WO2006119437A2  Method and system for managing project work using bayesian inference  Google Patents
Method and system for managing project work using bayesian inference Download PDFInfo
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 WO2006119437A2 WO2006119437A2 PCT/US2006/017165 US2006017165W WO2006119437A2 WO 2006119437 A2 WO2006119437 A2 WO 2006119437A2 US 2006017165 W US2006017165 W US 2006017165W WO 2006119437 A2 WO2006119437 A2 WO 2006119437A2
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Abstract
Description
METHOD AND SYSTEM FOR MANAGING PROJECT WORK
USING BAYESIAN INFERENCE
Inventor:
Deepak Kishore Kanungo
Assignee: CyberAlliances, Inc.
REFERENCE TO RELATED PROVISIONAL APPLICATION
[0001] This application claims the benefit of the filing date of U.S. provisional patent application Serial No. 60/677,296, filed May 3, 2005, by Deepak Kishore Kanungo and entitled METHOD AND SYSTEM FOR MANAGING PROJECT PORTFOLIOS USING BAYESIAN INFERENCE.
BACKGROUND
Field of the Invention
[0002] This invention is a method and system that permits the continual revision of forecasts of effort, budgets, schedules, resources and other project work metrics (collectively measurables) of projects, project programs and project portfolios (collectively project work) based on work in progress data reported on, for example, time sheets and expense reports by those responsible for creating deliverables, i.e. deliverable owners, so that managers can use such timely yet limited information to optimize their project work dynamically in the face of uncertainty. The invention accomplishes these ends through the application of Bayesian Inference, an alternative probability and statistical theory, to create a framework for managing risks and returns of project work. The system can be implemented on a wide range of platforms, including a clientserver system.
Background of the Invention
[0003] Managers of projects, project programs or project portfolios must determine on an ongoing basis, and based on variables whose ex ante projected and actual values often differ, the estimated resources  human, financial, physical and temporal  necessary to complete the projects, project programs or project portfolios.
Express Mail No. EQ 367318743 US 2 [0004] Projects are defined as temporary, nonoperational endeavors undertaken to create a unique product, service, or result in the face of uncertainty and resource constraints. The product, service or result of a project can vary widely and include endeavors as disparate as developing software, constructing physical assets such as buildings, developing a new type of capital good, such as a new type of aircraft or a developing a new consumer good, such as a new line of home furniture. Project management requires the application of knowledge, skills, tools, and techniques to ensure that project activities meet project requirements.
[0005] In the context of project management, a program consists of a group of related projects and other work managed in a coordinated way to obtain benefits and control not available from managing them individually. Program management involves the centralized coordinated management of a program to achieve the program's objectives and benefits.
[0006] A portfolio refers to a collection of projects and/or programs and other work that are grouped together to facilitate effective management of that work to meet specific business objectives. In contrast to a program, a portfolio need not be comprised of projects or programs that are interdependent or directly related. Portfolio management involves the centralized management of one or more portfolios, which includes identifying, prioritizing, authorizing, managing . and controlling projects, programs, and other related work, to achieve specific business objectives.
[0007] Project, project program and project portfolio shall be referred to herein collectively as "project work." The scope of project work is typically organized into discrete work packages or deliverables that are then delegated to different team members each of whom is required to produce and present deliverables within specified time, financial and other resource constraints.
Express Mail No. EQ 367318743 US 3 [0008] A manager seeking to establish a budget and schedule for completion of project scope faces challenging uncertainty that may be classified into two fundamental categories: ontological and epistemic. Ontological uncertainty (also called aleatory uncertainty) derives from the inherent variability of the nature of the world. It does not depend on the observer or the completeness of information about the process being observed and is therefore termed "objective." For instance, no amount of information about a fair coin will result in increasing the certainty of prediction of the next toss for any observer. On the other hand, epistemic uncertainty arises from the state of knowledge of the observer of the uncertain process and is therefore termed "subjective." As the observer's state of knowledge increases, epistemic uncertainty decreases. For instance, an observer may make an estimate, with a confidence level and error range, regarding the weight of a coin. However, the observer's knowledge may be increased, and this epistemic uncertainty may be eliminated altogether, by actually weighing the coin. \
[0009] Ontological uncertainty can be modeled using the traditional or "Frequentist" notion of probability. These Frequentist methodologies model probabilities of future events based on a theory of probability that computes the probability of an event occurring, given a certain scenario, based on the number of times (how frequent) the event has occurred in the past under the same conditions. In other words, if an experiment is repeated n times under essentially identical conditions, and if the event A occurs m times (frequency), then as n grows large the ratio m/n (relative frequency) approximates the probability of A. However, epistemic uncertainty cannot be modeled using a Frequentist notion of probability and requires the alternative, or Bayesian theory of probability.
Express Mail No. EQ 367318743 US 4 [0010] Frequentist notions of probability are difficult to apply and interpret in any real life situations  such as those that arise in project work  where events tend to be unique and infrequent, rather than repetitive and identical, as assumed by Frequentist notions of probability. For instance, what is the probability that a prospective customer will award a company the project contract? Because project work is by definition unique, epistemic uncertainty tends to dominate ontological uncertainty. However, project managers currently use Frequentist methods, such as Monte Carlo Simulation, for modeling both ontological and epistemic uncertainty in projects, which results in erroneous results especially in cases where the historical data on which it is premised is incomplete.
[0011] Current systems for managing uncertainty relating to project work also tend to be point or incomplete solutions because of the Frequentist probability framework on which it is based does not include a framework for incorporating incomplete information presented by work in progress. Such systems fail to be comprehensive and to integrate all steps necessary to manage uncertainty in project work from initiation to closure. For example, the predictive analysis of random variables, i.e. stochastic analysis, under current systems for managing project work is carried out separately from the actual managing of the project work.
[0012] Bayesian Inference is the only framework in the theory of probability and statistics by which managers can model ontological and epistemic uncertainty in project work and manage it on an ongoing basis based on new information gained from work in progress. Frequentist methods, whether analytical, numerical or simulated, model only ontological uncertainty and are therefore insufficient for managing the total and dynamic nature of uncertainty inherent in project work
Express Mail No. EQ 367318743 US 5 [0013] Predictions of project work resource consumption made before the work begins generally needs to be revised repeatedly once the work begins with such revisions informing the collective state of knowledge of the entire team. Projects proceed in stages with each stage often comprised of several deliverable owners. The completion of work in one stage being on time and within the original budget and other constraints depends on each of the independent deliverable owners completing its deliverable in timely fashion and within budget. Wrongly predicting or failing to revise the timeliness or costliness of work by one or more deliverable owners at one stage throws off projections concerning the completion of the next stage of the project, because work on the next stage often utilizes deliverables completed by deliverable owners in the previous stage.
[0014] As explained above, existing methods and systems for managing project work represent a poor fit for the complex nature of uncertainty inherent in project work. Current methodologies offer no systematic method for managing epistemic uncertainty and revising original estimates of stochastic quantities to reflect work in progress data. As a result project work managers often make no attempt at revisions of stochastic quantities or alternatively provide point estimates of stochastic quantities giving a false sense of certainty and compromising effective project work management.
SUMMARY OF THE INVENTION
[0015] The present invention advances a superior method and system for managing project work risks and returns of effort, budget, schedule and resources by building a framework for modeling and managing both ontological and epistemic uncertainty using Bayesian Inference.
Express Mail No. EQ 367318743 US . 6 [0016] B ayes' theorem provides the basis for computing the probability that a prediction (H) is true given additional, subsequent evidence (E). H represents a belief or prediction from some set of observations that is prior to observing of additional evidence (E). Bayes' theorem is represented by the equation: P(HpE) = P(EH) * P(H)TP(E).
[0017] The term P(H) represents the prior probability of H  the probability that hypothesis H is true before taking into account new evidence E. The lefthand term, P(HE) is called the posterior probability of H, given E, and represents the probability that hypothesis (H) is true after taking into consideration additional evidence (E). The term P(EH) is the likelihood function, and it gives the conditional probability of seeing the evidence (E) assuming the hypothesis (H) is true. The last term, P(E), is independent of H, and can be regarded as a normalizing or scaling constant.
[0018] The Bayesian theorem thus provides an analytical framework for repeatedly and dynamically recomputing the effort, budget, schedule, resources and other project work measurables likely to be necessary to complete a given project work, in light of actual work in progress data such as percentage work complete, error estimates for percentage work complete, time, cost and revenue. As each new piece of information is factored in, its effect on the probability that the preceding predictions regarding project work measurables are correct is computed to arrive at a new posterior probability function. That posterior probability function then serves as the new prior probability function in computing a revised posterior probability function based on the latest set of actual work in progress data.
[0019] More formally, the method involves using preproject work estimates for project work measurables of anticipated project work deliverables to create the initial prior probability distributions, P(H), for
Express Mail No. EQ 367318743 US 7 predicted project work measurables such as effort, budgets, schedules and resources of the project work, continually revising the likelihood functions, P(EH) for such project work measurables based on updated work in progress data from deliverables owners, using the prior probability distributions and likelihood functions, adjusted for the scaling factor, to update the posterior probability distributions, P(HE) for such project work measurables. The system can repeat these steps based on updated work in progress data using the calculated posterior probability function as the new prior probability function to compute a new posterior probability function based on the next round of actual work in progress data. Finally, during the closing of the project, the project manager can check the accuracy of the forecasts for project work measurables with actual outcomes to determine whether to modify or replace various statistical distribution functions used within the model and to adjust for biased estimates by particular deliverables owners.
[0020] The method encompassed by this invention can, but is not required to, be implemented as a web based application that follows the standard clientserver architecture.
[0021] Additional ways of implementing the method include but are not limited to using a standard multitier or NTier architecture, employing the method on a desktop computer or handheld device, and implementing the method using wireless networks accessible by handheld wireless devices.
BRIEF DESCRIPTION OF THE DRAWINGS
[0022] The objects, advantages and features of the invention will become more apparent by reference to the drawings, which are appended hereto and made a part hereof.
[0023] Figure 1 depicts the basic steps required to manage project work using Bayesian inference.
Express Mail No. EQ 367318743 US 8 [0024] Figure 2 illustrates numerically the derivation of the prior probability distribution for total project effort in the context of managing a software development project based on projected figures, estimated prior to beginning work on project deliverables.
[0025] Figure 3 represents work in progress data for hours actually spent on the software development project five weeks into the project together with estimates of how much work has been completed and the error range involved in making that estimation.
[0026] Figure 4 represents the likelihood function, which uses work in progress data available at the end of week five to revise the estimates of effort for deliverables that remain in progress. .
[0027] Figure 5 illustrates numerically the derivation of the posterior probability distribution for total project effort in the context of the same software development project based on the likelihood function and the prior probability distribution.
[0028] Figure 6 shows a client server system configured to enable the method herein.
[0029] Figure 7 illustrates how a manager can interact with a client system such as a web browser to input critical information necessary to create prior probability distributions for project work measurables.
[0030] Figure 8 illustrates how a server processes information received from a client system to create the prior probability distributions for project work measurables.
[0031] Figure 9 shows how a deliverable owner uses a client system to submit work in progress timesheet data.
[0032] Figure 10 shows how a deliverables owner would use a client system to submit nonlabor related work in progress data
Express Mail No. EQ 367318743 US 9 [0033] Figure 11 shows how a project manager or other user would use a client system to enter work in progress revenue data.
[0034] Figure 12 shows how a server uses work in progress data received from a client system to develop likelihood functions and posterior probability distributions for project work measurables.
DESCRIPTION OF THE PREFERRED EMBODIMENT
[0035] This invention's methodology for managing project work using Bayesian inference is depicted in Figure 1. A project work manager first estimates the project work measurables such as effort, budget, schedule and resources required to complete the work 10. The estimates are used to create prior probability distributions P(H) for the project work measurables 12. Once the project work begins, the system collects work in progress information, such as data regarding time spent on project work, percentage work completed, estimating error for percentage work completed estimate, cost of project and revenue generated from the work from deliverables owners, keeping in mind that a project work's budget is simply an aggregation of its costs and revenues 14. The system uses this work in progress data to create the likelihood functions P(EH) for project work measurables 16, keeping in mind that a project work's budget is simply an aggregation of its costs and revenues. Because the posterior probability is the product of the likelihood and pirior probability functions, adjusted for the scaling factor, the updated likelihood functions can be used to compute the posterior probability distributions P(HE) for the project work measurables 18.
[0036] The method can be repeated 21 to obtain revised estimates of measurables as more project work is completed and more work in progress information becomes available. The just computed posterior probability distributions become the basis for the revised prior probability distributions
Express Mail No. EQ 367318743 US 10 P(H) for that next round of project work 12. Updated work in progress data from deliverable owners will then be available to the project work manager on, among other things, percentage work completed, estimation error for percentage work completed, time, cost and revenue 14, which then underlies the computation of revised likelihood functions 16. The revised prior probability and likelihood functions generate revised posterior probability functions 18, which in turn serve as the prior probability distributions for project work measurables for the next stage of the project work.
[0037] Upon completion of the project work, the manager can check and attempt to correct for modeling error and bias by comparing the pre project work estimates for project work measurables with the actual figures upon project work completion 20.
[0038] This invention's method thus permits repeated revisions of project work measurable estimates to reflect actual work in progress data generated as the project work proceeds. The work in progress data generated will often be in the form of time and expense sheets submitted by deliverable owners on an ongoing basis but can also be derived from emails, letter, verbal discussions and through invoices.
[0039] The methodology claimed by this invention can be illustrated numerically using a software development project as an example. As is the case with projects more generally, the scope of project work is broken down into components or work packages whose completion requires the creation of deliverables by those tasked to complete the deliverable, i.e. deliverable owners.
[0040] As part of project planning, the manager obtains estimates of effort, in units of time such as hours, by eliciting low, base, and high estimates of effort, from each deliverable owner with low estimates defined as a 5% probability that the actual values will be at or below estimate; base
Express Mail No. EQ 367318743 US 11 estimates defined as a 50% probability that the actual values will be at or below estimate; and high estimates defined as a 95% probability that actual values will be at or below estimate.
[0041] The three estimates provided by each deliverable owner are used to construct the cumulative prior probability distribution for all effort required to complete the project. This preferred embodiment employs the Three Point Approximation Method or the Fractile Method.
[0042] The Three Point Approximation Method uses the low, base and high estimates provided, together with assumptions on the appropriate statistical distribution to apply, to compute the expected value (or mean value) and standard deviation for effort required to complete each deliverable, which in this example is measured by hours expected to be expended by a person. If the computations for the Three Point Approximation are based on the PearsonTukey statistical distribution, then for each deliverable owner: expected value = 0.63*Base + 0.185*(Low + High) and variance = 0.34*(High  Base) + 0.28*(Base  Low).
[0043] Other statistical methods or distributions may also be used to create a prior probability distribution based on estimates provided by deliverable owners.
[0044] The expected value for effort required to complete the entire project is the sum of the expected value of effort required of each deliverable owner. If each deliverable is independent or conditionally independent of the others, then the sum of the variance for each deliverable owner represents the variance for the entire project, with the square root of that figure representing the standard deviation. This condition of independence is sometimes called "Naive Bayes" or "Idiot Bayes" and has been shown to produce superior results despite the simplicity of the assumptions.
Express Mail No. EQ 367318743 US 12 [0045] Figure 2 illustrates the numerical derivation of the prior probability distribution for this software development example using the Three Point Approximation Method and an assumption that the distribution of estimates for a given deliverable owner is correctly represented by the Extended PearsonTukey distribution. This illustrative example makes the simplifying assumption that the software development project can be disaggregated into six major deliverables, which are organized under the column project deliverables 22: project initiation 22a, requirements analysis 22b, solution design 22c, software coding 22d, testing and debugging 22e and product rollout 22f .
[0046] The low 24, base 26, high 28, expected 30, and deviation 32 columns in Figure 2 depict the low, base and high estimates for effort required, which is measured in personhours estimated to be expended in this example, for each of the six deliverables, which are then used to compute the expected value and standard deviation for total effort required.
[0047] The bottom most row 34 of Figure 2  "Total Project Person  Hours" summarizes the low 34a, base 34b, high 34c, expected 34d, effort required values for the project as a whole, each of which is simply the sum of the work required values for the individual deliverables. The standard deviation of the project effort 34e is calculated by squaring each individual standard deviation, adding them and then taking the square root of the sum. Figure 2 shows that the estimates of total effort required to complete the software development project based on estimates by individual deliverables owners provided before work on the project begins has an expected value of 1535.9 personhours 34d and a standard deviation of 139.7 personhours 34e. Because the estimates for effort required for individual project deliverables are subject to many small variations, their sum  the total effort
Express Mail No. EQ 367318743 US 13 required  should approximate a normal distribution, consistent with the Normal Approximation Theorem.
[0048] In sum, the prior probability distribution for total effort required to complete the project has an expected value of 1535.9 person hours, a standard deviation of 139.7 personhours and is normally distributed. Normal tables allow the manager to predict the probability with which the total effort required to complete the project will fall at a certain level. For instance, the Zscores in normal tables show that, given a normal distribution with an expected value of 1535.9 personhours and a standard deviation of 139.7 personhours, there is a 95% probability that the total effort required to complete the project will be at or below 1766 personhours (1536 personhours + 1.64 * 140 personhours).
[0049] Once work on the software development project begins, the system begins to compile data on the effort actually required in order to compute the likelihood function P(EH) and then the posterior probability distribution P(HpE).
[0050] The cumulative effort measured in time t actually spent on a given deliverable is measured directly by adding up all the hours logged by the deliverable owner for that deliverable. When logging the time, the deliverable owner is also asked to estimate the percentage of work completed on the deliverable, α, within an error range, ε.
[0051] Error, ε, in the value of α arises because of ontological uncertainty inherent in the nature of work itself and epistemic uncertainty arising from the state of knowledge about the work in progress. This error may be quite large during the initial stages of the project work but generally gets progressively smaller as more information about the deliverable is acquired and work in progress is validated.
Express Mail No. EQ 367318743 US 14 [0052] Values of T, the current forecast for the total effort measured in units of time T required to produce the deliverable by the deliverable owner, ranges from t/(a+ε) to t/(aε) with the condition that α > ε. The project manager using the method and system set forth herein can generate the cumulative likelihood function for T given the data t, α, ε, using the Three Point Estimate Method/Fractile Method as before with the low estimate depicting a scenario in which the posterior probability of T < t/(α+ε) = 5%, the base estimate depicting a scenario in which the posterior probability of T < t/α = 50% and the high estimate depicting a scenario in which the posterior probability of T < t/(αε) = 95%.
[0053] Figure 3 summarizes actual work in progress data available for deliverables after the software development project has been in progress for five weeks. After five weeks' work on only three of the six deliverables, specifically project initiation, requirements analysis and solution design, has commenced with work on the remaining three deliverables to begin later in the project. The actual personhours column 36 in Figure 3 records the actual number of hours expended on each of the indicated deliverables by each deliverable owner in the first five weeks of the project with the total personhours worked 36a equaling the sum of the hours worked on each deliverable by every deliverable owner. The percentage complete column 37 in Figure 3 represents each deliverable owner's estimate of the percentage of that deliverable that has been completed in the first five weeks. The error column 38 in Figure 3 illustrates the margin of error provided by each deliverable owner for that deliverable owner' s estimate of his deliverable' s percentage complete.
[0054] Figure 4 represents the likelihood function for the software development project at week 5 based on the work in progress data reported
Express Mail No. EQ 367318743 US 15 in Figure 3. For each of the deliverables, the base case 39 in Figure 4 is computed by dividing actual personhours 36 in Figure 3 by percentage complete 37 in Figure 3. The low case 40 for each deliverable in Figure 4 is computed by dividing the actual personhours 36 in Figure 3 by (percentage complete 37 in Figure 3 + error 38 in Figure 3). The high case 41 for each deliverable in Figure 4 is computed by dividing the actual personhours 36 in Figure 3 by (percentage complete 37 in Figure 3  error 38 in Figure 3). Figure 4' s total personhour estimates 42 for the low 42a, base 42b and high 42c cases are the sum of the low, base and high cases for each of the individual deliverables.
[0055] Figure 5 shows how Figure 4's likelihood function based on actual work in progress data collected at week five of the software development project can be used to compute a posterior probability distribution. For each of the three deliverables for which work in progress data was available at week five (project initiation, requirements analysis and solution design), the low 40, base 39 and high 41 figures from the likelihood function, Figure 4, replace the low 24, base 26 and high 28 figures originally estimated for these three deliverables, as set forth in Figure 2, and become the low 44, base 45, and high 46 figures for the three deliverables in the posterior probability distribution as set forth in Figure 5. In comparing Figures 2 and 5, note that the probability distributions for the last three deliverables (software coding, testing and debugging and product rollout) remain unchanged since work has not commenced on these deliverables.
[0056] The project manager can use a statistical distribution, such as the extended PearsonTukey, to derive the expected values and standard deviation of the projected likelihood effort measured in units of time T for each of these three specific deliverable as follows:
Express Mail No. EQ 367318743 US 16 Likelihood Expected Value = 0.63 * t/α + 0.185 *[(t/(α+ε) + t/(αε)]
Likelihood Standard Deviation = 0.28 *[(t/α  t/(α+ε)] + 0.34 * [(t/(α ε) (t/α)]
[0057] Because of ontological and epistemic uncertainty, estimates of measurables for work in progress deliverables are subject to many small variations so that their sum, the likelihood function of work in progress, is approximately normally distributed. The expected value of the likelihood function is the sum of the likelihood expected values of all work in progress deliverables as calculated above. The standard deviation of the likelihood function is obtained by adding the squares of the likelihood standard deviations, as calculated above, of all work in progress deliverables and then taking the square root of the sum. Since the likelihood function approximates a normal distribution, it is completely specified by its expected value and standard deviation. In this example, the expected value is 723.9 personhours and the standard deviation is 186.8 personhours. The project manager therefore can say with 95% confidence that the work in progress will be at or below 1030.2 personhours (723.9 personhours + 1.64*186.8 personhours).
[0058] Figure 5 organizes the posterior probability distribution of effort required, as measured in personhours again, for each of the specific deliverables under the columns low 44, base 45, high 46, expected 47, and deviation 48.
[0059] As with the prior probability distribution, the posterior probability distribution also approximates a normal distribution  in accordance with the Normal Approximation Theorem. Estimates of effort required to complete individual deliverables are subject to many small variations so that their sum, the posterior probability distribution of total
Express Mail No. EQ 367318743 US 17 work required to complete the project, is normally distributed with expected value and standard deviation as calculated above.
[0060] The posterior expected value and posterior standard deviation for total project effort are now 1502.8 personhours 47a and 200.6 person hours 48a respectively and thus differ from the corresponding values for the prior probability distribution. Both the prior and posterior probability distributions are normal and by definition completely specified by their respective expected values and standard deviations. The posterior probability distribution of total work required to complete the software project reflects a measurable change in the manager's projections of the effort required to complete the project based on feedback from deliverable owners in the form of time sheets, expense sheets or other available work in progress data.
[0061] The posterior probability distribution enables the manager to update the prior probabilities for any prior estimates using standard Z scores from a normal table. The Z score for any Prior Estimate = (Prior Estimate  Posterior Mean)/Posterior Standard Deviation. A 1,766 person hours prior estimate for total project effort has a Z score of 1.31 (1, 7661, 502.8)/200.6 = 1.31). From the normal tables, a one tailed Z Score of 1.31 implies 90% probability that total project effort will be less than or equal to 1,766 person hours.
[0062] Before the project began, the manager believed that there was a 95% probability that total project effort would be at or below 1,766 person hours. At the end of week five, based on work in progress information, the manager now believes that there is a 90% probability that the total project effort will be at or below 1,766 person hours.
[0063] Using the posterior probability distribution, the project manager can also update his forecasts regarding the total project effort at any
Express Mail No. EQ 367318743 US 18 level of confidence. For instance, at a 95% confidence level, the project manager can estimate that the total project effort will be at or below 1,833 person hours (1,503 person hours+1.64*201 personhours).
[0064] To measure total percentage of project work completed to date at various levels of confidence, the project manager can merely divide the total effort actually expended (measured in personhours) for all deliverables in progress by the forecasted total project personhours. In this example, the project manager can say with 95% confidence that at the end of week five, the project is 7.7% completed (141 person hours/1833 personhours). This computation takes the forecasted effort from the posterior distribution since that is the best current estimate given the latest work in progress data.
[0065] Thus far, the manager of the software development project has applied the method specified by this invention through only one iteration involving only one time period and one check against actual work in progress data from project deliverable owners. To apply the method through successive iterations and time periods, the system takes the posterior probability distribution computed in the previous iteration and time period as the prior probability distribution for the current iteration and time period. The system then compiles new data (t,α,ε) from deliverable owners to compute a new likelihood function which is then combined with the prior estimates to calculate the posterior probability distribution of total work effort to complete the project.
[0066] As can be seen from the preceding numerical example, the posterior probability distribution then becomes the new prior probability distribution for the next iteration of the method.
[0067] Upon a project's completion, the manager can carry out model and individual bias checking if there appear to be systematic errors in the application of the method and system. For instance, based on actual
Express Mail No. EQ 367318743 US 19 performance, the manager may conclude that the Extended PearsonTukey distribution is an inadequate representation for the distribution of estimates provided by deliverable owners and may choose to substitute another distribution such as Triangle distribution or Lognormal distribution.
[0068] To generalize this method to a collection of project programs or project portfolios assuming independence or conditional independence, the following major additional computations for effort required must be made:
Program/Portfolio Prior Expected Value = Sum of Prior Expected
Values of All Projects in Program/Portfolio
Program/Portfolio Prior Variance = Sum of Prior Variances of All
Projects in Program/Portfolio
Program/Portfolio Prior Standard Deviation = Square Root of
Program/Portfolio Prior Variance
Program/Portfolio Likelihood Expected Value = Sum of
Likelihood Expected Values of All Projects in Program/Portfolio
Program/Portfolio Likelihood Variance = Sum of Likelihood
Variances of AU Projects in Program/Portfolio
Program/Portfolio Likelihood Standard Deviation = Square Root of Program/Portfolio Likelihood Variance
Program/Portfolio Posterior Expected Value = Sum of Posterior
Expected Values of AU Projects in Program/Portfolio
Program/Portfolio Posterior Variance = Sum of Posterior
Variances of AU Projects in Program/Portfolio
Program/Portfolio Posterior Standard Deviation = Square Root of
Program/Portfolio Posterior Variance
[0069] Effort is the main driver of project work. The method and system contained herein then includes data and standard project work
Express Mail No. EQ 367318743 US 20 algorithms familiar to those skilled in the art to create prior distributions, likelihood functions and posterior distributions for project work budgets, schedules and resources.
[0070] It is easy to see that multiplying the project work effort by the deliverable owner's hourly rate produces the project's estimated budget and by extension, the estimated budget for entire project programs and project portfolios. For instance, if all deliverable owners for the software project have an hourly rate of $100 per hour, the prior probability distribution for the budget would be specified by a normal distribution with expected value of $153,590 and standard deviation of $13,973 and there would be a 95% probability that the cost of the project would be below $176,506 ($153,590 + 1.64 * $13,973).
[0071] The method used earlier for estimating effort to produce deliverables to derive estimates for nonlabor costs and revenues, which can be combined with labor costs derived from estimating effort to derive the total budget distributions for project work.
[0072] Additional information such as resource availability, the sequence of deliverables and whether a deliverable is on the "critical path" is combined with effort estimates to develop duration and schedules for project work. The critical path is a series of activities that determines the duration of the project and represents the shortest completion time for project work. One skilled in the art would be familiar with preexisting algorithms for scheduling project work based on effort. The method and system described by this invention uses the standard scheduling algorithms, such as critical path, to construct schedules based on continually revised estimates for effort required to complete project work. Standard critical path methodology calculates the theoretical early start and early finish dates and the late start
Express Mail No. EQ 367318743 US 21 and late finish dates of all activities without regard to any resource limitations.
[0073] One skilled in the art would be familiar with resource leveling heuristic algorithms based on total effort required of a resource and available capacity of the resource within the relevant time period. The method and system of this invention use standard resource leveling heuristic algorithms to determine resource levels for project work based on method continually recalculating effort required of resources. Resource leveling is a heuristic technique that is applied after the critical path analysis is completed. It is used to the address the situation where a critical or shared resource has limited capacity or is available only at certain times and produces a critical path that is more realistic and used in practice.
[0074] The method and system encompassed by this invention can be implemented on a wide range of technology platforms, including but not limited to a web based application that follows the standard multitier or N Tier architecture, a two level client server architecture, employing the method on a desktop computer or handheld device, implementing the method using wireless networks and formatting a spreadsheet to carry out the computations required by this method.
[0075] Figure 6 illustrates how this method and system can be implemented on a standard two level client server system, which involves a client computer 49, or simply client, and a server computer 50, or simply server, connected through the Internet or some other network. A server connected by the Internet, or some other communications link 50a, to a client can use the World Wide Web service to send graphical web page 51 content to the client. Using browser application software 52, the client can download and display a web page by instructing the browser to locate the web page identified by a Uniform Resource Locator ("URL"). The request
Express Mail No. EQ 367318743 US 22 is sent to the server containing the web page, which then sends the requested web page back to the client. Web pages received from a server and displayed on a client can contain one or more templates into which data can be entered and then sent from client to server with a mouse click or other standard means such as hitting the return key on the client keyboard. Existing encryption techniques help ensure that sensitive project work related information exchanged between the client and server remain imcompromised. A client or a server can be based on any computer, with a computer defined herein as a device comprising at least one microprocessor.
[0076] Project work often requires the coordination of work submitted by deliverable owners, project managers and other team members even though they are located on different job sites. The World Wide Web, the Internet and a clientserver architecture provide a mechanism for coordinating such efforts. Each of the team members may access a client computer located on his own job site to update  by providing work in progress data  project work data previously stored on a server located in a physically distant location. Based on the updated data, the server can derive new likelihood functions and posterior probabilities, which can then be converted into the prior probability distribution with respect to the next iteration of the method set forth in this invention. A manager using a client computer can download and display information from the server in the form of web pages that allows the manager to oversee the project work.
[0077] As illustrated in Figure 6, each of the team members  deliverable owners and manager for instance  can be assigned a unique client ID 53 by the client system which stores the client ID in a file called a 'cookie'. The client IDs give deliverable owners and project managers a personalized experience and different levels of access. A deliverable owner for example may be able to download web pages that include templates into
Express Mail No. EQ 367318743 US 23 which updated work in progress data may be entered and may be denied access to data entered by other deliverable owners and to the likelihood function or posterior probability distribution derived from that data. The manager, on the other hand, can be given access to all work in progress data entered by every deliverable owner as well as other project work data and the likelihood function, posterior probability distribution or other conclusions derived from such data.
[0078] The server uses the client ID to identify each unique user by looking up the client ID/user table 54 which stores relevant attributes, including authentication information such as passwords, for all users. The web server engine 55 receives requests to access web pages 51 identified by the URL and client ID and provides various web pages to various client systems. The Bayesian software application 56 encapsulates the logic of the method described herein to continually generate prior probability distributions, likelihood functions and posterior probability distributions for project work measurables such as effort, budget, schedule and resources. This application 56 also retrieves, processes and stores information in a database 57.
[0079] Figure 7 shows how a project work manager enters deliverable related information into the client system to initiate the construction of the prior probability distribution function. The manager uses the browser 52 in the client 49 to display a web page 51 relating to the deliverable 58. The manager assigns a deliverable to a deliverable owner by selecting from a displayed web page a prepopulated list of team members and also selecting from a web page template the priority level of a deliverable which would determine the percentage of time the deliverable owner is required to devote to completing the deliverable 59. After discussions with the deliverable owner, the low, base and high estimates for effort required to complete
Express Mail No. EQ 367318743 US 24 deliverable is entered into a template on the displayed web page 60. The manager then enters on the web page template the calendar start date and other deliverables it is dependent on and whether the deliverable being assigned is on the critical path 61. The manager submits all the described information to the server and repeats this process until all required work on deliverables is accounted for 62.
[0080] To further develop the estimated budget, the manager enters low, base, high estimates for nonlabor related costs into the pertinent web page template and submits it to the server 63. The user then enters low, base, high estimates for revenue associated with project work into the web page template and submits it to the server 64.
[0081] Figure 8 shows how the server constructs the prior probability distribution for project work measurables such as effort, budget, schedule and resources. The server receives effort estimates for each deliverable, uses statistical algorithms contained in the Bayesian software application 56 to compute the expected values and standard deviation of effort involved for each deliverable and stores information 65 in the database 57. The server retrieves the unit labor rate for each deliverable owner from the database 57 and uses statistical algorigthms to calculate the expected value and standard deviation of the cost of each deliverable, which are then stored in the database 66. Next, the server uses statistical algorithms contained in the Bayesian software application to calculate the expected values and standard deviations of nonlabor costs and revenues for project work, which are then stored in the database 67. The availability of resources are retrieved by the server from the database to compute the duration required for each deliverable, which combined with the previously stored start date, is used to calculate the end date of each deliverable. This computed data is also stored in the database 68. The server aggregates all the above described
Express Mail No. EQ 367318743 US 25 information and other data regarding project work xneasurables and computes the prior probability distribution for effort, budget, schedule and resources and other project work measurables 69.
[0082] Figure 9 illustrates how a deliverable owner enters work in progress data for project work. A deliverable owner uses the client browser 52 to display a time sheet template for each deliverable assigned to him that that day 70. The deliverable owner enters time spent on each deliverable, how much of the work has been completed and the estimated percentage error in making that estimate 71. After entering the data, the deliverable owner submits the information to the server for processing 72 by activating the submit button the displayed web page with a mouse click or the return key on the client keyboard. The owner continues entering time against deliverables on a regular basis until all deliverables assigned to him are completed 73.
[0083] A deliverable owner who incurs nonlabor related costs downloads and displays the web page with the non labor cost sheet template on a client 74, enters his non labor costs and submits to the server 75. He continues to do this as and when he incurs such costs 76.
[0084] As illustrated in Figure 11, if during the course of the project work revenues are realized, the manager downloads and displays the web page containing the template for project work related revenue 77. He then enters any realized revenues into the template and submits it to the server for processing 78. He continues doing this until all revenue is realized 79.
[0085] Figure 12 shows how the server constructs the likelihood function and the posterior probability distribution for project work measurables. The server receives work in progress time sheet data for each deliverable, uses the Bayesian software application's statistical algorithms to revise the expected values and standard deviation of effort involved for each
Express Mail No. EQ 367318743 US 26 deliverable in progress and stores information in the database 80. The server retrieves the unit labor rate for each deliverable owner from the database, uses statistical algorithms to recalculate the expected value and standard deviation of the cost of each deliverable in progress and stores the information in the database 81. The server uses statistical algorithms to recalculate the expected values and standard deviations of nonlabor costs and revenues based on actual work in progress data received from the client and stores it in the database 82. The server retrieves availability of resources to recompute the duration based on revised estimates of effort required for each deliverable and combines that with the start date to calculate the revised end date of each deliverable and stores the information in the database 83. The server aggregates all the above information and computes the likehoold function for project work measurables. It then combines these likelihood functions with the prior distributions to construct the posterior probability distribution for project work measurables 84.
Express Mail No. EQ 367318743 US 27
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US20120253876A1 (en) *  20110330  20121004  Accenture Global Services Limited  Benefitbased earned value management system 
US20160004982A1 (en) *  20140703  20160107  International Business Machines Corporation  Method and system for estimating the progress and completion of a project based on a bayesian network 
US9406038B2 (en)  20120601  20160802  International Business Machines Corporation  GUI support for diagnosing and remediating problems that threaten ontime delivery of software and systems 
KR101729283B1 (en)  20140901  20170424  경희대학교 산학협력단  Apparatus and method for goal attainment diagnostic 
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US20030023470A1 (en) *  20010730  20030130  International Business Machines Corporation  Project risk assessment 
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US20030023470A1 (en) *  20010730  20030130  International Business Machines Corporation  Project risk assessment 
Cited By (7)
Publication number  Priority date  Publication date  Assignee  Title 

US20120253876A1 (en) *  20110330  20121004  Accenture Global Services Limited  Benefitbased earned value management system 
US9406038B2 (en)  20120601  20160802  International Business Machines Corporation  GUI support for diagnosing and remediating problems that threaten ontime delivery of software and systems 
US9501753B2 (en)  20120601  20161122  International Business Machines Corporation  Exploring the impact of changing project parameters on the likely delivery date of a project 
US9552561B2 (en)  20120601  20170124  International Business Machines Corporation  Incorporating user insights into predicting, diagnosing and remediating problems that threaten ontime delivery of software and systems 
US9563864B2 (en)  20120601  20170207  International Business Machines Corporation  Detecting patterns that increase the risk of late delivery of a software project 
US20160004982A1 (en) *  20140703  20160107  International Business Machines Corporation  Method and system for estimating the progress and completion of a project based on a bayesian network 
KR101729283B1 (en)  20140901  20170424  경희대학교 산학협력단  Apparatus and method for goal attainment diagnostic 
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