in order to quantitatively analyze and evaluate a common approach.

Main tools of Operations Research

When speaking of IO tools, refers to the different theoretical models (eg, transport models and queuing theory), and other disciplines (such as mathematics, management, economics, etc.) that are used as working tools professional standard for Operations Research. It should be clear, however, that each day there are more types of models and other disciplines.

Below in Table 1 presents a non-exhaustive list of different types of models that could be considered as tools of operations research.

Table 1. Main tools of operations research. Source: Delgado Landa (2008).

Similarly Operations Research is concerned, she as a tool for other disciplines. It is well known that the Business Administration has been benefiting greatly from the Operations Research now has started a revolution with the use of Strategic Planning, Reengineering and Total Quality programs, to name a few.

Given that models are tools within the IO is necessary to understand that: a decision model should be considered as a vehicle for summarizing a decision problem in a way that enables the identification and systematic evaluation of all the decision alternatives the problem. After a decision is reached by selecting the alternative that is deemed the best among all available options.

A solution to a model, however, if accurate, will not be useful unless the model itself provides an adequate representation of the real decision situation.

The decision model should contain three elements:

* Alternative decision, which makes a selection.

* Restrictions to exclude unfeasible alternatives.

* Criteria for evaluating and ranking feasible alternatives.

Business Decisions

Decision making is the process by which a choice is made among the alternatives or ways to solve different life situations, these can occur in different contexts: sentimental family at work, that is, at any time making decisions The difference between each of these is the process or the way in which they are reached. Basically consists in choosing among the available alternatives, in order to solve a current problem or potential (although not a potential conflict becomes apparent.)

Decision making is also considered as the creative act of choice, from a set of possible decisions, in which quantitative factors are combined with heuristic capabilities of the men who make the decisions [2]

To make a decision no matter what their nature is necessary to know, understand, analyze a problem, in order to resolve it, in some cases be as simple and everyday, this is done implicitly and solved very quickly, but other cases in which the consequences of a bad or good choice may have implications for life and if in a work context on the success or failure of the company, for which it is necessary to conduct a more structured process that can give more security and information to solve the problem.

It is important for decision making through a good sense indicates that a problem or situation is deeply valued and considered to choose the best way forward under the different alternatives and operations.

In making decisions, consider a problem and reach a valid conclusion, it means you have considered all alternatives and that choice was correct.

Decision making with multiple criteria

At present there are many mathematical tools suitable to be used to aid decision making with multiple criteria.

In making decisions with multiple criteria attribute the term refers to the characteristics that describe each of the available alternatives in a decision situation, this concept refers to values related to an objective reality.

For its part the criteria are attributes, objective or goals that are considered relevant to a decisional problem. From a general standpoint, Zeleny (1982) defines the criteria and measures, rules and standards that guide the decision. Therefore, the multicriteria decision theory provides a general framework or paradigm underlying decision-making in different attributes, objectives or goals.

Several authors have described, as a general rule, a decision process with multiple criteria, noting the different parts and phases. Among these authors are mentioned Zeleny (1982), Chankong and Haimes (1983) and Goicoechea, Hansen and Duckstein (1982), which have represented a source of reference in developing the algorithm steps of the process of multi-criteria decision .

Multicriteria methods are identified with problems where the number of alternatives to be considered by the central decision maker is finite and usually not very high. The practical interest of discrete multicriteria problems (multi-attribute) is evident. In fact, there are many decisional contexts in which a small number of alternatives or possible choices should be evaluated based on several attributes or criteria.

One of the most competitive approaches and analysis for decision making is the Operations Research; Since this is an important tool for management and operations.

It is important when making decisions require a set of actions to decide between the alternatives admittedly. First you must determine the need for a decision that is generated by a problem or a gap between desired and actual current status. Then you need to identify the decision criteria and assign weight to these criteria to prioritize the most important first in the decision. Later we proceed to develop all the alternatives or possible solutions to the problem and although it is not possible in most cases know all the ways you can take to solve the problem, the more alternatives are going to be much more likely find one that is successful. Evaluate each of the alternatives would be further action in this process or make a detailed study of each of the possible solutions individually regarding the decision criteria. There are tools, in particular for Business Administration to evaluate different alternatives, which includes operations research. Finally we proceed to select the best alternative (decision making): After selecting the best alternative to reach the end of the process of decision making. From this it is necessary to implement the decision to assess whether the decision was correct or not and evaluate the results.

Proposal to support decision making with multiple criteria.

One of the IO models are in multicriteria techniques which are multiattribute models (Figure 1).

SHAPE \ * MERGEFORMAT Figure 1 Classification of multicriteria problems. Source: Delgado Landa (2008).

For the development of this research is of interest only multiattribute techniques, within which presents the method of weighted average weights (Table 2).


A = alternatives.

C = decision criteria.

rij = value of alternative j according to criterion i

Wi = weight of criterion i

Sj = the expected value for alternative j

Table 2. Matrix array weights method of weighted averages. Source: Delgado Landa (2008).

This method provides a quick and easy to identify the preferred alternative in a multi-criteria decision problem. Table 3 summarizes the steps for the implementation of this modelo.Cuadro 3. Steps to apply the method of weighted average weight. Source: Delgado Landa (2008).

Table 3. Steps to apply the method of weighted average weight. Source: Delgado Landa (2008).

Procedure for applying the model multiattribute weights weighted averages.

It is necessary to explain every step, including techniques used to develop this model:

* 1. Identify the problem to solve: Find the problem and recognize that they must make a decision to reach this solution.

* 2. Identify decision alternatives: look what are the alternatives to the decision.

* 3. Identify criteria used in making the decision: To determine these criteria there are several techniques that can be used for this case we propose to use brainstorming, which is explained below.

Brainstorming is a group work tool that facilitates the emergence of new ideas on an issue or problem. It is a method that is used when the information source is the people and can be applied to-face, blended or face.

It is a particular type of group meeting whose sole purpose is to create ideas. Brainstorming is different from a group meeting because this meeting is only open to experts, that is very knowledgeable about the topic.

How to apply

* 1. Define the issue or problem.

* 2. Ideas are emitted freely (without drawing any conclusions at this stage).

* 3. We listed ideas.

* 4. We analyze, evaluate and organize them.

The main objective of the application of this technique is to get as many ideas as possible and not its quality.

Teams often use brainstorming as a tool to build consensus, and in situations where they need to generate a large number of ideas.

Key steps of brainstorming:

Step No.1: Start of the session.

* Set a time limit for the session, usually 30 minutes is sufficient.

* Designate one or more registrars, whose task is to write down all the ideas to be issued, where everyone can see them, as these are set.

* Set the rules:

* A. Do not modify what is said and refrain from criticizing ideas.

* B. Try to generate as many ideas as possible.

* C. Develop a process of reduction then, weighing.

* D. Encourage wild ideas or exaggerated.

* E. Build on the ideas of others.

Step No. 2: Determine the method to use storm idea.

Types of brainstorming:


* Team members set out all the ideas as they occur to him.

* The ideas are listed as they are issued.


* Each will take turns broadcasting their ideas.

* Anyone can “pass” when their turn comes.

* Continue until you generate more ideas.

* All ideas are listed as they are issued.

After completing the brainstorming session:

* Prioritize the ideas of how to help you decide where to start.

* When you find yourself confronted with large amounts of information, classify them according to common themes.

* You may need to collect data to support or test ideas.


The storm, or rain, of ideas has a number of features that make it very useful when trying to obtain a large number of ideas on possible causes of a problem, actions to take, or any other issue. An added observation is that this method is input, or upstream, for other analysis techniques.

Stimulate creativity with ideas helping to break old stereotypes. Produces a wide range of ideas. A component of the group are encouraged to express ideas that come to mind without any bias or criticism. Facilitates the involvement of all team members. It builds an environment that enables everyone involved and reduces the likelihood of conflict. Allows the proliferation of a number of ideas that are made synthetically. Ensures that the success of the ideas does not depend on the brilliance of the same exposure. Crystallizes the opinions of the group, balancing participation. Allows the team to quickly reach a consensus.

* 4. Standardization of the criteria matrix.

Although not always necessary, in many multicriteria methods is essential to proceed with the normalization of the different criteria into consideration. It should be noted that most of the decision context in which units are measured different criteria are often very different. Moreover, in many multicriteria problems, the values achievable by different criteria may be dissimilar. In such cases, without prior standardization of these methods applied may lead to biased solutions to the largest achievable value criteria.

The procedures of standardization of criteria may be several, one of the most used in practice is the transformation method to scale. Is to divide the values reached the criterion for its value “better.” Depending on what attribute the criterion formula:

Criterion of maximum: minimum criteria:

r = Equation.3 EMBED EMBED EMBED Equation.3 Equation.3 r = 1 – Equation.3 EMBED

Once normalized the matrix can move to the next step.

* 5. Assign weight to each criterion according to the degree of importance.

The relevant criteria in a decisional problem may have different importance for the super expert or expert groups. This means that in many decisional problems is necessary to obtain some money or indicators of the relative preferences of the expert by some criteria over others. It should be noted that as the task of standardizing criteria are exclusively technical information for the estimation of relative priorities involves a strong subjective which makes it necessary to estimate these weights preferential selection of experts is rigorous. To perform this step can employ various techniques in which he proposes the procedures suggested by Saaty [3] which is the basis of the methodology known multi Analytical Hierarchy Process (AHP). This procedure requires experts for simultaneous comparison of only two objectives, ie a comparison of subjective values by “partners.”

The numerical values proposed by applying Saaty (Table 4) are as follows: (1) when the criteria are of equal importance, (3) moderate importance of one criterion over another, (5) strong importance; (7) demonstrated importance, and (9) extremely important.

Furthermore, Saaty suggests intermediate values for adjacent value judgments. Experience indicates that a scale of 9 units is reasonable and reflects the degree to which one can discriminate the intensity of relationships between elements.

Table 4. Scale to define the degree of preference. Source: Delgado Landa (2008).

It is interesting to note that, by its very construction, these matrices have reciprocal properties (ie Equation.3 EMBED EMBED EMBED Equation.3 = Equation.3).

* 6. Calculate the expected value for each alternative

This is just the weighted sum of each criterion would be the sum of each weight by multiplying the standard value previously, led to a mathematical expression is:

Max S = EMBED Equation.3 Equation.3 EMBED

* 7. Select the highest expected value alternative

Finally, select the alternative with the highest value obtained in the previous step.

Implementation of the proposal developed in the Company X.

Characterization of the Company.

The Company’s mission: “To produce wheat flour and cereals for breakfast, frying Pellets Corn curls, sorbets, breads and assorted pastries, a high quality and efficiency to meet customer needs.

The company’s overall goal: Make the process of Molinacion of wheat for the production and wholesale trade in both currencies, Wheat for human and animal consumption as well as produce corn and wheat cereals for breakfast, flavored, natural, and frying pellets, straws, breads and pastries, in both currencies.

Description of the problem to be solved in the entity under study.

The Company has reported several weaknesses in the production of different products manufactured in the cereal plant. At present it is not possible to resolve all and want to know which of their productions focus to ensure the stability of at least one of them. Thus is defined as a problem: Deciding the three types of productions that are made in the cereal plant, in which to focus efforts to achieve stable production.

To solve the above problems of the techniques used in the method multiattribute weights weighted averages. The application of this model indicate the recommended alternative production for the company.

* Identify the problem to be solved

Decide on the three types of productions that are made in the cereal plant, on which to focus efforts to achieve stable production.

* Identify the decision alternatives

You must decide which alternative is most suitable production for the company, of the three possible:

* 1. Produce Pellets

* 2. Produce Chips

* 3. Produce Rizos

* Determine criteria used in decision making

It is extremely important to correctly identify the criteria to be considered for analysis. To determine these criteria are used to brainstorm. Which concluded the attributes or criteria to evaluate alternatives.

The decision criteria are:

* Gain ($)

* Employment (number of workers)

* Nutritional level

* Stability of production

* Degree of solution

In the case of winning the company’s objective is to consider the product that brings maximum benefit. In turn it also imports the product you require more workers employed, it is objective from the standpoint of maintaining social workers to a large group of people, knowing that after stopping the production of these switches is personal. Moreover, the nutritional status is of great importance when deciding which product to produce, because the higher the nutritional value of the product, the better for personal consumption. With regard to stability in the production of each product, is more feasible to produce that product in which the production is the most stable.

The degree of solution refers to the real possibilities and objective to resolve the various shortcomings in each of the productions. Clearly it is important to determine to what extent can solve the production problems that exist in the cereal plant, referred specifically to the use of machinery for working with Italian technology. This limitation is considered a barrier to productive stability. The production holds greater solution, of course will be most convenient to carry out. It is important to realize that all criteria are maximum.

Data from the previously described criteria necessary to implement this method appear in Table 5. Sometimes it is extremely difficult to obtain such data, which is why it is necessary to explain how to obtain them.

Table 5. Details of the decision problem. Source: Delgado Landa (2008).

To obtain the results of the annual average gain was necessary to consult the income statements of the company under study in different years. We calculated the average annual income of each commodity over a period of 5 years.

In the case of the number of workers required for production of various products was obtained from the human resources department, in consultation with the workforce that uses cereal plant.

Regarding the nutritional status of each product were consulted in the laboratory quality of different ingredients contained therein, as well as nutritional information, vitamins and minerals they have. The experts ranked each product at its discretion on a scale of 1 to 5, with 5 being the highest nutritional product.

To learn how stability in the production of each of the three products it became necessary to implement a survey to a group of 7 employees of the company were considered as experts, and the same are mentioned below:

* Technical Director for Quality and Development.

* Specialist company quality.

* Director of the BSU [4] Cereals.

* Two shift leaders Cereals BSU.

* Cereal Technologist BSU.

* Head of the brigade Cereals UEB container.

To determine the degree of solution to the various inadequacies present in the production of three products in question, a survey of experts mentioned above.

* Normalize the matrix of criteria

Given that data are not homogeneous criteria is necessary then normalize (Table 6), using the transformation method to scale. The formula to be used when the criterion is maximum is

r = EMBED Equation.3 Equation.3 EMBED

Table 6 shows the matrix of standardized criteria.

Table 6. Standardized criteria matrix. Source: Delgado Landa (2008).

* Assign weight to each criterion according to the degree of importance.

It is necessary to establish the degree of importance of each criterion for that will be used Saaty matrix. To make this matrix requires joint expert group who reached a consensus made judgments on the degree of preference between a criterion and another. Table 7 shows the results.

Table 7 Results of the degree of importance of each criterion. Source: Delgado Landa (2008).

* Calculate the expected value for each alternative

The expected value for each alternative is shown in Table 8. Their calculation using the following formula:

Max S = EMBED Equation.3 Equation.3 EMBED

Table 8. Results of the expected value for each alternative. Source: Delgado Landa (2008).

* Select the highest expected value alternative

As shown in the table above the alternative that has greater expected value and therefore should be chosen which is to produce pellets.

This solution provides the company the best option, provided it does not change the decision criteria.


The development of this research embodied in the theoretical and conceptual exposed, and their practical validation, can draw the following conclusions:

Decision making is essentially the choice of one of the possible solutions to a problem or potential, which previously required the detection of the problem under study and to seek internal and external information is required. Subsequently, the decision must be converted into concrete action.

The multi-criteria decision theory provides a general framework or paradigm in the underlying decisional criteria (attributes, objectives or goals).

Operations Research provides a quantitative basis for decision-makers to select the best decisions and enhance skills can make future plans.

Operations Research uses the scientific method to implement tools that seek to obtain the optimal result of the use of scarce resources and solve problems dissimilar business context.

The application of the weighted average weights indicates that the alternative of producing pellets is most recommended for the company under study.


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Ms. Adriana Delgado Landa

Negrin Dr.C Ernesto Sosa

Universidad de Matanzas Camilo Cienfuegos, Varadero Carretera

[1] Operations Research

[2] Lerner, V. S, Trujaiev, R. I (1974): Dynamic models of decision-making processes. Kishiniev.

[3] Thomas L. Saaty

[4] Business Unit Base