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ONLINE FILE W4.1

INFLUENCE DIAGRAMS

4-1

Once a decision-making problem is understood and defined, it must be analyzed. This canbest be done by constructing a model. Just as a flowchart is a graphical representation ofcomputer program flow, an influence diagram is a map of a model; it is, effectively, amodel of a model. An influence diagram provides visual communication to the modelbuilder or development team. It also serves as a framework for expressing the exact natureof the relationships of the MSS model, thus assisting a modeler in focusing on the modelsmajor aspects, and it can help eliminate the less important from consideration. The terminfluence refers to the dependency of a variable on the level of another variable. Influencediagrams appear in several formats. An influence diagram has the following standard parts(see Hugin Expert A/S, developer.hugin.com/tutorials/ID_example/; and LuminaDecision Systems, lumina.com/software/influencediagrams.html):

Rectangle = decision variable

Circle = uncontrollable or intermediate variable

Oval = result (outcome) variable: intermediate or final

The variables are connected with arrows that indicate the direction of influence(i.e., relationship). The shape of the arrow also indicates the type of relationship. Thefollowing are typical relationships:

Certainty

Uncertainty

Random (risk) variable: place a tilde (~) above the variables name

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4-2 Part II Computerized Decision Support

FIGURE W4.1.1 An Influence Diagram for the Profit Model

Preference (usually between outcome variables): a double-line arrow (=>) Arrows can be one-way or two-way (bidirectional), depending on the direction of

influence of a pair of variables

Influence diagrams can be constructed with any degree of detail and sophistication.This enables the model builder to map all the variables and show all the relationships in

the model, as well as the direction of the influence. Influence diagrams can even take intoconsideration the dynamic nature of problems (see Glaser and Kobayashi, 2002; Xiangand Poh, 2002).

Example

Consider the following profit model:

Profit = Income Expenses

Income = Units sold Unit price

Units sold = 0.5 Amount used in advertisement

Expenses = Unit cost Units sold Fixed cost

An influence diagram for this simple model is shown in Figure W4.1.1.

Influence Diagram Software

Several software products create and maintain influence diagrams. The solution process ofthese products involves transforming the original problem into graphical form. Most ofthese software products are capable of generating the actual model and solving it directly.Representative products are:

Analytica (Lumina Decision Systems, lumina.com). Analytica supports hierarchicaldiagrams, multidimensional arrays, integrated documentation, parameter analysis,risk and uncertainty, and Monte Carlo simulation capabilities.

DecisionPro (Vanguard Software Corporation, vanguardsw.com). DecisionProbuilds near-influence diagrams. The user decomposes a problem into a hierarchicaltree structure (thus defining the relationships among variables). At the bottom, thevariables are assigned values, or their values can be generated randomly.

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DecisionPro is an integrated tool that includes a wide range of decision-makingtechniques: linear programming (LP), simulation, forecasting, and statistical analysis.

TreeAge Pro (TreeAge Software Inc., treeage.com). TreeAge Pro includes influence di-agrams, decision trees, simulation models, and other tools. It integrates with spread-sheets and Web pages. There is even a special version for the health care industry.

iDecide(Decisive Tools, LLC, definitivesoftware.com). iDecide creates influence-diagram-based decision models that are bidirectionally integrated with Excelspreadsheets. The models can go directly from influence diagrams to Monte Carlomethods.

PrecisionTree (Palisade Corporation, palisade.com). PrecisionTree createsinfluence diagrams and decision trees directly in an Excel spreadsheet.

See decision-analysis.society.informs.org/Field/FieldSoftware.html?=Software.htmlfor more information on influence diagram software. Downloadable demosare available from each vendors Web site. All these Web-enabled systems create modelsthat have a treelike structure in such a way that the model can be easily developed andunderstood. Influence diagrams help focus on the important variables and their inter-actions. In addition, these software systems can generate a usable model and solve it with-out converting it for solution by using a specialized tool. For example, Analytica lets the

model builder describe blocks of the model and how they influence the important resultvariables. These submodel blocks are disaggregated by a model builder constructing amore detailed model. Finally, at the lowest level, variables are assigned values. NASA usedAnalytica to decrease the Space Shuttle turnaround time. A major auto manufacturer saved$250 million per year in warranty costs by using Analytica. (See Lumina Decision Systems,lumina.com.)

See the Decision Analysis Survey in OR/MS Today(updated annually every June,available online at lionhrtpub.com/orms/) for a survey of decision-analysis softwarethat includes influence diagrams. We next examine an important implementation vehiclefor models: the spreadsheet.

Chapter 4 Modeling and Analysis 4-3

Xiang, Y. P., and K. L. Poh. (2002, January). Knowledge-BasedTime-Critical Dynamic Decision Modelling. Journal of theOperational Research Society, Vol. 53, No. 1, pp. 7987.

Glaser, B., and H. Kobayashi. (2002). Efficiency VersusSustainability in Dynamic Decision Making. New York:Springer-Verlag.

References

Online File W4.1 Review Questions

1.What is an influence diagram? What is it used for?

2. Explain why an influence diagram can be viewed as a model of a model.

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