1. Introduction
As is known, according to PMBOK, both deterministic and probabilistic estimates of project parameters are used in project management [1].
Probabilistic methods for estimating the time of execution of individual operations and the project as a whole are used in cases of temporal uncertainty in achieving the project goal, that is, significant risks for estimating the duration of the project. As a rule, these are innovative projects [2], but the influence of other factors can also be considered, in particular, team characteristics, dynamic external environment, etc.
At the same time, the critical path method (CPM) is considered the most well-known method for constructing and analyzing a project network in terms of deterministic estimates [3].
The three-point estimation technique is used in management and information systems applications for the construction of an approximate probability distribution representing the outcome of future events, based on very limited information. One of the practically important from the point of view of probabilistic duration estimates is one among three point estimates [4] that is PERT (Program Evaluation and Review Technique) method [5]. The task duration estimate is based on the hypothesis that the duration of a separately selected operation is a random variable distributed according to the β-distribution law. For each task, it is obviously easier to obtain three duration estimates, namely, optimistic, most probable, and pessimistic, than one deterministic one. The mathematical expectation of the task duration is obtained by weighting these estimates.
Optimistic - the minimum realistic time period in which an operation can be completed. (There is a very small probability, usually estimated to be less than 1%, that a given operation will be completed in a shorter time frame.) Most likely - the most accurate guess as to the time period required to perform a particular operation. It is the most likely duration, this value also represents the mode of the β-distribution (the value that corresponds to the largest probability value in this distribution). Pessimistic - the maximum realistic time period during which the operation should be performed. (There is a very small probability, usually estimated as less than 1%, that the execution of this operation will take longer).
The PERT method allows you to take into account the unreliability of the initial estimates of the duration of the task by weighting them. Mean PERT average - the weighted average estimate according to the PERT method is obtained as:
PERT = (optimistic + 4*most likely + pessimistic) / 6
The weighted average duration estimate obtained by the PERT method is used as a deterministic estimate for calculating a network schedule, in particular, using CPM method.
2. Research Problem and Objectives
Unfortunately, in newer versions of the MS Project, the toolbar for calculating the project network using the PERT method is missing. However, apparently, given the relevance of such a possibility, you can find the corresponding macros on GitHub [6] written in Visual Basic, with which you can integrate such an analysis in Microsoft Project 2019 as well as in Microsoft Project 2016 and probably newest versions.
In this work, we focus on the possibilities of simple user programming using customized fields’ option, which is accessible to project users and does not require macro writing skills. It is also worth noting that the given approach can also be productive for the implementation of other methods of project planning and support, which are not available in the current version of the MS Project.
3. Results and discussion
If there are disagreements regarding the estimates of the duration of tasks or there is a need to model alternative scenarios for the project, the PERT method could be used. During the PERT analysis, the weighted average value of expert estimates of its optimistic, pessimistic and expected duration is used to calculate the task duration. And this value can then be used as a deterministic value for calculating the network schedule of the project using the critical path method. It is believed that this method is effective for project risk prevention. It allows you to calculate the project schedule taking into account possible or available time, resources or cost.
In MS Project we form the structure of the user scenario according to the following algorithm. Firstly, we need to add custom columns (fields) to the tabular part of the Gantt chart view (to do this, select Customize Fields in the context menu on the column headers):
Field headings from the Duration category (Type): optimistic, most likely, pessimistic, PERT. User input fields for entering the corresponding expert duration estimates are highlighted in bold, and the settings for these fields are selected by default as shown on Fig.1.
In this dialog box, you can specify field names, formulas, and the method of calculating (if the field is calculated) the values of the corresponding parameters for summary tasks.
Fig.1. A dialog box opened using the context menu of namely Gannt chart column headers.
Like for the PERT field, enter the formula by choosing corresponding button among Column attributes using previously named custom input fields - (optimistic +4*most likely + pessimistic) / 6 (see Fig.2). In this case we use other window settings by default (i.e., without calculation for summary tasks etc.). Thus, this part of the scenario is sufficient to form a user interface, for example, in a Gantt Chart tracking view to build a project schedule using the weighted average estimate as a deterministic one. Fig. 3 shows a corresponding representation of a hypothetical project in which there are already logical connections between tasks, a hierarchy of tasks according to the WBS, as well as expert estimates of task durations and a calculated PERT value.
Fig.2. Formula editor with a record for PERT field.
We displayed the columns we need in the user interface using the context menu of the table headers and the Insert Column command.
Fig.3. Tracking Gantt view with calculated PERT values.
In order to properly use the durations obtained in this way to build a network graph, we could copy the data from the PERT column to the Duration column (default column in a Gantt chart), as shown in the Fig. 4 below. And as a result, we get the Gantt chart, which MS Project calculates using CPM method with critical tasks displayed in red and non-critical tasks, respectively, in blue.
Fig.4. Tracking Gantt view with PERT values applied for CPM calculation.
If you save the built scenario as a template, it becomes easily accessible for use in subsequent plans for other projects.
4. Conclusion
Thus, the use of custom programming in MS Project allows you to easily implement not only the three-point analysis method. The above algorithm can actually be extended, for example, for scrum planning poker with the ability to enter user story points and convert them into task durations using the velocity parameter, or for using other, besides beta, different activity distributions. For example, the ability to change weights can also be implemented in our scenario by introducing additional custom fields of number type and then using their values in the formula for calculating PERT duration. However, in fact, according to [7] the usage of different activity distributions hasn’t significant influence from a practical point of view on the project duration, apart from the correctness of the expert assessments themselves.
References
1. The standard for project management and a guide to the project management body of knowledge (PMBOK) – 7th Edition / Project Management Institute, USA, 2021. 274 p.
2. Baffo I., Salvatori S., Introna V., Esdra A, Cesarotti V. An application of Project Management techniques for the estimation of processing times in industrial projects with a high degree of innovation. Proceedings of the XXIII Summer School “Francesco Turco”, September 12-14, 2018 / Palermo (Italy), 2018. P. 417-423.
3. Bagshaw K.B. PERT and CPM in Project Management with Practical Examples. American Journal of Operations Research. 2021. Vol. 11. P. 215-226. URL: https://doi.org/10.4236/ajor.2021.114013
4. Hopkinson M. Three-point Estimates: A brief guide, Practical Project Risk Management series. PM World Journal. 2022. Vol. XI, Issue XI.
5. Nafkha R., The PERT method in estimating project duration. Information Systems in Management. 2016. Vol. 5, no. 4. P. 542−550.
6. Sayan Kundu. Contains the macro for running PERT analysis in MS Project 2019. GitHub. URL: https://github.com/flametron/MSProject-2019-PERT
7. Miklos H., Orsolya B. The Effects of Different Activity Distributions on Project Duration in PERT Networks. Procedia - Social and Behavioral Sciences. 2014. Vol. 119. P. 766 – 775. DOI: 10.1016/j.sbspro.2014.03.086.
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