Monday, 15 October 2012

The Mathematics of Earned Value Management, Part – II


The Mathematics of Earned Value Management, Part – II


Before I directly plunge into the mathematics of Earned Value Management, I want to clear the concept of the cost management. Like time-management, cost management is very important thing in the field of project management. Most of the projects fail due improper management of cost. Even successful project goes over-budget. For successful project manager neither of the situations is appropriate.

CONCEPTS OF COST MANAGEMENT.

Project Cost Management consists of three knowledge areas Cost Estimation, Determine Budget and Control Cost, these three spread over in two processes groups Planning Process Group (Estimate Cost and Determine Budget) and Monitor and Controlling Process Group (Control Cost).

Cost Estimating: Developing an approximation of the costs of the resources needed to complete project activities. Resource consists not only Human Resource but anything required to complete the project.
Cost Budgeting: Aggregating the estimated costs of individual activities or work packages to establish a cost baseline.
Cost Control: Influencing the factors that create cost variances and controlling changes to the project budget.

While calculating the cost we should consider the following factors:

-          Cost of Quality
-          Cost of Risk
-          Cost of Human Resource
-          Cost of Project Manager’s Time
-          Cost of Project Manager’s Activities
-          Cost of Training (if required)
-          Office Expenses.
-          Other over-head cost.

We can segregate any cost in two ways, namely:
Variable Costs: Costs that change with the amount of production or the amount of work. Examples, cost of material, Fuel Charges.
Fixed Costs: Costs that do not change with the change in production changes. Examples include set up cost, warehouse rental, etc.

Also a cost can be either direct or indirect:
Direct Costs: Costs those are directly attributable to the work on the project. Examples are team salary, team wages, or material used on the project.
Indirect Costs: Any kind of cost which does not directly associated with the project. Example include office space expenses, CEO salary etc.


COST ESTIMATION AND BUDGETING

While doing the Cost Estimation we should have following inputs:

·         Scope Baseline: While making the estimation, we must know what is within the scope and what is out of the scope of the project. Once this is clear to us, we can easily estimate the cost of the project.

·         Schedule: This is another input to the cost estimation, this clearly tells us, in what quantity and which type of resource is required at what time. Once it is clear the timing of the resources, then we can plan the cost accordingly.

·         Human Resource: Since Human Resource is one of the major components of any project, in order to estimate cost we must know the quantity and quality of the Human Resource. There is another factor which we must know to increase the accuracy of the estimation, i.e. Rewarding Plan of the Human Resource.

·         Risk Register: It is another key input which helps to estimate cost, e.g. we know there is a risk in the earlier stage of the project and to mitigate that risk, we need to buy an insurance plan. This helps us to improve the costing of the project.

·         Project Management Cost: There are few cost are associated with Project Management.

·         Company Culture and Existing System: For a company with global presence, we need to understand, how the procurement is done and the cost of it.


COST ESTIMATION TECHNIQUES

Those estimation techniques uses in calculation of Time Estimation are used for Cost Estimation. In my previous write-up I have explained those techniques:

-          One Point Estimation
-          Analogous Estimation
-          Parametric Estimation
-          Three Point Estimation

Apart from all these techniques there is another technique which is used in the Cost Estimation;

-          Bottom-up Estimation: In this technique estimation start at activity lever or at work package level if it is defined in the WBS, so we need a detailed and accurate Work Breakdown Structure. Below is an example of the Bottom-up Estimation.



  

 Figure 1: Cost Aggression and Budgeting Example

Here we can see, how the cost of individual activity sum-up to Work Package level and from Work Package to Control Account and so on. This way we can achieve the total budget of the project.



Reserve Analysis: Reverse Analysis is one the very important ideas in the project management.
At the of analyzing the risk, we try to find out which activity in the project has the significant risk attached to it and much time and cost is associated with it. Then the project manager keep that much of time and money aside to deal with the risk if it happened in the future. The reserve fund has two parts, one is Contingency Reserve which is used to deal identified risk or the known risk, another part is the Management Risk, which is kept by the management to deal with the unidentified risk or unknown risk.

Accuracy of Estimate: This is another important concept in terms of estimation. When we try to cost estimation of the project, we must understand what should be the degree of accuracy of the estimation. May be at the earlier stage of the project we have less degree of accuracy (i.e. less accurate), but as we progress in the project, we make higher degree of accuracy (i.e. more accurate).
In order to understand estimation, we must clear that it is very difficult to measure the exact amount of any activity, so we always have range of the estimation. From the project management perspective we have three such range of estimation:

-          Rough Order of Magnitude Estimate (ROM):  At the initial stage of the project this kind of estimation is done, it has a range of ±50 percent of the project cost.


-          Budget Estimate: It is done at the planning stage of the project. This is more accurate that ROM with range of ± 20 percent.
-          Definitive Estimate: As we progress in the project the accuracy become more refined. It has range of ±10 (or ±5) percent depending on the project manger and the industry where project is happening.


BUDGET

 A budget is a compilation of the individual cost estimates. Activity costs are rolled up to work package level then Work package costs are rolled up to control account costs and finally into project costs. This process is called cost aggregation. Please refer Figure-1 for more clarification. Budgeting determine the amount of fund is required for the project. The stage no six of the Figure-1 give us the baseline of the cost. This create some kind of benchmark of the cost control, any deviation from the baseline will create an alarm for the project (either positive or negative side of the baseline).

I have already discussed the concept of reserve analysis, when contingency fund (amount of fund keep for unknown risk) is add up with the Cost Baseline we create total fund requirement for a project.


COST CONTROL

In the Cost Control process we try to measure the cost in-line with the cost baseline, so we do not deviate from it. The main reason of the cost control is to manage the project within the approved project budget. Not only managing changes but the preventing the unnecessary changes help us to correct the deviation. So both corrective and preventing action is important for us. Whenever the project manager finds or foresees any deviation of the cost from its baseline, he gets an alarm message and tries to find root-cause of the problem. And try to provide solution without affecting the original budget.







Tuesday, 25 September 2012

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, 2nd 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.