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Problem Definition

The Decision Analysis Paradigm

The techniques that are used when conducting systems analysis depend on the type of problem being modeled. There is, however, a common systems approach to problem solving in general. Insofar as decision analysis is concerned, this approach is best exemplified by the following paradigm:

0.  Recognize the problem
1.  Define the problem and its context
2.  Formulate a basic model (prototype)
3.  Gather information and refine the model
4.  Solve the model (computationally)
5.  Verify and validate the model
6.  Perform sensitivity analysis
7.  Interpret model results
8.  Recommend a course of action

The steps need not be performed in a strictly sequential manner. It is common practice to revert to previous steps and rework them as one gains more experience with the problem.

0.  Recognize the Problem

Before a problem can be analyzed, one must become aware of the existence of a problem. The apparent problem, however, may not be the real problem. The analyst must distinguish between symptoms and actual problems. Symptoms are signs that indicate that certain conditions, possibly detrimental, exist somewhere in the system. Treating a symptom, doctors well know, will not cure the underlying illness. Therefore, the analyst must strive to uncover root causes and not be misled by superficial appearances.

Another important aspect to keep in mind is the type of problem present. The word problem has a negative or pejorative connotation: something is not going right. There are, however, positive problems: opportunities that perhaps should be pursued. Negative problems must be corrected, surely, for they are obstacles to progress. But positive problems may well prove more profitable in the long run. World-class decision makers set their bearings with respect to opportunities, not obstacles. Positive problems are typically harder to detect, for no symptoms may be apparent. Opportunities call for visionary yet practical individuals capable of transforming hazy unconventional ideas into concrete, profitable realities. The epitome of the visionary manager, of course, is the problem solver with a knack for converting negative problems into clever golden opportunities.

For a more complete discussion of problem recognition, please see the section «0. Recognize the Problem» in The Linear Programming Paradigm page.

1.  Define the Problem and Its Context

Decision analysis requires that seven elements of the problem be clearly defined by the analyst. The first three are of a general nature and serve to focus the context of the problem: the overall setting in which the decision will be made. The remaining four are problem-specific and serve to structure the model.

1A. Contextual Elements

Decision Maker - Who is the person or persons charged with making the decision? Participation in the analysis by the decision maker(s) is necessary in order to establish values (matters considered of paramount importance), problem scope, objective(s) and constraints, inherent uncertainties, and risk preferences. When more than one decision maker is involved, achieving consensus on contextual and structural elements is indispensable. Decision analysis presumes that such a consensus exists. If consensus is lacking, the situation calls for negotiation. Decision analysis can contribute to productive negotiations by throwing light on the structure of the problem and how different issues relate to each other, thereby facilitating communication between the negotiating parties.

Objective(s) - What does the decision maker want to accomplish with this decision? Objectives are expressed as maximization or minimization of particular variables of interest, say, profit or customer satisfaction in the former case, and cost or risk in the latter. Multiple objectives increase problem complexity but are perfectly acceptable. In such cases, they are categorized as either fundamental objectives (the ends that are being sought) or means objectives (those that contribute to achieving other objectives). Objectives are derived from the decision maker's values and the scope (extent) of the problem under consideration.

Constraints - What restrictions must be complied with while pursuing the objective(s)? Constraints are anything that imposes a condition that must be fulfilled. Constraints include physical, technical, economic, financial, legal/regulatory, ethical, and policy factors that impinge on the problem.

1B. Structural Elements

Action Alternatives - These constitute the possible courses of action open to (that is, under the control of) the decision maker. Decision alternatives must be mutually exclusive (clearly distinct options where choosing one of them precludes all others) and collectively exhaustive (covering all possible options). Determining a realistic set of action alternatives demands effort, creativity and experience on the part of the decision maker. Managerial intuition is extremely valuable at this stage of the analysis. The alternative “do nothing” should always be entertained; this means keeping the status quo (existing state of affairs) which, being a known system state, is useful as a benchmark with which to compare other hypothetical scenarios.

States of Nature - These are the possible outcomes for each contingency (uncertain future event) that could arise when taking a course of action. They are not under the control of the decision maker. As with action alternatives, states of nature must be defined so as to be mutually exclusive and, to the extent possible, collectively exhaustive. In reality, it is not possible to include all potential states of nature in a model because nature is sovereign. Killer meteorite impacts and Krakatoa-class volcanic eruptions are always a possibility, yet are seldom relevant to most decision analyses. Judgment and experience are needed to choose which contingencies to include and which to leave out of a model. Formally, however, the assumption is that the states of nature for every contingency are collectively exhaustive.

Payoffs - A payoff is a quantitative measure resulting from taking a particular course of action and experiencing a specific state of nature. It is the net gain or loss obtained as the result of the decision. In business, payoffs are usually expressed in monetary units. In decision analysis models, however, one can make use of either monetary values or abstract utilities. Payoffs are simply consequences that have been quantified using some metric.

Probabilities - Courses of action are chosen by the decision maker. States of nature, however, are not under the decision maker's control. So probability distributions are used to describe the degree of possibility of occurrence of the uncertain events. Each state of nature is assigned a probability that depends on the relevant information available to the decision maker at the time the decision is made. Such probabilities are called subjective because they encode the decision maker's personal judgment about the likelihood that a given state of nature will occur.

2. Formulate a Basic Model

Once the problem is defined, the analyst can build a prototype model. The prototype is a first attempt at representing the decision problem, and as such should be as simple as conditions permit. Minute details are best left out of the prototype. As knowledge about the problem increases, the model can be refined and reformulated to include additional factors. The art of modeling is iterative: start simple, then refine. A word of wisdom: more detail does not necessarily yield a better model. It is often the case that added details have little or no effect on the decision, in which case they should be removed from the model. We shall look into this in a forthcoming discussion on sensitivity analysis.

Three equivalent representations can be used to formulate a model: decision matrixdecision tree and influence diagram. The first two are introduced on the next page and are used throughout this module. Influence diagrams allow for more compact representations but in turn depend on special-purpose software (by and large proprietary) to handle the model's internal complexity that is concealed from the user. Due to this custom software dependency, influence diagrams will not be discussed.

3. Gather Information and Refine the Model

Information must be collected from the "real world" because a model is a representation of reality. Such information is typically incorporated into the model in the form of parameters and uncontrollable variables. A parameter is a number: a quantity that remains constant throughout the analysis. An uncontrollable variable is a quantity that may vary within the analysis but is not controlled by the decision maker; its values depend on factors external to the model. (Controllable or decision variables, on the other hand, are the action alternatives, which are under the control of the decision maker.) Environmental information provides much parametric data, examples being market prices, demand forecasts and prevailing interest rates.

4. Solve the Model

Carry out the required computations and obtain the model output.

5. Verify and Validate the Model

Model verification means ensuring that the model is computationally correct, that it calculates what it is supposed to. A model containing errors —of both omission and commission— is useless. Model validation means ensuring that the model is representationally correct, that it accurately reproduces the real-world system or situation being modeled. Verification deals with the internal consistency of the model while validation addresses its external (representational) correctness. Here's a quick overview of these important concepts: Model V & V.

6. Perform Sensitivity Analysis

Examine the decision (managerial course of action) prescribed by the model. Models being idealized simplifications of reality, their outputs must be viewed as proposed solutions to the problem. Changes in the values of parameters and uncontrollable variables may affect the solution. Sensitivity analysis must be performed by varying those values throughout their plausible ranges —singly as well as in relevant combinations— and examining their impact on the solution. If the solution is sensitive to changes in certain parameter or uncontrollable variable values (that is, if the recommended decision changes significantly), more detailed fact finding should be carried out to better assess those critical quantities. Alternatively, preventive measures such as hedging can be taken if the level of risk is deemed unacceptable. If the range of values assumed by an uncontrollable variable causes no major changes in the recommended solution, that uncontrollable variable should be fixed as a parameter at its nominal (most likely) value.

7. Interpret Model Results

Decision analysis models seek out optimal solutions based on the model structure and the decision maker's knowledge, assumptions and preferences. Still, other factors may bear on the problem. For instance, the difference in expected benefits between the prescribed solution and the second-best alternative may not be significant when taking into consideration externalities (collateral consequences such as, say, intangible benefits) that were not included in the model. In such cases, model results should be interpreted in the light of broader realities. Nevertheless, the model still proves useful since a clear understanding of the basic problem has been obtained, thereby providing a strong foundation upon which to reconsider, evaluate and justify any modified subjective decision.

8. Recommend a Course of Action

Presentation of the findings concludes the work of the analyst. Implementation of the decision is a separate managerial function.


Action Alternative – a possible course of action that may be exercised by a decision maker

Analyst/Decision Analyst – the person conducting the modeling and analysis of a decision problem

Constraint – a restriction that must be satisfied while pursuing a goal or objective

Controllable or Decision Variable – a model element under the control of the decision maker

Context – the set of circumstances that provide the setting in which a problem is embedded

Decision – a deliberately chosen course of action intended to accomplish a goal or objective

Decision Alternative – another name for action alternative

Decision Maker – the person(s) responsible for making the decision

Decision Matrix or Decision Table – a tabular representation of a decision problem

Decision Objective – the aim or intended result that is pursued when making a decision

Decision Tree – a graphical representation of a decision problem

Fundamental Objective – the ultimate aim or reason why a decision is made

Means Objective – an intermediate result that facilitates the attainment of other objectives

Model – an idealized representation of a system (an object, process or evolving situation)

Model Validation – ensuring that the model is representationally correct (externally accurate)

Model Verification – ensuring that the model is computationally correct (internally consistent)

Negative Problem – a situation that is not proceeding according to expectations

Objective – that which one intends to accomplish; the thing aimed at as the result of some process

Parameter – a quantity assumed constant in a model

Payoff – the net result (gain or loss) of taking a particular course of action given the occurrence of a particular state of nature; a quantitative measure of the consequence of a decision

Probability – a quantitative measure of the degree of possibility of occurrence of an uncertain outcome

Probability Distribution – a complete listing of the set of possible outcomes associated with a given event along with the probability corresponding to each outcome

Problem – a state of affairs requiring intelligent human intervention

Prototype – the original version of a model

Positive Problem – a situation that presents an opportunity

Sensitivity Analysis – a computational process performed to determine if variations in parameter or uncontrollable variable values significantly affect the model output

State of Nature – a possible outcome of an uncertain event which, if it occurs, partly determines the consequences of a decision

Subjective Probability – a measure of the belief a person has that a particular outcome will occur

Symptom – an indication or sign that some condition of interest exists somewhere in a system

Uncontrollable Variable – a quantity which can assume a range of values and that is not under the control of the decision maker

Values – "Values are what we care about."  Ralph L. Keeney, Value-Focused Thinking: A Path to Creative Decisionmaking, 1992, Harvard University Press, p. 3.

Subpages (1): Problem Representation