Dimitar Bakardzhiev

Managing Partner

Taller Technologies Bulgaria @dimiterbak

#NoEstimates Project Planning using Monte Carlo

simulation

Clients come to us with an idea for a new

product and they always ask the questions -

how long will it take and how much will it cost

us to deliver? They need a delivery date

and a budget estimate.

WE CAN’T CONTROL THE WAVES OF

UNCERTAINTY, BUT WE CAN LEARN

HOW TO SURF!

TO ME #NOESTIMATES MEANS

No effort estimates

Effortless estimates

No estimates of effort

Deterministic planning used these days forces certainty on uncertain situations and

masks the uncertainty instead of highlighting it.

How can we forecast project delivery time without a detailed schedule - that is assessing the

dependencies between the work, the cost of the work, and

the sequence of the work?

We challenge the project management paradigm and suggest that for

planning purposes it is better to model projects as a flow of work items

through a system.

A project is a batch of work items each one representing

independent customer value that must be delivered on or before

due date.

We don’t try to estimate the size of the work items. There are only two "sizes" - “Small Enough" and

“Too Big". "Too big" should be split and not allowed to enter the

backlog.

A Project in a Kanban System

Input QueueDEPLOYED!

Project Backlog

Development Test QA

WIP 5 WIP 4 NO WIPWIP 2

High-level probabilistic planning

• The initial budget and the range of the time frame • Does not include detailed project plans • The plan is created with the appropriate buffers • Schedules are the execution of the high-level plan • Keep focus on the project intent

Reference class forecasting

The forecast on a given project is based on knowledge about actual performance in a reference class of comparable projects.

Daniel Kahneman

Reference class forecasting • Identification of a relevant reference class of past,

similar projects. The class must be broad enough to be statistically meaningful but narrow enough to be comparable with the specific project.

• Establishing a probability distribution for the selected reference class.

• Comparing the new project with the reference class distribution, in order to establish the most likely outcome for the new project.

IDENTIFICATION OF A REFERENCE CLASS OF

SIMILAR PROJECTS

Are the Team structures comparable?

Are the Technologies used comparable?

Are the Development processes comparable?

Are the Client types comparable?

http://blog.7geese.com/2013/07/04/7-reasons-why-i-decided-to-work-for-a-startup/

Are the Business domains comparable?

http://www.mindoceantech.com/

ESTABLISHING A PROBABILITY

DISTRIBUTION FOR THE SELECTED

REFERENCE CLASS

WHAT METRIC WILL BE USED IN THE FORECAST?

Takt Time!

Takt Time is the time between two successive deliveries

How manufacturing measure Takt Time?

How knowledge workers measure Takt Time?

Takt Time (TT) is the time between two successive deliveries

Start 5 days 7 days 2 days 2 days 1 day 5 days Finish

TT = 0 days

TT = 0 days

TT = 5 days TT = 7 days

Project delivery time (T) = 5 + 7 + 2 + 2 + 1 + 5 = 22 days

Average Takt Time

𝑇𝑇 =𝑇𝑁

• T is the time period over which the project was delivered • N is the number of items to be delivered in period [0,T] • 𝑇𝑇 is the Takt Time for period [0,T]

Average TT calculation

𝑇𝑇 =𝑇

𝑁=22 𝑑𝑎𝑦𝑠

10 𝑠𝑡𝑜𝑟𝑖𝑒𝑠

= 2.2 𝑑𝑎𝑦𝑠/𝑠𝑡𝑜𝑟𝑦

Average Project Delivery time

𝑇 = 𝑁𝑇𝑇 • T is the time period over which the project will be delivered

N is the number of items to be delivered in period [0,T] • 𝑇𝑇 is the Takt Time for period [0,T]

Project Delivery time

𝑇 = 𝑁𝑇𝑇 =

45 𝑠𝑡𝑜𝑟𝑖𝑒𝑠 2.2 𝑑𝑎𝑦𝑠

𝑠𝑡𝑜𝑟𝑦= 99 𝑑𝑎𝑦𝑠

We should NOT use the Average Takt Time as a single number but a

distribution of the average Takt Time instead!

Bootstrapping • Introduced by Bradley Efron in 1979

• Based on the assumption that a random sample is a

good representation of the unknown population.

• Does not replace or add to the original data.

• Bootstrap distributions usually approximate the shape, spread, and bias of the actual sampling distribution.

• Bootstrap is based on the assumption of independence.

1. Have Takt Time (TT) sample of size n 2. Have the number of work items delivered (N) 3. Draw the same number of observation 𝑻𝑻𝒊 as the

sample size n with replacement out of the sample from step 1

4. Calculate Project Delivery time (T) for the sample from step 2 using 𝑻 = 𝑻𝑻𝒊

5. Calculate Takt Time (TT) by 𝑻𝑻 = 𝑻/𝑵 using T from step 3 and N from step 2

6. Repeat many times 7. Prepare distribution for Takt Time (TT)

Bootstrapping the distribution of Takt Time

Example: Monte Carlo simulation of Takt Time (TT)

Sampled Takt Time data 𝑻𝑻𝒊=(0,0,1,1,1,2,2,2,5,7)

𝑻 = 𝑻𝑻𝒊 = 𝟐𝟏 𝒅𝒂𝒚𝒔

𝑻𝑻 = 𝑻/𝑵 = 2.1 days/story

Another 998 draws with replacement

Historical Takt Time data 𝑻𝑻𝒊=(0,0,0,0,1,2,2,5,5,7)

𝑻 = 𝑻𝑻𝒊 = 𝟐𝟐 𝒅𝒂𝒚𝒔

𝑻𝑻 = 𝑻/𝑵 = 2.2 days/story Sampled Takt Time data 𝑻𝑻𝒊=(0,1,1,1,1,2,5,5,5,7)

𝑻 = 𝑻𝑻𝒊 = 𝟐𝟖 𝒅𝒂𝒚𝒔

𝑻𝑻 = 𝑻/𝑵 = 2.8 days/story

1st draw with replacement

1000th draw with replacement

Result: Takt Time (TT) distribution

Median 2,2

STD 0,788833

Average T 2,1943

85 Perc 3

95 Perc 3,5

Mode(s) 2,4

SIP size 1000

Stochastic Information Packet (SIP) • Comprised of a list of trials of some uncertain

parameter or metric generated from historical data using Monte Carlo simulation (resampling)

• Represents an uncertainty as an array of possible outcomes (distribution)

• It is unique per context (business domain, team, delivery process used etc.)

COMPARING THE NEW PROJECT WITH

THE REFERENCE CLASS

DISTRIBUTION

𝑇 = 𝑁𝑇𝑇 assumes linear delivery rate

Project Delivery Time (T)

Project Delivery Time (T)

Completed Work (N)

22 days

10 work items

Most projects have non-linear delivery rate

Z-curve

Each leg of the Z-curve is characterized by:

• Different work type • Different level of variation • Different staffing in terms of headcount and level of

expertise

1st leg – Setup time

• climbing the learning curve • conducting experiments to cover the riskiest work

items • Innovation! • setting up environments • adapting to client’s culture and procedures • understanding new business domain • mastering new technology

2nd leg – Productivity period If the project is scheduled properly the system should be like a clockwork – sustainable pace, no stress, no surprises…

3rd leg – Cleaning up • Clean up the battlefield • Fix some outstanding defects • Support the transition of the project deliverable into

operation

https://www.ocoos.com/me/professional-dog-training-in-home/

Project delivery time T

𝑇 = 𝑇𝑧1 + 𝑇𝑧2 + 𝑇𝑧3 Where: 𝑇𝑧1 – is the duration of the 1st leg of the Z-curve 𝑇𝑧2 – is the duration of the 2nd leg of the Z-curve 𝑇𝑧3 – is the duration of the 3rd leg of the Z-curve

Project delivery time T

𝑇 = 𝑁𝑧1𝑇𝑇𝑧1 + 𝑁𝑧2𝑇𝑇𝑧2 + 𝑁𝑧3𝑇𝑇𝑧3 Where: 𝑇𝑇𝑧1 is the Takt Time for the 1st leg of the Z-curve

𝑇𝑇𝑧2 is the Takt Time for the 2nd leg of the Z-curve

𝑇𝑇𝑧3 is the Takt Time for the 3rd leg of the Z-curve

𝑁𝑧1 is the number of items delivered during the 1st leg of the Z-curve

𝑁𝑧2 is the number of items delivered during the 2nd leg of the Z-curve

𝑁𝑧3 is the number of items delivered during the 3rd leg of the Z-curve

Monte Carlo simulation of Project Delivery Time (T) based on Z-curve

1. Have three Takt Time SIPs (𝑇𝑇𝑧1, 𝑇𝑇𝑧2, 𝑇𝑇𝑧3) each one of size n for each of the three legs of the Z-curve

2. Have the number of work items to be delivered for each of the three legs of the Z-curve (𝑁𝑧1, 𝑁𝑧2, 𝑁𝑧3)

3. Draw one observation out of the n, with replacement (bootstrap) from each of (𝑇𝑇𝑧1, 𝑇𝑇𝑧2, 𝑇𝑇𝑧3)

4. Calculate Project Delivery time (T) for the sample from step 3 using 𝑇 = 𝑁𝑧1𝑇𝑇𝑧1 +𝑁𝑧2𝑇𝑇𝑧2 + 𝑁𝑧3𝑇𝑇𝑧3

5. Repeat many times 6. Prepare Delivery time (T) probability distribution

EXAMPLE: MONTE CARLO SIMULATION OF PROJECT DELIVERY TIME (T)

The New Project to be delivered

• THE SAME Fortune 500 Staffing company

• THE SAME development organization

• THE SAME technology – Java; Spring; Oracle;

• Delivery time TO BE PREDICTED

Takt Time distributions for each of the three legs of Z-curve for the reference

class

Project scope After some analysis the team have broken down the requirements into user stories, accounting for Cost of Delay, added work items for Dark matter and Failure load and decided that:

• 12 stories TO BE delivered in the 1st leg of Z-curve

• 70 stories TO BE delivered in the 2nd leg of Z-curve

• 18 stories TO BE delivered in the 3rd leg of Z-curve

Monte Carlo simulated summation of…

…will give us the time needed to deliver the project!

12 work items 70 work items 18 work items

Monte Carlo simulation of Project Delivery Time (T)

Simulated one Project Delivery Time value 𝑻 = 𝑁𝑧1𝑇𝑇𝑧1 + 𝑁𝑧2𝑇𝑇𝑧2 + 𝑁𝑧3𝑇𝑇𝑧3= 12 × 1.43 + 70 × 0.3 + 18× 1.11 = 58.14 𝑑𝑎𝑦𝑠

49998 draws with replacement from each of (𝑇𝑇𝑧1, 𝑇𝑇𝑧2, 𝑇𝑇𝑧3)

Takt Time SIPs: 𝑇𝑇𝑧1, 𝑇𝑇𝑧2, 𝑇𝑇𝑧3 Work items: 𝑁𝑧1, 𝑁𝑧2, 𝑁𝑧3

1st draw with replacement from each of (𝑇𝑇𝑧1, 𝑇𝑇𝑧2, 𝑇𝑇𝑧3)

50000th draw with replacement from each of (𝑇𝑇𝑧1, 𝑇𝑇𝑧2, 𝑇𝑇𝑧3)

Simulated one Project Delivery Time value 𝑻 = 𝑁𝑧1𝑇𝑇𝑧1 +𝑁𝑧2𝑇𝑇𝑧2 + 𝑁𝑧3𝑇𝑇𝑧3= 12 × 1.81 + 70 × 0.54 + 18× 0.64 = 71.04 𝑑𝑎𝑦𝑠

Mode = 76 days; Median = 77 days; Mean = 78 days; 85th perc = 90 days

By taking an outside view when forecasting a new project we will

produce more accurate results faster than using the deterministic inside

view.

References Here are the distributions for the baseline project SIPs_MonteCarlo_FVR.xlsx Here is the planning simulation in Excel High_Level_Project_Planning.xlsx What is SIP?

Dimitar Bakardzhiev is the Managing Director of Taller Technologies Bulgaria and an expert in driving successful and cost-effective technology development. As a Lean-Kanban University (LKU)-Accredited Kanban Trainer (AKT) and avid, expert Kanban practitioner, Dimitar puts lean principles to work every day when managing complex software projects with a special focus on building innovative, powerful mobile CRM solutions. Dimitar has been one of the leading proponents and evangelists of Kanban in his native Bulgaria and has published David Anderson’s Kanban book as well as books by Eli Goldratt and W. Edwards Deming in the local language. He is also a lecturer and frequent speaker at numerous conferences and his passion is to educate audiences on the benefits of lean principles and agile methodologies for software development.

@dimiterbak