Sunday, April 24, 2011

Earned Value at Frequency Domain

Abstract

EVM is a known Project Management Technique that could be considered ineffective in activities that do not ordinarily contain temporal work to create a unique result (projects), such as services or ongoing operations. A good analogy is proposed to use EVM in services, converting the model to the Frequency Domain using Fourier Transform. A simple example is shown to obtain conclusions about how to manage a continuous service with this new technique.

Introduction

Earned Value Management (EVM) is a very known, elegant and effective Project Management Technique. It unifies the three main knowledge areas (Scope, Time and Cost) of Project Management in a common framework that mathematically represents the relationship between them. It can be used to dramatically improve the success rate in projects when it is complemented with other techniques of Project Management.

A project could be defined as a temporal work to create a unique result. Unfortunately, the application of EVM to efforts that may be categorized as “non-schedule-based”, i.e., those that do not ordinarily contain temporal work to create a unique result, could be considered ineffective. “Non-schedule-based” efforts include services composed primarily of Level of Effort (LOE) activities, such as maintenance services or continuous services.

Almost every product of a project have a continuous operation phase after a transition stage. Different skills and techniques needed to manage continuous operations are the reason to divide this cycle in a "project phase" and an "ongoing operations phase". Even more, many projects have a portion of their first activities responding better to the definition of ongoing operations. It is a challenge to fight against the ineffectiveness of EVM in ongoing operations, extending the model to manage “non-schedule-based” efforts.

Let’s name this model EVM[t] to differentiate from the model EVM[w] that is proposed in this document. If you are already familiarized with EVM, just skip following title and go to the next one.

EVM[t] basics

Earned Value Management is founded in the use of three variables: Planned Value (PV), Actual Cost (AC) and Earned Value (EV). The first two concepts are easy to understand. The last variable is a good measure of progress.

PV is also known as Budgeted Cost of Work Scheduled (BCWS). The curve obtained of the accumulated planned cost (PV) is also known as "Baseline" and is the reference for the cost performance for the whole project.

AC is also known as Actual Cost of Work Performed (ACWP). The Actual Cost (AC) is clearly associated with work, because the units of cost that are measured by AC are those generated by tasks that have been worked. In other words, when a unit of work has been done, AC adds the real cost for that unit of work.

EV is also known as Budgeted Cost of Work Performed (BCWP). When a unit of work has been done, EV adds the same value that was planned for that unit of work, no matter how much was the cost of finishing that unit of work.

A project's Cost Variance (CV) is simply the difference between the Earned Value (EV) and the Actual Cost (AC). The value is positive if the budgeted cost of the work performed is greater than the actual cost of the work performed. In other words, CV is positive whether a project is under the budget.


A project's Schedule Variance (SV) is simply the difference between the Earned Value (EV) and the Planned Value (PV). The value is positive if the budgeted cost of the work performed is greater than the budgeted cost of the work scheduled. In other words, SV is positive whether a project is ahead of schedule.


The Earned Value Analysis mainly observes SV in order to know the speed of the project. It also observes CV in order to know if the project is on budget. There are many other index and concepts, but these are the basics.


EV[t], AC[t], PV[t], CV[t] and SV[t] are functions of the time. They are measured in units of economic value ($). Mathematically, the domain of them is time and the range is economic value ($).

EVM[w] fundamentals

Let’s talk about “services” instead of “projects”, because in frequency domain could be more appropriate. Let’s use “w” to represent frequency, even though w is the common representation to frequency measured in radians, not in hertz. In this case is not important. “w” will be our representation of frequency, no matter the measurement unit of frequency.

Different from EVM[t], the variables of EVM[w] are non accumulated variables. The reason is clear. If any of these variables is defined as the accumulated amplitude of the concept, then this variable would has an infinite value, because services are continuous by definition. More precisely, let’s define EV’[t] in the following way:


Let’s define analogically AC’[t], PV’[t]. The interpretation is very simple: these are the non accumulated variables. In a discrete model, these are the increments in each measurement period.

Let’s define EV’[w], AC’[w], PV’[w] as new functions of the frequency. They will be measured in units of economic value ($) as the homonymous variables of EVM[t]. Mathematically, the domain of them will be frequency (w) and the range will be economic value ($).

A shortcut can be used to precisely define these functions. If you are not familiarized with Fourier Transform, ignore the following formula and go directly to the next definitions. Lets define EV’[w] as follows:


Let’s define analogically AC’[w], PV’[w].

Even though EVM[w] is not a model based on time, it’s clear that the model describes a physic situation that could be modified. EVM[w] describes past, present and future states of a service as we could know them. Nevertheless, EVM[w] analysis could make recommendable to do changes to the service.

PV’[w] will be known as Budgeted Cost of Planned Goal (BCPG). The curve obtained from the planned cost (PV’[w]) will be known as "Frequency Distribution of Value" and will be the reference for the cost performance for the whole service.

AC’[w] will be known as Actual Cost of Recurrent Achievement (ACRA). The Actual Cost (AC’[w]) is clearly associated with work, because the units of cost that are measured by AC are those generated by recurrent services that have been worked. In other words, if a level is recurrently achieved, AC’ will be the real cost for that achieved level, even though is not the planned level.

EV’[w] will be known as Budgeted Cost of Recurrent Achievement (BCRA). If a level of service is recurrently achieved, EV’ will be the cost that was planned to achieve that level of service, no matter how much is the recurrent real cost to achieve that level of service.

A service's Cost Variance (CV) will be simply the difference between the Earned Value (EV’[w]) and the Actual Cost (AC’[w]). The value will be positive if the budgeted cost of the recurrent work is greater than the actual cost of the recurrent work. In other words, CV[w] will be positive whether a service is under the budget, for the work planned to be done with frequency w.


A Service Level Agreement Variance (LV) will be simply the difference between the Earned Value (EV’[w]) and the Planned Value (PV’[w]). The value will be positive if the Budgeted Cost of Recurrent Achievement is greater than the Budgeted Cost of Planned Goal. In other words, for the work planned to be done with a given frequency w, LV[w] will be zero if the service is achieving goals and less than zero if not.


EVM[w] will be useful to observe LV[w] in order to know the achievement of the Service Level Agreement (SLA). It will be useful to observe CV[w] in order to know if the service is on budget.

Example

In the following table you could see the data of an example. A discrete model is used to facilitate the understanding. Let the red squares be the actual cost of each recurrent work. Suppose that we normally achieve (green) the goals of the first Service Level Agreement (SLA), we are progressing (green) in the second SLA excepting with the weekly and monthly goals (blue). With the third SLA only the weekly goals are recurrently achieved (green). The goals of the fourth and fifth SLA are recurrently achieved (green).




It's possible to see the last example drawn in the following curves. Hourly the service is going according to plan. Daily, the goals of the plan are achieved but the actual cost is recurrently over the budget. Weekly, the goals are not achieved but the cost is what was planned for that level of achievement. Monthly, the situation is worst, the goals are not achieved and even the cost is greater than what was planned for the levels achieved. Yearly, we save money but the goals are not achieved.


There is no apparent reason to not increase weekly efforts in order to achieve weekly goals, because the cost of those efforts are giving the expected results (CV[week] = 0 & LV[week] < 0). Normally, the goals of the year depend on the goals of the months and so on. It’s preferable to analyze the effects of a weekly increment of efforts before deciding to increment other efforts, but apparently there are money each year (CV[year] > 0) that can be used for that.

Concluding Remarks

EVM[t] could be considered ineffective in activities that do not ordinarily contain temporal work to create a unique result (projects). A good analogy can be done to use EVM project’s technique in ongoing operations or services. An Earned Value Management technique in Frequency Domain (EVM[w]) has been defined using Fourier Transform to prove this possibility. Non accumulated variables are needed to do so. An example has shown that homologous indexes can offer interesting information to obtain conclusions about how to manage a continuous service.

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