The Mathematics of Earned Value Management, Part - I

  The Mathematics of Earned Value Management, Part - I

Project Management is playing an important role in today’s organizations. As companies restructuring itself from hierarchical structure to more horizontal structures, more people with project management skills are needed. Project Management is required in various business segment, from high-end information technology to real-estate companies. This skill helps the organization, in order to launch the new products on time and in budget, and to coordinate people within the organization.

Unlike, other management disciplines, modern project management is pretty new. It first started to be used in the USA by government programs in 1950s, but it has been used widely in all sectors beginning from 1990s and it still improves. Today, it is seen that although human skills are important in order to establish the necessary coordination between people and departments, technical skills are equally important to measure the project performance objectively and to take necessary actions.

Here I will concentrate on an important mathematical project management technique “Earned Value Management”, which is a pain area for newly appointed Project Managers.

At the very beginning I will discuss some necessary concepts about project management. In the following parts I will discuss the concept of project management constraints and it association with the “Earned Value Management” technique.

INTRODUCTION TO PROJECT MANAGEMENT

PROJECT MANAGEMENT INSTITUTE

Project Management Institute (PMI, www.pmi.org) is a not-for-profit professional association, whose goal is to advance the practice, science, and profession of project management throughout the world in order organizations to embrace value and utilize project management and then attribute their success to it.

PMI was founded in 1969 by working project managers. Today the association has approx 420,000 members and credential holders. PMI organize the project management frame work in a structural way under “A Guide to Project Management Body of Knowledge (PMBOK Guide)”.

In this study, all the concept descriptions will be given based on PMI standards.

DEFINITION OF PROJECT AND PROJECT MANAGEMENT

Project is:

- A temporary endeavor i.e. with a definite beginning and an end,

- Creates a unique product, service or result,

- And progressively elaborated (the characteristics of each unique project will be progressively detailed as the project progress).

Project Management is the discipline of planning, organizing and managing the resources to bring about the successful completion of specific project goals and objectives.

The projects need to be managed and delivered under certain constraints. Traditionally, these constraints have been listed as scope, time and cost. The time constraint refers to the amount of time available to complete a project. The cost constraint refers to the budgeted amount available for the project. The scope constraint refers to what must be done to produce the project’s end result.  These are also referred as the “Project Management Triangle”, where each side represents a constraint. Now, if one side of the triangle change then other sides of the triangle change automatically. For example if we change the scope of the project then it effect the both the time and cost of the project.

Figure 1: Project Constraints “Triple Constraint”

The Project Management Institute divided the entire project into nine project management knowledge areas :

1. Scope,

2. Time,

3. Cost,

4. Quality,

5. Human Resources,

6. Communications,

7. Risk,

8. Procurement,

9. Integration.

(Project Management Institute, PMBOK Fourth Edition)

The Project Management Institute divided the projects in five process groups as given below:

1. Initiating

2. Planning

3. Executing

4. Monitoring and Controlling

5. Closing

Figure 2: Single Phase Project Management Process Groups Mapped to Plan-Do-Check-Act (Project Management Institute, PMBOK Fourth Edition)

From the above picture we can understand how the process groups of the project management interact with each other for single phase project.  For any multi phase project this cycle may occur several times.

The key of any successful project is planning. And this begins with, defining the project objective into detail information. At first we define project scope of work in terms of deliverables then we further decompose this deliverables into component. This process is known as Work Breakdown Structure. The WBS creation process is necessary for subdividing the major project deliverables and project work into smaller, more manageable components.

To reach the activity level we further break down WBS, an activity level is small enough to estimate, schedule, monitor and manage. Then these activities are sequenced; on the basis of this sequence, resources are allocated, schedule is made and ultimately cost estimates are made. Parallel to these, project manager also creates; quality plan, communications plan, risk management plan and procurement plan (if necessary for the project).

Figure 3: A project WBS example. ( Inspired by “Practice Standard for WBS, 2^nd Edition, PMI)

Here I will discuss the mathematical concept of two constraints “time” and “cost” and how it use in project management.

TIME MANAGEMENT

 NETWORK DIAGRAMS

Sequencing the activities in the project is necessary, activities are sequenced based on how the work will be performed. The result of the sequenced activities is known as network diagram. We can draw the network diagram in two ways:

A.     Precedence Diagramming Method

B.     Arrow Diagramming Method

Precedence Diagramming Method (PDM)

Precedence Diagramming Method is also known as Activity-on-Node (AON). In this method, nodes  represent activities, and arrows show activity dependencies. There are three type of dependencies, which are as follows:

Finish-to- start An activity must finish before the successor can start.

Start-to- start An activity must start before the successor can start.

Finish-to- finish An activity must finish before the successor can finish.

Start-to-Finish An activity must start before the successor finish.

Arrow Diagramming Method (ADM)

Arrow Diagramming Methods is also known as Activity-on-Arrow (AOA). In this method of network diagram, the arrows are used to represent activities. The nodes (in this case circles) represent activity dependencies. Any activity (arrow) coming into a node is a predecessor to any activity leading the node. 

- It uses only finish-to-start relationships between activities.

- May use dummy activities. Dummies are usually represented by a dotted line and are

inserted simply to show dependencies between activities. (Rita Mulcahy)

            

                                     

ACTIVITY DURATION ESTIMATION

Once activity defined, the next process is to define, the amount of time each activity is expected to take. There are few techniques are used to calculate the estimation. The techniques are as follows :

• One-Time Estimate: When estimating using a one-time estimate, one estimate per activity is received. This estimation required Expert Judgment. One-time estimates should only be used for projects that do not require a detailed, highly probable schedule.

• Analogous Estimating: Analogous estimation is based on the expert judgment and historical information e.g. if an activity took 5 days to complete then it is assume the activity will take 5 days to in this new project.

Parametric Estimation: In this process we calculate project duration from historical data or from    other date which involve more statistical data like e.g. time(days) taken by individual to design each module.

• Three-Point Estimates: We must understand that statistically there is a very small probability of completing a project on any one date. Therefore, time estimates for an activity or a project must be in a range. In this form of estimating the activity provides an optimistic (O), pessimistic (P) and most likely (M) estimate for each activity. The resulting estimates for an activity will be stated like 10 days plus or minus 4 days, which means that the activity will take anywhere from 6 to 14 days.

• Heuristics: This is rule of thumb. It is like requirement study take 30 percent of the entire project duration.

After duration estimates are made, we have to make the whole project duration and schedule estimation. There are two widely methods are in use:

·         Critical Path method

·         PERT methods.

CRITICAL PATH METHOD:

The critical path method includes determining the longest path in the network diagram which is known as CRITICAL PATH and the earliest and latest an activity can start and the earliest and latest it can be finished. An example will be helpful to define this concept:

Example : A Project has the activities and durations given below :

Activity	Preceding Activity	Estimate in Months
A	Start	2
B	Start	4
C	Start	2
D	C	3
E	A	7
F	G,E	5
G	B	6
H	D	4
I	F,H	6

On the basis of the above data following network diagram is created.

        

Now here there three path through we can reach from start to finish.

1.      AàEàFàI and duration of this path is 2+7+5+6 = 20

2.      BàGàFàI  and the duration of this path is 4+6+5+6 =21

3.      CàDàHà and the duration of this path is 2+3+4+6 = 15

The longest path in the Network Diagram is known as Critical Path, So from the above calculation we can easily conclude that the path BàGàFàI is the longest path in the network diagram so it is the critical path.

In the Network Diagram there is an important concept which is called Float or Slack. Float or Slack gives the flexibility to the project. All the activity on the critical path has zero float but it is not necessary that, if an activity has zero float then it lay on the critical path.

Free Float: An amount of time an activity can be delayed without delaying its immediate activity (s).

Total Float: An amount of time an activity can delay without delaying the project end and nearby milestone date.

Project Float: An amount of time an activity can delay without delaying the project end date as imposed by the project sponsor or high level committee.

PERT (PROGRAM EVALUATION AND REVIEW TECHNIQUE):

The Project Evaluation and Review Technique or PERT is a method to analyze the involved tasks in completing a given project, especially the time needed to complete each task and identifying the minimum time needed to complete the entire project. It was developed primarily to help to simplify the planning and scheduling of large and complex projects. In order to find the duration and standard deviation for a project, PERT estimates for each activity on the critical path should be added.

Terminology:

• Optimistic time (O): The minimum possible time required to accomplish a task, assuming everything proceeds better than the expectation.

• Pessimistic time (P): The maximum possible time required to accomplish a task, assuming everything goes wrong.

• Most likely time (M): The best estimate of the time required to accomplish a task, assuming everything proceeds as normal.

• Expected time (duration) : The best estimate of the time required to accomplish a task, assuming everything proceeds as normal.

Ø  Expected completion time (duration)  =  (P+4*M+O) / 6

Ø  Variance of an activity (σ²) = (P-O / 6)²

Ø  Standard deviation of an activity = P-O / 6

• At first, for every activity on the Critical Path, the Expected Completion Time (Duration) and Variance is calculated.

• Next, Expected Completion Times of all activities are added to calculate the Expected Completion Time for the whole project.

• Finally, the corresponding variance for each activity is added to calculate the variance for the overall project.

Activity	O	M	P	Expected Duration	Activity Standard Deviation	Activity Variance	Range of the Estimation
Requirement Studies	15	20	30	20.83	2.5	6.25	20.83±2.5
Analysis	18	27	38	27.33	3.33	11.11	27.33±3.33
Designing	40	63	82	62.33	7	49	62.33±7
Coding	45	68	92	68.16	7.83	61.36	68.16±7.83
Testing	25	31	44	32.16	3.16	10.02	32.16±3.16
Packaging	10	19	26	18.66	2.66	7.11	18.66±2.66
Delivery	8	14	27	15.16	3.16	10.02	15.16±3.16

Project Duration Calculation :

Total Expected Duration :  20.81+27.33+62.33+68.16+32.16+18.66+15.16 = 244.66

Project Variance : 6.25+11.11+49+61.36+10.02+7.11+10.02 = 154.88

Project Standard of the project = √154.88 = 12.44

Range of Project Duration = 244.66±12.44

TECHNIQUES TO COMPRESS PROJECT DURATION:

Once the project got delayed from the schedule baseline and we want to bring back the project in-line of the schedule or when the customer ask to complete the project earlier than the scheduled date, then we need to compress the project duration. There few ways to compress the project duration.

• Fast Tracking – When we try to complete the activities in parallel that are originally planned in series on the critical path is known as Fast Tracking. One point to be remember here, while doing the Fast Tracking we increase the risk of the project.

• Crashing – Adding more resources to critical path activities to decrease their duration. Now from the concept of triple-constraint of project management we can assume that this way we trade-off between Cost and Time.

• Reducing SCOPE – This may reduce the both cost and time of the project but this will decrease the customer satisfaction level.

• Cutting Quality – By cutting the quality we may save both time and money but at the same time we increase the risk of the project.