Quantitative Analysis for Business

Managers are frequently faced with complex decisions that need to be made. These decisions often have far-reaching impact on the profitability of the organization as well as the decision maker's career. Therefore, it is essential that the decision maker be given the best information available to aid in the process. A range of quantitative techniques are available for helping the decision maker in this task. Mathematical or computer models can help quantify the variables in the situation under consideration as well as the probabilities of the various outcomes. Model building tends to be an iterative process in the search to develop a model that realistically represents the real world situation. Quantitative analysis is only part of the equation, however. The decision maker must also use his/her expertise and experience in interpreting the results of the analysis. In addition, the worth of the decision aid depends on a number of factors both controllable and uncontrollable.

Every day, business managers are required to make decisions that can affect their organization, their industry, and their careers. Sometimes these decisions are sound and aid the parties affected. Sometimes, however, these decisions are not sound and embarrass or harm the parties involved. Brown cites several examples of business decisions gone awry. For example, a $4 million probabilistic risk assessment of a nuclear reactor indicated that the facility was safe. However, inspection by a regulator indicated the opposite and the facility was put on a watch list. The results of a transportation study led a vehicle manufacturer to close three parts depots. It soon became evident, however, that the remaining depots could not handle the demand for parts and the three depots had to be reopened. On the other hand, an award-winning decision analysis indicated three nuclear waste sites should be studied further by the Department of Energy. The Secretary ignored the analysis and picked three other sites for study and was widely criticized for his efforts.

Complex Nature of Real-World Business Decisions

These examples illustrate that the decisions that managers need to make often not only have far-reaching effects but can be quite complicated. As opposed to the problems in the back of a textbook, real-world problems are typically very complex and require the consideration of multiple variables, some of which may not seem important to the casual observer and some of which might even be unknown. Even when the variables are known, their values may not be known and multiple possible inputs need to be considered. In addition, the answers to real world problems are typically not black and white; there are many possible answers and frequently none of them is perfect. The decision maker must pick and choose among them in order to optimize the effectiveness of the alternative chosen. One of the objectives of quantitative analysis is to give decision makers tools to support them in this process. There are several disciplines that approach decision making using quantitative tools and techniques, including operations research, decision analysis, and mathematical modeling.

Part of the reason that business decisions can be so complex is that the organization does not act in isolation: it is affected by both internal and external factors. To make an effective decision, the decision maker needs to take all these factors into account. Business theorists refer to this approach as systems theory. This approach assumes that the organization comprises multiple subsystems and that the functioning of each affects both the functioning of the others as well as of the organization as a whole. In addition, the organization itself is part of a larger system whose component parts (e.g., the total economy, the political environment, the supply chain) affect it. As part of this greater system, the organization depends on inputs of raw materials, human resources, and capital in order to do its work as well as exports of goods or services, employee behavior, and capital to other parts of the system.

Decision Theory

In general, decision theory is a body of knowledge and related analytical techniques designed to give the decision maker information about a situation or system and the consequences of alternative actions in order to help him/her choose among the set of alternatives. One of the primary tools of decision making is model building. The basis of much quantitative analysis work in support of decision making involves the development of models. Models are representations of a situation, system, or subsystem. Conceptual models are mental images that describe the situation or system. Conceptual models are the first step in creating mathematical or computer models that represent the situation or system using one or a series of mathematical equations. The development of a model that accurately represents the situation or system is often an iterative process. Models typically must be tested and refined until they represent the real world to the degree desired by the analyst or decision maker. Initial conceptual models tend to be broad or general representations without much detail but which span the range of variables to be considered. The initial model helps the analyst better understand the situation or system under consideration and to refine the representation of the real world. As the model is analyzed and more information about the situation or system is known and understood, the model can be refined to better reflect the underlying reality. When enough information is known, data can be gathered and quantitative techniques used to turn the conceptual model into a mathematical model.

The use of models is particularly helpful for making business decisions in complex situations that cannot be solved intuitively. Models create a representation that the decision maker can examine and manipulate to include relevant variables and relationships in the decision making process. However, a model needs to be validated at each step to determine how well it reflects the real world situation. It can be consequently adjusted as necessary and revalidated in order to optimize its use in decision making. After a satisfactory, validated model has been developed, a decision can be made and implemented. This process is illustrated in Figure 1.

Categories of Business Decisions

The decisions facing managers in the business world can be classified into several categories. Decisions may be made under certainty or uncertainty, under risk, or even under conflict. A decision made under certainty means that all the facts of the situation are known and the model provides the decision maker with the exact consequences of choosing each alternative. This situation, however, does not mean that the decision is obvious or trivial. There may be many possible courses of action that can be taken, and the decision maker needs to consider the advantages and disadvantages of each and weigh them against each other.

Decisions made under uncertainty, on the other hand, are decisions for which there is no meaningful probability distribution for the various outcomes. In such situations, the decision maker simply does not know what will happen for the various decision alternatives.

Decisions made under risk are decisions in which there is a meaningful probability distribution that governs the outcomes. These are decisions for which the outcome is not certain but for which probabilities can be assigned to the possible occurrences (i.e., the process is stochastic in nature). For example, if one flips a coin and calls heads or tails, by the laws of probability, the probability of winning the toss is 0.5. This situation can also apply in business settings. For example, one may not know how high the demand for a widget would be at various prices. However, a series of probability statements could be developed to describe the possible prices. This approach to decision making is frequently used in setting production and inventory policy, developing marketing strategies, and other decisions in the business world.

Decisions made under certainty, uncertainty, and risk assume that there is only one decision maker. Often, however, this is not true in business setting. An entire board of trustees, for example, may have to come to a consensus to reach a decision. Or, the actions of nature (e.g., when drilling for oil) or a thinking opponent (e.g., a business competitor) may need to be taken into account.

Model Use & Selection

As observed above, model building tends to be an iterative process. However, this does not mean that the analyst is trying to build a model that accounts for every variable that has the slightest effect on the outcome of the situation. Rather, models are meant to be simplified representations of the empirical situation. The ideal model strips the real-world situation down to its essential components and offers an elegant solution. This approach has the advantages of being more easily understood and more quickly and effectively modified than would more complex models.

The selection of the most appropriate type of model to represent a real-world situation depends to a large extent on the nature of the variables to be considered. If the variables can be measured and quantified in some way, it is often best to build a mathematical model. This approach to modeling helps the analyst approach the problem in an orderly way and to specify what assumptions are being made. In addition, mathematics is a powerful tool for relating variables in a logical way and enabling the analyst and decision maker to draw rational conclusions from the data. Mathematics also allows the building of models that represent complex situations and the specification of relationships more easily than can conceptual models.

Criteria Used for Decision Making

There are a number of possible criteria on which a business decision can be made. One approach is to maximize the maximum possible profit (the maximax rule). However, this approach is seldom used for a number of reasons. Although the potential for profit is maximized, this approach also ignores both the probabilities of possible loss as well as the probability of not making a profit. Although the maximax rule may have appeal on occasion, it does not lead to long-term success. Another criterion that can be used in making business decisions is assuming that the events are equally likely. However, this is seldom the case in actuality, and business analysts and managers often have some idea of the different probabilities associated with the various events under consideration. To assume that the events are equally likely to occur, therefore, is to not have a realistic model. If an estimate can be made about the probability of the events, it is better to use that than to assume that the events are equally likely. Another approach to decision making is the minimax rule, in which one chooses the option that offers the minimum maximum loss (i.e., that the chosen option would not result in a loss of greater than $X) or the maximum minimum profit (i.e., that the chosen option would earn at least $Y in profit). One could also make a decision based on the profits associated with the event that has the highest probability of occurring. For example, if one knows that there will be an order for a dozen widgets but does not know how many other widgets might be ordered, only 12 widgets would be produced to satisfy the known demand (i.e., with the 1.0 probability).

Bayes Decision Rule

Although each of these approaches has its place, a better approach to making a decision is to apply the Bayes decision rule. In this procedure, one multiplies the consequences of each act by the probability of the several occurrences, and then adds the products together. The option with the largest expected value is the most desirable decision. In essence, this strategy has one choose the option for which the expected payoff is greatest. Application of the Bayes decision rule allows a decision to be made that is consistent with the decision maker's beliefs even if there are not objective probabilities that can be applied. One of the advantages of this procedure is that it focuses attention on all possible events and requires the analyst to calculate the consequences of each act in each state. For those situations where cost or profit is a linear function, it is possible to simplify the Bayes decision computations.

Limitations to Statistical Methods & Mathematical Modeling

Although statistical methods and mathematical modeling are less prone to bias than are judgments and also tend to be more reliable and are better able to account for and efficiently use data, they do have their limitations. They can only work with the data given and cannot incorporate or quantify experience or expert opinions in the same way as a human. Judgmental decision making, on the other hand, is useful when there are recent events about which the decision maker is aware but which have not yet had sufficient time to result in observable data in a time series. Judgments also allow one to include information about events that have happened in the past but are not expected to recur in the future or events that will affect the future but have not occurred in the past (e.g., the effect of an innovation on the marketplace; governmental or industry policy changes). However, judgmental-only forecasts have disadvantages. Human error can result in models that are more optimistic (or pessimistic) than actually warranted, allow trends or factors that are not actually there to be read into the data, or that do not take into account the effects of correlated variables. It is often helpful, therefore, to combine quantitative methods with expert opinion. The best way to make complex decisions is often to form a team between the quantitative analyst and the expert decision maker. The combination of these two sources of input and types of analysis often work together synergistically to yield a better decision than either approach could have alone.

Applications

Although the use of statistics can support managers in making business decisions, statistics are, in the end, merely tools. Statistics can help one better understand the world by organizing and quantifying data and by analyzing them to see patterns and trends. This information, in turn, can be used to forecast future needs, shape the direction in which a business should grow, and help decide the best way to remain competitive in a changing marketplace. However, in the end, statistics are merely numbers: it is not the numbers themselves but their interpretation that shapes business decisions.

Once one introduces the human element into the pristine mathematics of statistics, reality is altered. It is the human being who determines what statistical methods to use. If the method is incorrectly chosen, the resultant statistics will be meaningless or misleading. It is the human being who determines which data are important and which are not. If the data set is not chosen appropriately, the mathematical answer may apply only in artificial cases not seen in the real world or may not adequately explain observable behavior.

Factors that Affect the Decision Making Process

As discussed at the beginning of this article, decision aids are not always successful. As shown in Figure 2, this can be attributable to a number of factors. Controllable factors in the decision aiding process (box 1) include the choice of the person developing the aid (e.g., his/her qualifications and expertise in developing decision aids), what incentives this person has for developing the aid (e.g., an already overworked analyst with higher priority tasks is not necessarily going to do the best possible job), and the degree to which the decision maker is involved in the development process for the decision aid (i.e., the decision maker typically has knowledge about the situation that can be invaluable to the analyst in developing a model that realistically represents the real world). In addition, there are uncontrollable factors (box 0) such as the tools and techniques available for developing the decision aid (i.e., the state-of-the-art in quantitative decision making continues to evolve) and the training and experience of the decision maker in how the aid can distort the aider's priorities (box 2). These all can affect the overall usefulness of the model or other decision aid. This, in turn, can result in a situation where the essential information for building a useful decision making aid are not gathered (box 3). For example, if the situation is not well-communicated to the decision aid developer, if the developer decides for some reason not to use all the knowledge available about the situation or does not receive all the necessary information, if the development and structure of the aid are not sound, or the results of the aid are not well communicated, the usefulness of the decision making aid is negatively affected (box 4). As a result, the aid will not enable decision makers to make sound decisions or give them a clear rationale for making decisions. When the utility of the decision aid is affected in this way, it will not be -- nor should it be -- well used or accepted either by the decision maker or by the organization (box 5).

Terms & Concepts

Bayes Decision Rule: A decision making strategy in which one chooses the option with the largest expected payoff. This is determined by multiplying the consequences of each act by the probability of the several occurrences and then adding the products together.

Data: (sing. datum) In statistics, data are quantifiable observations or measurements that are used as the basis of scientific research.

Decision Analysis: A collection of procedures, methods, and tools used to identify, represent, and assess the important aspects of a decision being considered in a decision-making process.

Decision Theory: A body of knowledge and related analytical techniques designed to give a decision maker information about a situation or system and the consequences of alternative actions in order to help choose among the set of alternatives.

Model: A representation of a situation, system, or subsystem. Conceptual models are mental images that describe the situation or system. Mathematical or computer models are mathematical representations of the system or situation being studied.

Operations Research: An analytical method of problem solving and decision making in which problems are broken down into basic components and solved using mathematical analysis.

Stochastic: Involving chance or probability. Stochastic variables are random or have an element of chance or probability associated with their occurrence.

Systems Theory: A cornerstone of organizational behavior theory that assumes that the organization comprises multiple subsystems and that the functioning of each affects both the functioning of the others and the organization as a whole.

Variable: An object in a research study that can have more than one value. Independent variables are stimuli that are manipulated in order to determine their effect on the dependent variables (response). Extraneous variables are variables that affect the response but that are not related to the question under investigation in the study.

Bibliography

Armstrong, J. S. & Collopy, F. (1998). Integration of statistical methods and judgment for time series forecasting: Principles from empirical research. In Wright, G. & Goodwin, P. (Eds.). Forecasting with Judgment. New York: John Wiley & Sons.

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Plane, D. R. & Kochenberger, G. A. (1972). Operations research for managerial decisions. Homewood, IL: Richard D. Irwin.

Vaitkevicius, S., & Kazokiene, L. (2013). The quantitative content processing methodology: Coding of narratives and their statistical analysis. Engineering Economics, 24 (1), 28-35. Retrieved November 20, 2013 from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=86234877&site=ehost-live

Venkatesh, V., Brown, S. A., & Bala, H. (2013). Bridging the qualitative-quantitative divide: guidelines for conducting mixed methods research in information systems. MIS Quarterly, 37 (1), 21-54. Retrieved November 20, 2013 from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=85634550&site=ehost-live

Suggested Reading

Bonvicini, S., Ganapini, S., Spadoni, G., & Cozzani, V. (2012). The description of population vulnerability in quantitative risk analysis. Risk Analysis: An International Journal, 32 (9), 1576-1594. Retrieved November 20, 2013 from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=78909578&site=ehost-live

Petty, J. W. & Bowlin, O. D. (1976). The financial manager and quantitative decision models. Financial Management, 5(4), 32-41. Retrieved May 21, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=5030230&site=ehost-live

Rice, G. H. Jr. & Hamilton, R. E. (1979). Decision theory and the small businessman. American Journal of Small Business, 4(1), 1-9. Retrieved May 21, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=5751685&site=ehost-live

Shachtman, R. H. (1980). Decision analysis assessment of a national medical study. Operations Research, 28(1), 44-59. Retrieved May 21, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=14619524&site=ehost-live

Shpilberg, D. & de Neufville, R. (1975). Use of decision analysis for optimizing choice of fire protection and insurance: An airport study. Journal of Risk & Insurance, 42(1), 133-149. Retrieved May 21, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=5205276&site=ehost-live

Williams, S. (2012). Analytics: A tool executives and managers need to embrace. Mworld, 11 (4), 13-16. Retrieved November 20, 2013 from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=84928877&site=ehost-live