Decision Making Under Uncertainty

Every day, managers make decisions that affect the profitability, effectiveness, and viability of the organization. Sometimes the factors affecting the predictability of events can be determined. However, not all variables affecting outcomes are neatly predictable. Decisions made under uncertainty are decisions for which there is no meaningful probability distribution underlying the various outcomes. In these situations, the decision maker simply does not know what will happen for the various decision alternatives. There are several approaches to decision making under conditions of uncertainty, including application of the Bayes' Decision Rule, Markov processes, and gaming. In the end, however, virtually every decision requires judgment. Knowledge of stochastic processes alone are insufficient to guide decision making.

Keywords Bayes' Decision Rule; Decision Analysis; Decision Theory; Gaming; Markov Chain; Model; Probability; Stochastic

Statistics > Decision Making Under Uncertainty

Overview

Every day, managers make decisions that affect the profitability, effectiveness, and viability of the organization. Although in some of these cases the parameters are known (e.g., if Harvey gives a raise to the production workers, there will not be enough money left over to buy parts to make widgets), in other cases they are not known (e.g., if Harvey does not give the production workers a raise, he does not know whether or not they will stay and continue to make widgets). Similarly, many of the decisions facing managers are complex (e.g., Harvey can ask the workers to postpone getting a raise and continue to make widgets while the company tries a new marketing strategy; if the workers do not continue to make widgets, the company cannot afford the new marketing campaign. However, there is no way to predict with 100 percent accuracy whether or not the campaign will be successful enough to bring in the added revenue to enable the company to give the workers a raise).

Factors Affecting the Predictability of Events

Trends, Business Cycles & Seasonal Fluctuations

Sometimes the factors affecting the predictability of events can be determined. These deterministic variables are those for which there are specific causes or determiners and include trends, business cycles, and seasonal fluctuations. Trends are persistent, underlying directions in which a factor or characteristic is moving in either the short, intermediate, or long term. In most cases, trends are linear rather than cyclic; growing or shrinking steadily over a period of years. For example, the increasing tendency for business to outsource and offshore technical support and customer service in many high tech companies over the past few years is a trend. However, not all trends are linear. Trends in new industries tend to be curvilinear as the demand for the new product or service grows after its introduction and then declines after the product or service becomes integrated into the economy. Another type of deterministic factor is business cycles. These are continually recurring variations in total economic activity. Business cycles usually occur across most sectors of the economy at the same time. For example, it has been noted that several years of a boom economy with expansion of economic activity (e.g., more jobs, higher sales) are often followed by slower growth or even contraction of economic activity. Business cycles may occur across one industry, a business sector, or even the economy in general. A third type of deterministic factor is seasonal fluctuations. These changes in economic activity occur in a fairly regular annual pattern and are related to seasons of the year, the calendar, or holidays. For example, office supply stores typically experience an upsurge in business in August as children receive their school supply lists for the coming year. Similarly, the demand for heating oil is typically greater during the cool months than it is in the warm months.

Stochastic Variables

However, not all variables affecting outcomes are so neatly predictable. Stochastic variables are caused by randomness or include an element of chance or probability. These include both irregular and random fluctuations in the economy that occur due to unpredictable factors. For example, a natural disaster such as an earthquake or flood, political disturbance such as war or flu epidemic that causes high absenteeism is often unpredictable and can affect a business' profitability. In conditions of uncertainty, there is no meaningful probability distribution for the various outcomes. In these situations, the decision maker does not know what will happen for the various decision alternatives.

Conflicting Interests in Decision Making

Another factor complicating real world decision making processes is the fact that there is often more than one party to the decision and the parties may have conflicting interests. In fact, systems theory posits 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. So, for example, in the illustration above concerning giving raises to the workers during a time of flux, there are at least two major parties to the decision. From the workers' point-of-view, getting a raise now is better than maybe getting a raise later. Their raise or lack thereof, in turn, affects other parties not directly in the discussion such as their families (e.g., if there is no raise, the family cannot pay for Johnny's tuition) and their creditors (e.g., if there is no raise, the family cannot meet the increased payment on their adjustable rate mortgage). Management, of course, has a different point-of-view. If they give the workers a raise now, they will not have sufficient funds available for the new marketing campaign that will bring in more revenue. Without the additional revenue, they will have to lay off some of the workers, which means that they will not be able to meet an increased demand for widgets even if they do launch the new marketing campaign. They could take money to pay the production workers from the monies set aside for raises for new product development, but then they would not be able to gain a competitive edge over the companies offering similar items in the marketplace. In addition, management needs to report to its stockholders, and increased wages may mean decreased profits.

Categories of Decisions to be Made

Certainty & Uncertainty

The decisions facing managers in the business world can be classified into several categories: decisions made under certainty or uncertainty, under risk, or under conflict. A decision made under certainty occurs when all the facts of the situation are known and the model provides the decision maker with the exact consequences of choosing each alternative. This knowledge, however, does not mean that the decision is either obvious or trivial. There may be many possible courses of actions that can be taken, each with different consequences, 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 underlying the various outcomes. In these situations, the decision maker simply does not know what will happen for the various decision alternatives.

Multiple Criteria Decision Making

Multiple criteria decision making is a discipline that deals with the problem of making decisions in complex situations where there are conflicting objectives. Multiple criteria decision making is founded on two interrelated, key concepts. Satisficing is the attempt to find solutions that satisfy all the constraints rather than optimizing them. For example, the workers may be given a raise, but only in six months after the new marketing campaign goes into effect. This would still give them a raise, but would also give the company an opportunity to get back on its feet. From the workers' point-of-view, the optimal situation would be to get raise now. From management's point-of-view, the optimal situation would be to keep wages low so that there are more profits. Neither one of these situations is optimized in this solution, but the constraints of both are satisfied. The second key concept of multiple criteria decision making is bounded rationality. This process involves setting the constraints of the situation and then attempting to find solutions that satisfy the constraints. This is an iterative process in which the constraints are adjusted as necessary and the search for solutions is continued until a satisfactory solution is found. For example, the workers at Widget Corporation may be willing to postpone getting a raise only if the raise that they get in six months is greater than the one that they would accept today.

Methods for Solving Multiple Criteria Decision Making Problems

As shown in Table 1, there are a number of methods available for solving multiple criteria decision making problems. Deterministic decision analysis is used to find the most preferred alternative in the decision space using value functions. Stochastic decision analysis does the same thing, but uses utility functions and stochastic outcomes. In the stochastic approach, both the utility function and the probability of the various outcomes are estimated by the decision maker. The multi-objective mathematical programming approach includes both multi-objective linear programming and multi-objective integer programming.

Decision Theory

Decision theory is a body of knowledge and related analytical techniques designed to give 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 tool often useful in decision making is modeling building. Models are representations of a situation, system, or subsystem. Conceptual models are mental images that describe the situation or system. This type of model is 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 models that accurately represents the real world is typically an iterative process. Models must usually be tested and refined until they represent the real world to the degree desired by the analyst or decision maker. Initially, conceptual models tend to be broad or general representations without much detail but which span the range of variables to be considered. However, 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 the situation is better understood, the model can be refined to better reflect the underlying reality.

Applications

Approaches for Decision Making Under Uncertainty

Bayes' Decision Rule

There are several approaches to decision making under conditions of uncertainty. One of these is the application of Bayes' Decision Rule. This is 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. Decision models in these situations are characterized by several basic elements. First, there is a set of options from which the decision maker may choose as well as a set of consequences that may occur as a result of a given decision. In addition, Bayes' Decision Rule assumes that there is an underlying probability distribution that can be used to quantify the decision maker's beliefs about the relationship between the various choices and resultant consequences. Further, this approach involves a utility function that quantifies the decision maker's preferences among the various consequences.

Markov Processes

Another frequently used approach in this type of situation is the application of Markov processes. These are stochastic processes in which the probabilities of future events are completely determined by the current state of the process. So, for example, if one knows the current state of the process, no additional insight can be gained from previous states of the process. A Markov chain is a random process comprising discrete events in which the future development of each event is either independent of past events or dependent only on the immediately preceding event. Markov chains are often used in marketing, for example, to model subsequent purchases of products (i.e., the probability of the customer making a purchase from a particular business or brand is dependent only on his/her last purchase of that brand or independent of the brand).

Gaming

A third approach to decision making under uncertainty is the application of gaming to real world problems. Gaming is an activity in which two or more independent parties attempt to achieve objectives within a limiting context. In business, gaming involves the use of mathematics in determining optimal strategies and making the best possible decisions in context. Gaming, however, is a controversial approach to decision making, and is typically more art than science. However, it is possible to gain insights into a real world situation by designing, playing, or analyzing a game. Game design is a multi-stage process. First, one sets the objectives for the game and defines the parameters in which the game will be played. Once these constraints are articulated, a conceptual model is developed and decisions are made as to how best to represent it. The game is then constructed and refined. As opposed to other methods for making decisions under conditions of uncertainty, gaming is not a solution method nor does it lead to a forecast, solution, or prediction. However, a game does help the decision maker to better understand the situation about which a decision needs to be made, including its constraints, consequences, and greater ramifications.

Compromises in Decision Making

From a scientific point-of-view, it would be comforting to be able to collect data, build a mathematical model or perform a statistical analysis, and be given a number that could be looked up in a table to tell one whether to choose Option A or Option B. Unfortunately, real world decisions are not so simple. As discussed above, real world decisions often are made in situations where it is impossible to predict or even know all the parameters that affect the decision. Further, real world decisions are more complicated than decisions made in a laboratory setting because even in those few situations where there is only one decision maker in a business setting, a decision can ripple throughout the organization and its stakeholders. A decision that results in an optimal situation for one stakeholder may be disastrous for another stakeholder. Frequently, there is no best answer and the decision must be made as a series of compromises. In addition, it must be remembered that the interpretation of data analysis as, indeed, the very data themselves, are subject to the skill and qualitative assessment of the decision maker or analyst. In addition, it has been argued that the probabilistic and value-related factors of Bayesian methods imply a degree of precision that is impossible to obtain in the real world. As a result, the conclusions drawn on this methodology are too precise to be given much credence. Others have argued against the presumption of normalcy underlying Bayes' rule.

Forecasting for Business Decisions

Opinion about the best way to forecast for business decisions can be sharply divided between those that rely on statistical methodology and those that prefer to use their "gut" to determine where the industry, supply chain, or market is going. Both approaches have advantages and disadvantages, however. Statistical methods can be less prone to bias than are judgments. In addition, statistical methods tend to be more reliable and can more efficiently make use of historical data. On the other hand, statistical techniques can only work with the data they are given. Judgmental decision making can be useful particularly 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 for analysis. There are, however, risks inherent in decisions that are made purely on subjective criteria. Human error can make the analyst or manager more optimistic (or pessimistic) than actually warranted, trends or factors may be read into the data that are not actually there, or the effects of correlated variables may not be taken into account.

The Importance of Judgment

In the end, virtually every decision requires judgment. First, judgment is key to determining which data are relevant to the model or game or that is considered in the analysis. Potential variables affecting decisions in the real world are virtually limitless. However, no statistical model or analysis can take all variables into account. Even if it could, spurious positive results would be seen due to the effects of probability alone. Therefore, it is essential that expert judgments be used to reduce the inputs into the process. Judgment is also important in decision making because different analytic techniques can yield different results. It is the judgment of the analyst that determines which technique is most appropriate to analyze the data. The worth of the end result of the analysis depends heavily on correctly choosing the most appropriate analytical method. Finally, expert judgments can be essential to help the analyst understand the situation and give insight into the parameters through which the data and subsequent analysis should be interpreted. Statistical processes alone are insufficient to guide decision making.

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.

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.

Forecasting: In business, forecasting is the science of estimating or predicting future trends. Forecasts are used to support managers in making decisions about many aspects of the business including buying, selling, production, and hiring.

Gaming: An activity in which two or more independent parties attempt to achieve objectives within a limiting context. In business, gaming involves the use of mathematics to determine optimal strategies and make the best possible decisions in context.

Markov Chain: A random process comprising discrete events in which the future development of each event is either independent of past events or dependent only on the immediately preceding event. Markov chains are often used in marketing to model subsequent purchases of products (i.e., the probability of the customer making a purchase from a particular business or brand is dependent only on his/her last purchase of that brand or independent of the brand).

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.

Probability: A branch of mathematics that deals with estimating the likelihood of an event occurring. Probability is expressed as a value between 0 and 1.0, which is the mathematical expression of the number of actual occurrences to the number of possible occurrences of the event. A probability of 0 signifies that there is no chance that the event will occur and 1.0 signifies that the event is certain to occur.

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

Strategy: In business, a strategy is a plan of action to help the organization reach its goals and objectives. A good business strategy is based on the rigorous analysis of empirical data, including market needs and trends, competitor capabilities and offerings, and the organization's resources and abilities.

Table 1: Taxonomy of Multiple Criteria Decision Making Approaches: (From Ramesh & Zionts, p. 539)

Bibliography

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Suggested Reading

Borgonovo, E. (2006). Measuring uncertainty importance: Investigation and comparison of alternative approaches. Risk Analysis: An International Journal, 26, 1349-1361. Retrieved August 9, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=22674895&site=ehost-live

Courtney, H., Kirkland, J., & Viguerie, P. (1997). Strategy under uncertainty. Harvard Business Review, 75, 67-79. Retrieved July 31, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=9711071077&site=ehost-live

Eichberger, J., Harper, I. R., Pfeil, C., & Scheid, F. (2002). Decision-making under uncertainty. In J. Eichberger, I. R. Harper, C. Pfeil, & F. Scheid (eds.), Solutions manual for financial economics (pp. 1-19). New York: Oxford University Press. Retrieved August 9, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=25608783&site=ehost-live

Foss, N., Mahnke, V., & Sanchez, R. (2000). Demand uncertainty and asset flexibility: Incorporating strategic options in the theory of the firm. In N. Foss, V. Mahnke, & R. Sanchez (eds.), Competence, governance & entrepreneurship (pp. 318-332). Retrieved August 9, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=7672238&site=ehost-live

Gottlieb, D. A., Weiss, T., & Chapman, G. B. (2007). The format in which uncertainty information is presented affects decision biases. Psychological Science, 18, 240-246. Retrieved August 9, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=24719389&site=ehost-live

Goyal, M. & Netessine, S. (2007). Strategic technology choice and capacity investment under demand uncertainty. Management Science, 53, 192-207. Retrieved August 9, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=24272429&site=ehost-live

Hitsch, G. J. (2006). An empirical model of optimal dynamic product launch and exit under demand uncertainty. Marketing Science, 25, 25-50. Retrieved July 31, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=19991298&site=ehost-live