Project Management Institute

Optimizing project plan decisions

by John Schuyler, PMP

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MANAGERS OFTEN FACE decision problems when choices are more complex than simply yes or no. This article continues the discussion of “Exploiting the Best of Critical Chain and Monte Carlo Simulation” begun in the January PM Network.

In project schedule planning, decisions fall into three primary decision categories:

Structure of the activity network. Sequencing the activities, including which to execute in parallel. The decision about the network structure is discrete, choosing from among the available limited options though the possibilities may be many.

Resources and resource levels. Identifiable resources, with perhaps variable levels of commitment for each.

This straightforward project is realistically complicated by having two potential rework activities. The arrows show the precedence relationships. Branches with decimal fractions, representing probabilities, show two potential rework activities

Exhibit 1. This straightforward project is realistically complicated by having two potential rework activities. The arrows show the precedence relationships. Branches with decimal fractions, representing probabilities, show two potential rework activities.

This table shows distributions for two traditional deterministic CPM solutions, using earliest starts and latest starts. Then, the schedule shows three progressive stages of optimizing the stochastic model (on a 300 MHz Pentium II), starting from the latest-starts CPM solution. The decision variables are planned dates, in weeks, to start the respective activity. The base case in each column is the deterministic solution. The mean value—used for making decisions—represents the stochastic solution

Exhibit 2. This table shows distributions for two traditional deterministic CPM solutions, using earliest starts and latest starts. Then, the schedule shows three progressive stages of optimizing the stochastic model (on a 300 MHz Pentium II), starting from the latest-starts CPM solution. The decision variables are planned dates, in weeks, to start the respective activity. The base case in each column is the deterministic solution. The mean value—used for making decisions—represents the stochastic solution.

Planned start dates for each activity. Date/time assignments, too, are usually variable, and these sometimes need to be planned around resources with commitments elsewhere. Even within the same project, a resource critical path (i.e., critical chain) controls.

This article focuses on the optimization of the already-structured schedule model: choosing best planned activity start dates so as to minimize overall project cost and thus maximize project value.

To the extent possible, avoid having the same people work on parallel activities is one of the tenets of critical chain project management. This means restraint in starting activities. Small buffers at the end of “feeding chains” merging with the deterministic critical path minimize risk of project delay. The main buffer—to protect the customer—is placed at the end of the project. However, this view oversimplifies.

A better approach is to explicitly represent project uncertainties in a stochastic evaluation model. Decision analysis is an alternative and improvement over traditional and critical chain deterministic methods.

A Simple Project Model. Exhibit 1 shows a simple project model for delivering a custom technology system. The stochastic model embodies uncertainties in two forms: activity completion times and possible rework. Ideally, a rework activity would be modeled as a looping-back cycle until we get it right. However, representing this in the model is much simpler if we can reasonably assume that only one rework pass is required to remedy defects. The Assemble Equipment (AE) activity is singled out in this and the January article to show example information available for this activity's manager.

In addition to judgments about the need for the rework activities in Exhibit 1, Modify Software and Major Rework, project planning includes judging activity completion times, including contingencies. The planned activity start dates are the decision variables in this model.

Optimizing Activity Starts. Project planning includes when to schedule activity starts. Planned start dates are choices that can be optimized. Crew time is wasted if the actual start is after the planned start due to waiting. Opposite, the project may be delayed and crash costs incurred if the planned activity start is too late. The example model includes cost penalties for idle crews, an incentive rate for early completion, and a penalty rate for late completion. A more complete model would also include the effects of changing requirements, with the amount of rework exacerbated by premature completion; multitasking inefficiencies affecting time to complete and quality, which is worsened by premature activity starts; and correlations between times to complete various activities. Everything important to the decision should be included in the model despite that some of these details may involve highly subjective judgments.

Decision analysis is an alternative and improvement over traditional and critical chain deterministic methods.

Note that there are no explicit buffer representations in the model. Certainly, there should be slack between completion of some activities and the start dates of their successor activities. Activity and resource buffers are intrinsic to the model and not a focus item for the project manager. This reduces temptation to “waste the slack.”

Optimization Experience. Solving stochastic models is computationally more time-consuming than conventional analyses because calculations with probability distributions are so difficult. Monte Carlo simulation solves a difficult calculus problem using a simple and elegant random sampling process. Because Monte Carlo is an approximation technique, 100 to 1,000 times more computer time is needed to get reasonably precise results. Fortunately, computer power is accessible and inexpensive. Nonetheless, computation efficiency requires that project models be kept reasonably simple.

In the past two years, two stochastic optimization tools have become available for project models in Microsoft Excel spreadsheets. They use very different methods, though both have the same calculation goal:

RiskOptimizer, by Palisade Corporation. This tool uses a genetic algorithm approach to optimizing @RISK models.

OptQuest for Crystal Ball, by Decisioneering Corporation. This tool applies tabu search and neural network technologies for optimizing decision variables.

Depending upon the problem, one tool may be better than the other. My testing thus far is inconclusive as to advantage, so I've disguised the particular analysis tool used in the exhibits.

The CPM solution results for the example model are shown in Exhibit 2. Columns 2 and 3 show penalties for delay being worse than costs of early starts. The difference between the “base case” and “mean” is caused by “merge bias” (more generally called “stochastic variance”). Means should be used in making decisions. The corrections to the base case result from carrying probability distributions through the calculations.

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This chart shows sensitivity to the one decision variable. All other activity planned starts are at optimal values

Exhibit 3. This chart shows sensitivity to the one decision variable. All other activity planned starts are at optimal values.

Both earliest starts and latest starts from CPM solutions were the references. This model behaves such that an early-starts solution is nearly optimal because the penalties for late finishes dominate.

The automated optimization started with the latest-starts values for activity start dates. After three computer-hours, the mean project cost fell from $242K to $233K. Another five hours further, the mean cost dropped to $226K. Then, operator-guided optimization finished the job, resulting in an expected value cost of $222.6K. With 5,000 trials, the standard error of the mean is approximately $0.6K.

Monte Carlo simulation solves a difficult calculus problem using a simple and elegant random sampling process.

An intelligent automated assistant could guide most or all of the optimization. Further, another automated assistant could guide the activity network construction, which I'll explore in a future article.

Three exhibit figures in the January PM Network article show distributions useful for the manager of an Assemble Equipment (AE) activity. Those exhibits were generated before the final hand-optimization round.

Here, Exhibit 3 shows the sensitivity to the planned AE activity start date in the stochastic model. This would enable the activity manager to optimally plan the activity's start date. We could show a distribution for the time between activity AE's completion and the start of the next-starting successor activity, though this is unnecessary, and people checking on the distribution of the implicit buffer might be tempted to waste slack. The criticality index for AE is 0.32, meaning that AE has a 32 percent chance of being on the critical path and directly affecting time to complete the project.

DECISION ANALYSIS PROVIDES a more realistic and more accurate representation of the project. As such, the project manager is better informed when making decisions under uncertainty.

The core theme in critical chain project management is to avoid wasting slack. Rather than planned intervals, buffers are revealed as distributions in a stochastic model. The reality is that there isn't a confident amount of slack available to waste. Focusing on project value provides a better perspective for making decisions.

The next two articles in this series will discuss ways to express judgments about resource availability, productivity, and other uncertainties. ■

John Schuyler, PMP, of Decision Precision in Aurora, Colo., provides training and assistance in economic decision analysis and in project risk management. Questions about this article should be directed to [email protected]. Comments on this series should be directed to [email protected].

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This material has been reproduced with the permission of the copyright owner. Unauthorized reproduction of this material is strictly prohibited. For permission to reproduce this material, please contact PMI.

March 2000 PM Network

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