Planalyzer-2

Contents

Planalyzer-2 is an advanced software tool for express quantitative analysis and day-to-day schedule/WBS management of risky industrial projects. It also improves new schedule-cost applications (such as JCL), assesses lower-risk projects (Government, oil/gas etc.) on file-specific basis, analyzes business plans of government-backed ventures and compares competing proposals.

System Requirements

CPU: Pentium III or later; Memory: 512MB or more; Required disk space: 300 MB; Operating System: Windows.

Required Software: Microsoft Project 2003 or later; Microsoft Excel 2003 or later.

Introduction: Historical Approach to High and Low, Static and Dynamic Risk

Project duration and cost always differ from their planned values (below, repeated references to costs will be often omitted for brevity). Considering activity durations random variables does not explain why projects usually last longer than planned, or why deviations towards shorter durations are much less frequent than deviations towards longer durations. To account for this asymmetry, project schedules are declared to depend on "risks", or external circumstances directing variations of project activities towards "bad outcomes". Risk Management became a conventional routine predicting schedule delays and providing mitigation of risk qualitatively and quantitatively. Applicable to all types of projects, the idea of risk might take very different shapes; though respective theoretical understanding is very subtle, different forms of risk assessment and mitigation are well established in practice. To clarify the matter, consider two "projects" with different risk profiles. Let patient visit the doctor's office; the doctor makes a plan how to cure him minimizing recovery time and side-effects. Bills, as usual, are paid by insurance companies interested not in the specific but rather "statistically justified" patient. Obviously, the risk assessment should be based on well-known historical "expert opinions" and Monte Carlo simulations of cost probability. The second example is a high-risk project; imagine a passenger flying overseas, with his schedule showing that "historical" probability to reach the airport on time is very small. To catch the plane, he has to speed (high risk) and have a dynamic route plan with very high (within seconds!) accuracy minimizing the required time. For this project, the conventional quantitative approach is virtually useless. What works is a qualitative express analysis with ready-to-go dynamic plans to "monitor and prepare to act" ( low risk) to "immediate implementation of risk response plan" (high risk). For dynamic risks, the response should be also dynamic; for the air passenger it means developing, on qualitative or quantitative basis, a real time route navigation, for risky industrial project - a day-to-day risk monitoring routine followed by updates and decisions at the management meetings.

Planalyzer-2 offers a quantitative tool for dynamic and/or risky projects. Today, the field of quantitative risk assessment is dominated by "historical approach" based on definition of activity distribution functions from "expert interviews" followed by Monte Carlo simulations of the final milestone/WBS Total probability. Though reliable, accurate and mandatory for several government entities, this methodology is still barely accepted by the Project Management community, almost never applied to day-to-day schedule/WBS management and has very limited commercial market. One reason is much higher cost of the quantitative analysis; also, the historical approach is inert and unable to provide instant feedback to schedulers and planners because it operates not with data taken from the project itself but rather with a "replica" projects compiled from activities with historically justified distributions. The execution management, to the contrary, makes all possible efforts to minimize the final milestone delay or cost overrun of the given project by compensating uncontrollable variations of some activities by re-formatting other activities. These management actions depend primarily not on the activity itself, but on its "environment", e.g. on specific project details. Unless these actions are described in the mathematical algorithm, the history-based quantitative schedule and cost analysis will stay a useful, but stand-alone "driving with a rear-view-mirror" approach.

In Planalyzer-2 algorithm, the activity uncertainties expected at the execution stage and currently determined from expert interviews, are calculated within a new theoretical model directly from the schedule.

Uncertainty in Negatively Correlated State

In the execution, if one of the activities is delayed beyond the management team's power, efforts are made to compensate for the delay by shrinking or re-formatting other activities (for example, by re-distributing resources). Thus, the activities are strongly (negatively) correlated rather than statistically independent. The state of negative correlation is easily explained verbally but difficult to describe analytically. For example, if arbitrary variations are applied to the set of independent activities, exact adjustment to the same milestone date or $Total is impossible. The model of activity distribution function has only one parameter (time/$) and is inadequate; to accomplish the goal, the statistically independent elements have to be "re-normalized" and operate with at least two independent parameters, one responsible for the activity variation, and another one - for adjustment to milestone/$Total.

Model

The following figure introduces the re-normalization procedure in the negatively correlated state on the example of a simple six-element WBS.

To emphasize strong negative correlation, the first (blue) WBS element is "summed" (connected) with all other elements by springs imitating system elasticity: when the length of the first element changes, the lengths of all other elements also change to adjust the "$Total" cost to the planned value. The system of correlated WBS elements shown in the figure may be interpreted as a series of spring-loaded heavy masses; if one of the masses moves, its movement is transferred through springs to other masses causing propagation of a classical wave with the wave period defined by parameters of springs and masses. By direct analogy, each WBS element is associated with its own wave; in the vicinity of $Total, all waves interfere, and normalized intensity of the interference pattern presents the probability density. There is no paradox, the statistics of independent activities/WBS elements adequately defined as "bricks" of time or $ converts into statistics of waves if these activities are negatively correlated. In case of schedule, the resulting wave diagram presents the set of correlated activities exactly as the Gantt Chart presents the same set of independent activities. In the following paragraphs, the model of uncertainty and risk in negatively correlated state is applied to several types of project files, with more detailed discussion of the wave formalism left for Appendix 1. Planalyzer Model of Risk and Uncertainty.

Application to Summary Level Projects, Example: "Satellite"

The file presents a typical early stage project of manufacturing, testing and launch of a new satellite and rocket engine. The figure below is the project Gantt chart of statistically independent project activities drawn as bricks of time with their Start and Finish dates, superimposed with a Wave chart presenting each activity in the negatively correlated state by a wave, propagating towards the milestone.

The next figure explains why the model of negatively correlated activities is much more appropriate and powerful than the model of their statistical independence. This figure shows schematical functional dependencies between CoVs (Coefficient of Variation, ratio of Variation to Mean) of activities and milestones for both models. The straight blue line is a functional dependence between CoVs of milestone and statistically independent activities. Analytically, any point on this straight line has the same probability to represent the project; to determine the expected CoV from historical perspective, expert interviews may be conducted asking for the activity uncertainty, or triangular distribution with (MostLikely -Low) = (High-MostLikely).

Similar result, however, may be achieved in the model of negatively correlated activities without expert interviews, directly from the schedule analysis. This model is presented in the figure by a hyperbolic function reflecting the fact that for large variation of correlated tasks, the width of wave phase correlation function in the vicinity of milestone narrows down. The intersection point is a result of Monte Carlo simulations of the project "history" given by the model of negative correlation; if this history is similar to the "conventional" one obtained from the expert interviews, the average CoVs (intersection points) could be very close.

The next figure demonstrating uncertainty of the project milestone is a typical interference pattern centered at the planned milestone date. Each activity duration was normally distributed, and many Monte Carlo project samples (30 in the figure) were analyzed.

The data are file-specific and include, in obvious advantage to the historical approach, all project activities. To include risk dependency, additional (external to the project file) information is still required.

Schedule (WBS) Risk

In the new model, unlike uncertainty characterized by full negative correlation of activities in the vicinity of milestone, risk is introduced as a result of partial correlation. Full correlation means that in the process of Monte Carlo simulations, when the activity durations and their respective wavelengths change, the wave phases at the milestone remain fixed (meaning that no matter how the durations change, it is still possible to fully restore the schedule and keep the milestone date unchanged). The situation becomes different if the correlation is partial meaning that the task variation could not be fully compensated and some fraction of it shows up at the milestone. A typical result is shown in the following figure:

The interference pattern (probability density) becomes strongly asymmetrical; milestone S-curve (black line) predicts 1500 days contingency and has increased, compared to full compensation, by an order of magnitude. All these changes caused by only one parameter (degree of phase compensation) is natural to link to manifestation of qualitatively defined risk, with risk = 0 corresponding to milestone uncertainty (full phase compensation). To make the results realistic, risk scale has to be calibrated against the degree of phase compensation, and this has to be done by careful comparison with historical data; however, there is one point on the risk scale that allows to make some reasonable conclusion without any additional information, directly from the project file. This is the point, when all task variations appearing in the Monte Carlo simulations are transferred directly to the milestone (case shown in the figure). On the scale from 0 to 1, respective risk is convenient to associate with risk = 0.5 (to keep some room for manifestation of higher risk). The result is file-specific and allows for preliminary judgment of "average" risk manifestation.

Risk Register Input

Beyond "autonomous" information on schedule uncertainty and average risk obtained directly from the project file, Planalyzer-2 provides results with more traditional user inputs through risk register and individual variations of project activities. "Risk Register input" communicates user-operated risk map, usually 5x5 risk color matrix, with the algorithm calculating PDF and S-curve. The Risk Table (see figure) has 19 risk categories separated in 3 groups: Cost Risk, Performance Risk and Management Risk. Risk items are editable (user might edit existing risk item or suggest his own one, and Risk Register will be saved as part of the milestone file).

The default Cumulative risk value = 0.5 is assigned to numerical parameters of Schedule (WBS) Risk calculated in the previous paragraph. All other cumulative risk values are scaled to these parameters. Thus, the need for quantitative Low, High and Most Likely inputs is avoided, and qualitative evaluation of Likelihood and Consequence in each risk category provides meaningful probability density and S-curve. The function linking activity CoV and cumulative risk is shown in the figure:

For all projects, Cumulative risk = 1 corresponds to CoVs = 25%. (maximum risk is set to describe variation of each activity within 0.5 to 2 times of its initial duration). CoVs corresponding to all other risks > 0 are project-specific; two different projects have, depending on project maturity, different contingencies for the same risk level.

The following figure demonstrates reduction of milestone contingency when cumulative risk reduces from 0.5 (left figure) to 0.1 (right figure). It also shows that even at small risk, the milestone uncertainty is still substantial (compare with Task CoV input where small CoV automatically means low uncertainty).

Together with Schedule (WBS) Risk, Risk Register input provides objective comparison of competing proposals and estimates risk acceptable for given schedule (WBS).

Task CoV Input

"Task CoV input" defines milestone or $Total contingency as a function of activity CoV suggested by user and obtained in expert interviews. Thus, it is a bridge between the conventional and new algorithms. The input works as an iteration to Schedule (WBS) Risk where the "average" contingency and CoV were determined, and needs only one parameter (CoV), instead of 3 parameters (L, ML and H) needed for conventional simulations.

Task CoV input is conducted through the interactive table

initially filled by "average" CoV values calculated in Schedule (WBS) Risk procedure. Filled CoV Table may be saved as part of the milestone file. The following figure demonstrates effect of small CoV and shows another distinction between risk and uncertainty compare with Risk Register input where small risk might co-exist with large uncertainty).

Task CoV input also calculates Average CoV suggested by user, and compares it to CoV calculated from schedule. If Average CoV > Schedule CoV, there is no need in further schedule detail. However, if Average CoV < Schedule CoV, this is an indication that schedule (WBS) is too coarse and has to be finessed.

Application to Late Stage Projects; Gate Milestones

Late stage projects need, before analysis, some user input. In a late stage project, its sub-projects become increasingly independent from each other, and correlation between activities belonging to different sub-projects becomes very small. Still, correlations stay strong within sub-projects making the negative correlation model applicable to them and leaving calculation of the final milestone to conventional Monte Carlo simulations of the network of sub-projects. Thus, the analysis of large projects requires definition of sub-projects that might be considered negatively correlated; the new approach might be applied to these sub-projects separately, with the rest of the analysis similar to the conventional approach.

In Planalyzer algorithm, the sub-projects are usually identified as Summaries with milestones at their ends separating the project into several parallel or sequential sub-projects. Each of these sub-projects has a final milestone called Gate Milestone. The following Table of Gates is an example of milestone "network" with milestone 6 gated by milestone 5, milestone 7 - by 6 and 47 in parallel, and milestone 9 - by 7, 8 and 59 in parallel. With the Table of Gates, user designs a milestone "network" of arbitrary topology - a full analog of "Summary" network in the conventional methodology. To that extent, grouping of negatively correlated activities and designing the "Summary" network relies on experience and project understanding by expert or analyst, and makes analysis of large projects similar to conventional risk analysis.

The following figure compares milestone S-curve and probability density with and without gate effect, and shows how a multi-modal interference pattern converts to the almost normal distribution well familiar to risk practitioners.

Application to Planning and Execution

Planalyzer improves project schedules by correcting file errors and modeling schedule modifications that reduce project risks. Error correction includes finding "orphan tasks", or activities not reporting to any milestone, and milestones having no activities, or just one activity reporting to them. This analysis of the file integrity is usually done by schedulers and is unrelated to risk analysis, but in the Planalyzer algorithm, the results of file analysis depend on errors directly. Thus, correcting errors becomes a mandatory procedure leaving no room for "improving file quality later".

The second tool is Task CoV input that models, by reducing CoV of an activity or a group of activities, the milestone contingency (for solitary activities, this problem is also addressed by Tornado Chart (see Other Functions). In many cases, reduction of CoV of several activities might substantially reduce the milestone contingency. No general recipe may be offered for this action but usually milestone probabilities are mostly affected by the longest and poorly-determined activities. CoV reduction may be achieved by more careful activity management or by sub-division into several activities.

Specifics of WBS analysis

Unlike well-defined Microsoft Project files, Microsoft Excel files might have arbitrary formats. To analyze WBS presented by Excel file, Planalyzer requires specific file format (see figure below):

All "Baseline" estimates of the second column should sum together to the second column "TOTAL"; for each row, the sum of "FY 200..." should be equal to its "Baseline". The file format is verified by "Check file" command from "Actions" menu.

Other Functions

Correcting Errors

When clicked by user, Error Correction returns Table of Errors listing Orphan Tasks, Empty or one-task milestones and mis-assigned tasks. Orphans are tasks not reporting to milestones directly or through their successors. Milestones having no reporting tasks or just one task are considered errors. Tasks are considered mis- assigned if they end after the milestone they report to. In WBS case, errors are arithmetical: wrong "Totals" for overall project or for specific fiscal year.

Analysis Summary

When user chooses "Analysis Summary" from Action menu, Analysis Summary Table is returned listing four milestone parameters from the project file (ID, name, scheduled date and number of reporting tasks), and four parameters calculated by Planalyzer: Task CoV, Schedule 70% Contingency, 50% and 70% confidence level date.

All data presented in Analysis Summary Table are obtained from schedule or WBS without user input. By code setting, only milestones with 10 or more reporting tasks are analyzed ; this threshold may be changed by custom order. When one of the milestones with 10> tasks is checked, the Function Panel shows up and offers 4 different options for more detailed analysis: Schedule Risk, Risk Register Input, Task CoV Input and Tornado Chart.

Tornado Chart

"Tornado Chart" evaluates relative "importance" of milestone tasks by evaluating reduction of milestone probability caused by each task variation.

In calculations of the milestone probability, only one task is considered risky, and all other tasks introduce zero risk. The procedure is repeated for all tasks and puts most harmful ones on the top of the list.

Tornado Chart attracts project manager's attention to most harmful tasks and has the same content as in conventional Monte Carlo simulations.

Troubleshooting

If program encounters a problem and can not open the file for analysis, general message is sent by internal executable file:

Usually, this message is caused by some problem with the original ".mpp" or ".xls" files. Most frequently, these errors indicate that file's milestones are not associated with tasks, or file has no milestones at all. Error could also be caused by obsolete version of Microsoft Project, or some action expected from the user, such as adding or removing links with other project files.

After the error is corrected it could be necessary to manually remove the text (.txt) version of the file from the folder where all analyzed filed are stored (trial version). In the full version, this purpose is served by special command "Reset" in "File" menu.

Contact

Ibico, Inc

www.ibico-cor.com

Office hours: M - F 9 am to 5 pm PST

Telephone: 650.224.1620

Fax: 650.856.9884

Email: support@ibico-cor.com

Ibico team appreciates user feedback especially if our and conventional results diverge.

Appendix 1. Planalyzer Model of Risk and Uncertainty

This Appendix introduces some analytics describing activities by waves in negatively correlated systems. The figure below is a Gantt Chart of a two-task project and a milestone.

Both tasks are associated with waves having periods equal to activity duration, propagating towards the milestone:

where task durations D and phases are different for both waves.

Intensity of the interference pattern I is calculated as square of the sum

and probability density P is a normalized intensity I.

The state of negative correlation (adjustment to the planned milestone date) is described by different phase distributions. If both tasks are statistically independent and normally distributed, the conventional milestone distribution is also normal. Different states of correlation are presented by distributions with the same mean and different dispersion values, from

for full negative correlation to

for full positive one.

The following figure shows the distributions for intensity and phase, with both tasks having CoV = 0.25:

For fully correlated phases, the phase distribution is a delta-function (dispersion is zero). The intensity distribution is symmetrical relative to the milestone and is interpreted as the milestone uncertainty: even though the phases are fixed, the milestone date is not determined exactly. Next figure shows the phase and intensity distributions for phase CoV = 0.25 which corresponds to statistically independent tasks (no correlation):

In this figure, milestone distribution in time is combined with phase distribution where phase is measured in units

The distribution of phase is normal and symmetrical, but the intensity distribution is strongly asymmetrical and shifted to longer date. The intrinsic reason for that is that the phase shift to the right is caused by waves with longer periods, and shift to the left - to shorter periods. All longer waves are accumulated to the right, and all shorter ones - to the left of the milestone. Interference contribution from longer waves is substantially higher than from shorter waves causing shift of the interference pattern mean.

The next figure shows the case of task CoV = 50%, (full positive correlation)

Qualitatively, it is not different from the previous figure, with asymmetrical intensity distribution and further shift to longer date. Increased dispersion of phase (higher risk) does not necessarily mean wider distribution of intensity but rather shift to later times.

The following figure goes back to Application to Summary Level Projects, Example: "Satellite" and shows relations between task and milestone CoVs of "Satellite" project for statistically independent (blue lines) and negatively correlated (red line) activities:

Self-consistent system description independent of the correlation state is achieved only in the intersection point of the straight line (statistical independence) and the hyperbolic function (model of strong correlation). Depending on the schedule structure, the straight line tilt is determined by the structure of links. For all tasks linked sequentially (thin blue line),task and milestone CoVs are equal, and for schedule without links, milestone CoV is less than task CoV (marked blue line). In Planalyzer-2, we have chosen the worst-case scenario:

(cross-section of red marked and thin blue line in the figure). This CoV value depends on the degree of schedule/WBS detail and varies, for different schedules, from ~2% (late stage) to ~ 15% (early stage) projects. Respective milestone contingency is published in Analysis Summary Table.

Iterations, Signal and Noise

Number of Iterations chosen from "Iterations" menu defines number of Monte Carlo simulation samples. In terms of signal-to-noise ratio, statistical analysis of waves is more efficient than conventional Monte Carlo analysis leaving only one point on the time axis after each simulation cycle; in the wave analysis, random harmonics are summed along the full time axis. Default number of iterations = 30 is often adequate for project analysis. If noise is too large user can increase number of iterations before the "Analysis Summary" step. Still, the number of iterations defines signal-to-noise:

Qualitatively, high intensity peak near the milestone corresponds to all N harmonics summed almost in phase:

Far from the milestone, harmonics amplitudes are added randomly, providing intensity

Thus, for large number of iterations N, signal-to-noise ratio

These relations well-known in optics, laser physics and radio/microwave antennae design show the origin of sharp and narrow milestone peaks in wave modeling.

Published with MATLAB® 7.5