# Decision analysis in projects

## modeling techniques - part 1

**Concerns of Project Managers**

PM TUROTIAL

**John R. Schuyler, Decision Precision®, Aurora, Colorado**

Decision analysis is an approach, and the associated techniques, that help a decision maker choose wisely under conditions of uncertainty. Application is based upon:

- Having a choice between alternatives;
- Having importantly different possible outcomes between at least two alternatives, as a result of uncertainty for example; and
- Evaluating each alternative by weighting the possible outcomes with their probabilities of occurrence. This is the expected value calculation described in the first article in this series [1].

This article focuses upon the first and second steps: constructing a model that is used to project different possible outcomes. Every projection, or scenario, is summarized into a single quantitative value. This value measures goodness or progress toward the organization's objective.

**Editor's Note:** This is the seventh tutorial in this series about decision analysis. At present it is planned to have 12 installments:

**DECISION ANALYSIS IN PROJECTS**

**Expected Value—The Cornerstone.**Representing a probability distribution as an unbiased, single value.**Optimal Decision Policy.**Appraising value or cost: a consistent approach suited to all decision types.**Decision Trees.**Graphical decision model and expected value calculation.**Value of Information.**Evaluating an alternative to acquire additional information.**Monte Carlo Simulation.**An alternative, popular technique for calculating expected values and outcome probability distributions.**Other Probabilistic Techniques.**Other established and new probability techniques suited to simple situations.**Modeling Techniques - Part I (this article).**Project and cash flow projections: approaches, tools and techniques.**Stochastic Project Modeling.**Decisions and other dynamic behavior in models; sensitivity analysis.**Judgments and Biases.**Encoding expert judgments about risks and uncertainties.**Utility and Multi-Criteria Decisions.**Decisions involving objectives other than maximizing monetary value.**Implementing and Using Decision Analysis.**Overcoming barriers to accepting and using decision analysis in projects; management implications.**Summary and Recap.**

*This series is about the probabilistic methods of decision analysis. Key to the analysis of alternatives is being able to value every possible outcome. Deterministic, or non-probabilistic, models underlie most analyses. The model accepts parameter values and calculates the final outcome. This article provides an overview of deterministic models and their construction.*

*We invite readers to submit written questions and comments on this series to the author via PMI Communications.*

**PREDICTIONS FROM MODELS**

It can be said that predicting the future is one of the most important analytic problems in business. Nearly every decision presupposes some sort of prediction. A prediction is a scenario that reflects a set of assumptions, typically that tomorrow is going to be like today. A forecast is a prediction that incorporates specific assumptions about the future that includes someone's opinion about how the future may be different. The differences may be in structure or in values of parameters. For example, the introduction of microcomputers changed the structure of information processing for PM. A change in volume of information used in PM would be a change in parameter value. In the context of this discussion of decision analysis, the forecast is the expected value outcome.

**Predicting Approaches**

There are three general approaches to predicting the future:

- Guessing or using intuition;
- Extrapolating the past, such as by linear regression; and
- Modeling the system, and using the model to generate a forecast.

The first approach provides predictions that are of questionable credibility. Intuition is believable only if the pre-dicter has recognized experience and a record of reasonably accurate judgments. Seldom are the assumptions clearly stated.

Extrapolation requires suitable historical data and is based on the *ceteris paribus* (all other things being the same) assumption. Note that this implies that tomorrow will be like yesterday.

Modeling involves designing and building a representation of the system. The model is an abstraction of the real world based upon someone's best understanding. Modeling is particularly valuable in situations that involve new or unique and complex situations.

Most often, a prediction is based upon a set of initial assumptions. Examples include activity costs and completion times. Single-value assumptions result in a single-value outcome calculated through the prediction model. Such models are called deterministic because every value is singly determined.

**Deterministic Cash Flow Model**

In this article, the perspective will be decision making in a business enterprise, although decision analysis applies to all types of entities.

In business, value derives from cash flow. The present value (PV) calculation transforms an incremental cash flow prediction into incremental corporate value. This is the basis for most modem financial analysis. There are many arguable details, such as inflation, tax, and cost of capital assumptions. However, the general process is straightforward.

The second article in this series, about “Optimal Decision Policy,” described how to value outcomes [2]. Project managers are traditionally concerned with performance, schedule, and cost. While these dimensions are important, it is impossible to make consistent decisions without a way to determine composite value. A single value measure is needed. The author recommends that non-monetary dimensions be converted into cash flow or money equivalents. This is the simplest approach to deal with multiple objectives.^{1} Thus, project performance and schedule are translated into cash flow impact and combined with costs. This single value measure approach is illustrated in Figure 1. In this illustration, the shaded blocks indicate commonly generated outcomes that inherently lead to multi-criteria decision making. Information generated in the development model and feasibility model can be used to generate net cash flow and ultimately the present value (PV) or expected monetary value (EMV). The project model's main purpose, then, is to forecast net cash flow.

**Figure 1.** Cash Equivalents

**Figure 2.** Life-Cycle Scope

**Problem and Model Scope**

A good project model contains sufficient operating and financial detail as to reasonably represent the impacts of the relevant alternatives in the business decision. Thus, the appropriate model detail depends upon the decision at hand. Sometimes analysis of outputs from the model will indicate that the decision is obvious. In other situations, the differences in outcomes may be marginal. When this is the case, additional analysis effort is warranted, perhaps incorporating additional detail in the model.

The scope encompassed by the model is important. The system analyzed may be all or part of an industry, business, project or transaction. The scope usually needs to consider the remaining life-cycle of the project and sometimes the life-cycle of the product of the project. Sometimes managers concern themselves only with the development or construction phase. This is usually inadequate. Completion time and asset performance also impact value as illustrated in Figure 2. Decision analysis techniques are filly general, and apply to construction or non-construction projects equally well. All important details and aspects of the problem should be incorporated into the model.

Projects often impact other areas of corporate operations and even other projects. Simplifying assumptions are almost always necessary. One wants to avoid modeling the entire corporation for each decision. However, sufficient detail is needed to adequately predict the impact on corporate net cash flow. Incremental cash flow effect is generall_{y} the most useful measure. Accuracy is usually better regarding the difference between alternatives than for absolute values.

**Figure 3.** Influence Diagram

**THE MODELING PROCESS**

Initially, someone identifies a problem: a choice about allocating resources. Often, a decision arises because something happens or because a new idea or information surfaces. Increasingly, and importantly, people are recognizing the value of proactively creating new alternatives. Professionals should continually ask, “What can we do to improve the value of this project?”

Often, a project team is involved or assigned to the problem. The team should first define the problem. This definition includes a situation description. The scope of the problem-solving process is important, and this is often dictated by the need that the model measure incremental corporate value.

The following sections describe modeling approaches, system diagrams, other techniques and software tools.

**Modeling Approaches**

Understanding the project and its elements is essential to developing a valid model. The model should reflect the way the project behaves under different conditions.

A logical framework for developing the model must be chosen. Since there is an inherent flow relationship of the factors in the model, it usually works well to adopt one or more of the following as a theme for the modeling process:

- The sequence of activities
- The flow of units
- The flow of labor hours and material quantities
- The flow of cash
- The flows of income and expenses (accounting book basis)

The idea of conservation of mass, money, etc., is widely applicable, so it is wise to build in checks and balances to ensure that all units of resources are accounted for.

The model is usually built with mathematical formulas and variables. Here are two examples:

Net Cash Flow = (Cash Operating Costs (opcost)) - (Income Tax) - (Capital Expenditures)

Date Prototype Testing Begins = Maximum (Prototype Construction Finish, Testing Facility Construction Finish)

**System Diagrams**

The first step in any modeling effort is to identify the objectives of the analyses to be performed. For example, in one modeling effort the objective was to develop the basis for selecting the melt process for a casting plant. Three alternatives were available: cupola, induction furnace, and arc furnace. It was not necessary to replicate the exact operating conditions, which would not likely have been optimal. However, it was possible to compare the optimal operating conditions for the three alternatives as derived from linear programming models. In another modeling effort, it was not necessary to replicate actual operating conditions, but to represent these conditions sufficiently that the players (of a business game) felt that it behaved consistent with reality.

Before beginning to actually construct a model, it is helpful to conceptualize the model's organization or structure. A diagram of the problem is a good early investment. This can be developed with little time and effort, before laboring with the details of formulas and values. A conceptual error found at an early stage is much easier and less costly to correct. A system flow diagram can depict the essential features.

In project management, the starting point is often the project plan represented as a work breakdown structure (WBS). This provides a list of the project's activities. The project plan is represented by listing predecessor activities or drawing a project net. work diagram (PND), often referred to as a CPM diagram. Costs and performance details flesh out the inputs to the model.

A similar approach, focusing more on the variables, is an influence diagram. Figure 3 shows an example. This representation shows decision variables (rectangles), chance events (ovals), and the EMV decision variable (rounded rectangle). Variables derived solely from a deterministic calculation are shown as double-ovals. The arrows on the arcs show the direction of influences or causality.

In Figure 3, a decision is being made whether to accelerate an activity, Constructing Prototype, in a large project. This is part of a much larger program or project. Prototype Testing follows, although there may be some delay. Prototype Testing's start date affects its costs and the project's overall time to complete. Whether an activity is on the critical path determines whether delaying the activity directly delays the project's overall completion time.

**Business Modeling Tools**

While a computer is not needed for business modeling, it can be very helpful. Computer assistance is preferred for all but the simplest decision problems. Computers allow a much greater scope of considerations to be modeled explicitly.

There is a well-established industry in project software. Much of the commercial software is limited to certain aspects of project management, e.g., controlling cost, resources or completion time. Construction costs are often detailed, but this is one component of corporate net cash flow. Other tools are being developed, or are available but not used extensively, that permit more sophisticated modeling of project network diagrams. These rely on PNDs that permit other logical relationships between activities that are not available in typically available commercial programs for project planning, scheduling and control.

Often a custom model is needed, tailored to the situation at hand. Available tools include:

- Computer spreadsheets
- Formula-based modeling tools, such as Lotus Improv
- Procedural programming languages, such as Microsoft Visual Basic
- Graphical modeling tools, such as High Performance Systems' ithink
- Simulation languages some of which now permit visual display of the results of dynamic interactions
- A variety of other tools to aid in defining and refining logical relationships between variables, i.e., flows

Spreadsheet programs have become the world's favorite business modeling tool. For larger problems, formula-based tools, such as Improv or Execu-com Systems Corp.'s IFPS, provide a more manageable and productive environment. For the largest models or those with complex formulas or conditional branching, the author prefers procedural programming languages. Microsoft Visual Basic is powerful, and its models are easily understandable by non-programmers. The graphical modeling tools will become increasingly functional and important.

Beyond the current tools, there is potential that much of the modeling effort can be reduced through rule-based expert systems. This subset of artificial intelligence computer programs allows the capture of human expertise and implementation as an automated assistant. The author once developed a prototype expert system modeling tool that incorporated selected knowledge about model-building, accounting and finance.

**Other Modeling Concepts**

Modeling proficiency comes with practice. One hallmark of a good model is simplicity. There is elegance in a straightforward representation that matches the project manager's view of reality.

*Decomposition*is the analytic process of breaking down something complex into understandable components. This technique is pervasive in most analysis. Decomposition allows greater advantage to be taken of intuition and allows dealing with details that would otherwise be excluded.*Synthesis*is the process of combining components into a larger whole. In modeling, synthesis would naturally follow decomposition. Having decomposed the problem into its understandable components and modeled them, the components are then combined to produce larger components and eventually the overall model.*Sensitivity analysis*is very important in deciding which elements significantly impact the outcome. It permits the modeler to examine the degree to which an outcome variable is affected by changes in an input variable. If a relationship is found to be very sensitive, additional research may be warranted to further define the possible values of the input variable or to more precisely define the relationships in the model.

Unfortunately, new situations most often require partially- or wholly-custom models. The bulk of a decision analysis effort is usually constructing the cash flow model. For this reason, developing a deterministic project cash flow model is typically 60 percent of the effort of a decision analysis. Some research has been conducted to show how modules of model logic can be constructed of many phenomena in projects typical of a given organization [3]. Using such standard modules may lead to more efficient model development in the future.

**TOWARD CREDIBLE VALUATIONS**

This article describes the central role of the deterministic project model in making decisions. This model is the core of decision analyses, regardless of the probabilistic technique involved.

The model is an aid to making forecasts. Its main function is to generate predictions for each possible outcome scenario. Probabilities can then be used to weight the outcome values into the forecast of the value of a single decision variable such as expected monetary value. Every path through a decision tree and, usually, every trial scenario in a Monte Carlo simulation is evaluated with a deterministic model.

The aim of decision analysis is more accurate, more confident decisions. Model building looks time-consuming, and it can be. However, the extent of the analysis should always be appropriate to the decision being made. Analysis only adds value when the analysis outcome may affect the decision. The alternative to decision analysis is intuition. While the intuition of the experienced manager can add significantly to the decision making process, the wise decision maker uses every available means to supplant, or at least supplement, intuition with logical and rational decision aids, subject to appropriate time and resource constraints and potential value of further analysis.

This discussion about modeling continues in the next installment. Sensitivity analysis shows which variables affect the project outcome the most, and thus deserve added attention. Modeling can represent how a project behaves dynamically.

**REFERENCES**

1. PMNETwork, January 1993, p27.

2. PMNETwork, April 1993, pp31-34.

3. Singh, Amarjit, and Ebeling, Ken. Construction Process Simulation Using a Standardized Configuration and Model (accepted for publication in the *Project Management Journal).*

**NOTES**

1. There are at least two schools of thought on decision making with regard to objectives: single objective and multiple objective. The author is a proponent of a *single* objective, stating it clearly in a mission statement. Other considerations encompassed by the objective are sub-objectives. ❑

**John R. Schuyler,** *PE, CMA, is principal of Decision Precision®, an Aurora, Colorado, firm providing training and assistance in risk and economic decision analysis. Mr. Schuyler teaches Petroleum Risks and Decision Analysis worldwide in association with Oil & Gas Consultants lnternational. His services focus on modeling capital investments, acquisitions, and other corporate planning decisions. He received B.S. and M.S. degrees in engineering from Colorado School of Mines and an M.B.A. from the University of Colorado. His prior experience includes vice president and evaluation engineer with the nation's fifth largest bank, planning and evaluation analyst for a major oil company, and senior management consultant with a national CPA firm.*

**PMNETwork • July 1994**

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