1.07.15Tecolote Research Business Sensitive Information

Modern Methods for Budget-Constrained Schedule AnalysisNick DeTore

August 2018Tecolote Research PRT-244

Slide animation:

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Introduction

This presentation discusses methods for calculating the impact of a budget profile on a schedule analysis• If the yearly budget for a project does not cover the estimated yearly

cost, the schedule will inevitably see delays as activities are stretched or delayed until funding becomes available

• There is no standard approach for how to predict the impact of this common discrepancy between the cost estimate, budget, and schedule

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The Path Forward

Projects that merge cost and schedule into one model (or at least attempt to analyze the relationship) are heading in the right direction but there is further still to travel• This includes, but is not limited to, a JCL model

The next step to ensure maximum return on the effort placed into this analysis is to reconcile the discrepancy between the results of the analysis with the realities of the budget

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Where We Begin: Ground Rules and Assumptions

1. Work cannot be performed until funding is available2. The estimated cost resulting from the model represents

the amount of effort needed to be completed 3. The budget comes from a single source and covers all

the activities modeled in the schedule4. Delay causes a “smooth slip” domino effect of schedule

content • As opposed to a re-plan/re-baseline

These are necessary but not exhaustive

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Where We End: The Solutions

Create a profile (expenditure rate curve) where the area is equal to the budget instead of the estimated cost for a given yearThis new profile can then be used to calculate the extended duration caused by a year’s budget that still maintains the cost (effort) estimated by the modelAfter iterating through all the years of the project, the overall delay in the schedule due to the budget constraint is revealed

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Solution 1:Rectangles

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Solution 2: Trapezoids

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Solution 3: Generalized

!(#) = #

!(#) = &# + (

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Solution 3: Generalized

Solution 1: single value representing the adjusted rate: 𝑓(𝑥) = 𝑥 Solution 2: straight line representing the adjusted rates: 𝑓(𝑥) = 𝑚𝑥 + 𝑏 Solution 3…? Solution 𝒏…?In order to provide a flexible and comprehensive management strategy, the next logical step is towards a generalized method of calculating the adjusted rate to predict the delay

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Framework for a Generalized Method: Linear Proof

The solution for the extended duration, d’, is the exact same formula derived either geometrically or using calculusThus showing that the generalized formulation of the budget constrained problem is versatile and accurate

Proof of equivalence in backup slides

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How to use these solutions

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What do you do next?

Regardless of the method for calculating the extended duration, the next step is performing this process repeatedly for each year• At each step there are a series of checks and adjustments needed

1. Check that the budget is indeed less than the cost2. Calculate the extended duration

3. Check that there are enough funds in the following year to cover the extension cost and the originally planned work• If there are enough funds, subtract from that next year’s budget• If there are not enough funds, re-calculate the extension that exists in the

next year to spread it even thinner, pushing the original work in that year completely out of its planned year

4. Adjust the following year’s budget, then calculate the adjustment necessary to account for the work remaining in that year to fit the remaining budget

5. Repeat from step 1

What do you do next?

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See the paper for a detailed description and images of how to run the adjustment algorithm

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Reconciling the Discrepancy

How the yearly phased results look after the adjustment

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Accounting for the type of costs?

If the schedule model contains costs broken out into time-independent (TI), time-dependent (TD), level-of-effort (LOE) and/or program management (PM) costs, these need to be accounted forManagement should decide:1. What, if any, control over reducing labor force is possible in order to

achieve the predicted results? 2. Can any of the LOE or PM work can be reduced or is that a fixed rate?3. What year do the largest TI costs (material purchases, e.g.) occur? Are

they fixed in time or can they be pushed out?

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What about the type of costs?

Example of the model setup needed prior to calculation:

n For example, with this budget:1. What is the average delay?2. What is the probability I exceed my schedule reserve?3. What is the probability I hit my 70% finish date target?4. How do results change if I use the 50% yearly rate for adjustments

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What about the simulation?

Applying this method to each iteration of an uncertainty simulation provides a powerful, new, and exciting analysis

Planned 70% Target

Planned 70% Target

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No Budget? No Problem!

The formulas laid out in this framework can all be solved for any variable of interest, most notably: the budget This allows answers to questions like:1. If I don’t want to be delayed by more than 100 days, what budget

profile do I need? 2. How can I reallocate the budget to minimize my delay?

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Thank you!Questions?

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Contact Information

Please feel free to contact me with any questions:

Nick DeTore (Advanced Analyst)

NDeTore@Tecolote.com

2231 Crystal Dr # 702

Arlington, VA 22202

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Back Up Slides

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Framework for a Generalized Method: Linear Example

To demonstrate the applicability of this framework, calculus is used instead of geometry to solve for the adjusted rate, assuming linearity in the rate change• Ideally concluding with the exact same results

12 #$% + '$ = ) 1

2 #$*% + '$* = +

./

0(23 + 4) $6 = ) .

/

07(23 + 4) $6 = +

Eq. 1 Eq. 2

&

&

Three methods to solve this underdetermined system of equations for d*:1. Introduce another equation/objective (e.g. rate begins to increase when funding is available)

2. Solve for extended duration $*as a function of another variable (e.g. b, the initial rate)

3. Assume the value of one variable (e.g. ' = +/$ )

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Framework for a Generalized Method: Linear Example

If we prefer control over the rate, we can solve the system as a function b (method 2), since b represents the year’s starting rate

If we prefer a deterministic solution, we can use the original rate for b (method 3), since we know ! = #/%

Eq. 1

Eq. 2

Method 2:Same as “Start up, end down” equation!

Method 3:

12 (%) + !% = + ( = 2(+ − !%)

%)

( = 2(+ − !%)%)

12 (%,) + !%, = # 1

22 + − !%

%) %,) + !%, = #

%, =−! ± !) + 4# + − !%

%)2 + − !%

%)%,2 =

−#% ± (#%))+4#+ − #%)

2 + − #%)

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Is it really true? Proving Generalized Method

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Framework for a Generalized Method: Quadratic Example

A similar process can be used with any polynomial or other nonlinear equation • Although there may be little justification to branch far from a linear form

Math happens here

Note: There may not be a real valued solution in some cases

!"

#

(%&' + )) +& = - !"

#.

(%&' + )) +& = /

1

3%+2 + )+ = -

1

3%+′2 + )+′ = /

+4 = 5ℎ7 89:;<=9> <9 <ℎ7 );?=):

(ABC

DE) d4

2+G

#d4 − / = 0

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Yes it is true

Trapezoid (geometric) method with !" = !: Generalized (calculus) method using a linear formula:

Set both equations equal to each other:

Moving denominators of each side to the opposite side:

Factoring the left side and distributing the right side: Concluding equality:

$% = 2'

( + (* + 4C - − ($$* $′ =

−( + (* + 4C - − ($$*

2 (- − ($)$*

2'

( + (* + 4C - − ($$*

=−( + (* + 4C - − ($

$*2 (- − ($)$*

2' 2 - − ($$* = −( + (* + 4C - − ($

$* ( + (* + 4C - − ($$*

4' - − ($$* = −(* + (* + 4C - − ($

$* 4' - − ($$* = 4C - − ($

$*

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Where We Begin: What Data Is Needed?

This process requires a few pieces of information:• Project’s estimated cost on a yearly basis• Project's budget on a yearly basis• Project’s scheduled finish date

Ideally, and for the most robust results, a few more pieces of information could be well used:• Cost types, e.g. time independent/dependent breakout, level-of-effort• Iteration results containing yearly costs • Any important dates tied to budgetary decisions

n Quadratic is the longest delay

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How do the solution methods compare?

Rectangle solution is the shortest and quadratic is the longest“Trapezoid with Increase” seems a realistic balance

!" ($% !&'()*+,) !". (/0)/,!/! !&'()*+,)

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When is the slope too steep?