How to Calculate Dates in the Critical Path Method · How to Calculate Dates in the Critical Path...

MURRAY B. WOOLF

ICS-WHITE PAPER

How to Calculate Dates in the Critical Path Method

The Ten Essential Formulas

WPB-KI-13

by Murray B. Woolf

ICS-PublicationsA Division of the International Center for Scheduling, Inc.

ICS-Compendium White Paper WPB-KI-13

How to Calculate Dates in the

Critical Path Method

Including theTen Essential Formulas

Copyright, 2012 International Center for Scheduling, Inc. (ICS-Global) All rights reserved.

ICS-Compendium: Project Management Critical Thinking

ICS-White Paper WPB-KI-13Version 1.0

Published September 13, 2011

� Note: This White Paper was designed to function as a stand-alone reference document. It presumes a minimum understanding of the basics of the Critical Path Method. If you do not feel that you have this level of understanding, or if you find the content of this White Paper a little “over your head,” you would quite likely receive great benefit from reading CPM MECHANICS.

CPM MECHANICS is Volume 1 of the ICS-Compendium* and forms the basis for both the DOMINANT PROJECT MANAGEMENT SERIES and the COGNITIVE PROJECT MANAGEMENT SERIES. This White Paper is heavily referenced in CPM MECHANICS, and was written to serve as a supplement to that book.

To learn more about CPM Mechanics, we encourage you to investigate it at www.CpmMechanics.com.

* The ICS-Compendium is a five-year project that began in January 2011. The primary eight volumes are scheduled for issuance in six-month increments, starting with CPM Mechanics, which is already on bookshelves. Release Dates for the other volumes are posted at the ICS-Placement website. Simply go to www.ics-placement.com.

� Note: Words appearing in bold font are defined in the glossary at the end of the White Paper. You may wish to consult the ICS-Dictionary for additional terms not defi ned in the glossary.

We wish to thank the following individuals for their tireless help in the development of this White Paper. Their advice and guidance was instrumental in achievement of this work product, so important to the Scheduling Community:

Gunnar Lucko (Professor, Catholic University of America)Ronny Warren (Instructor, University of North Texas)


WPB-KI-13

Table of Contents

I: Overview: Date Calculation Concepts . . . . . . . . . . . . . . . . . . . . . . . . 8I.A: Date Calculation Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8I.B: Four Basic Calculated Dates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9I.C: Date Calculation Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9I.D: Date Calculation Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10I.E: Date Calculation Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11I.F: Date Calculation Arithmetic Formulas . . . . . . . . . . . . . . . . . . . . . . . . 12I.G: Arithmetic Formulas Identifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . 13I.H: Arithmetic Formulas Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . 14

II: How to Calculate EARLIEST START . . . . . . . . . . . . . . . . . . . . . . . 15II.A: Condition ES|dr: Earliest Start thru Default Restriction(s) . . . . . . . . . . . . 16II.A.1: Date Calculation Process, in Plain English . . . . . . . . . . . . . . . . . . . . 16II.A.2: Date Calculation Technical Specifications and Formula . . . . . . . . . . . . . 16

II.B: Condition ES|sr: Earliest Start thru Start Restriction(s) . . . . . . . . . . . . . . 17II.B.1: Date Calculation Process, in Plain English . . . . . . . . . . . . . . . . . . . . 17II.B.2: Date Calculation Technical Specifications and Formula . . . . . . . . . . . . . 17

II.C: Condition ES|mx: Earliest Start thru Restriction Type Mixture . . . . . . . . . . 18II.C.1: Date Calculation Process, in Plain English . . . . . . . . . . . . . . . . . . . . 18II.C.2: Date Calculation Technical Specifications and Formula . . . . . . . . . . . . . 18

II.D: Condition ES|no: Earliest Start with No Restriction Linkages . . . . . . . . . . . 19II.D.1: Date Calculation Process, in Plain English . . . . . . . . . . . . . . . . . . . . 19


Page 4 Copyright, 2012 International Center for Scheduling, Inc. (ICS-Global) All rights reserved.

II.D.2: Date Calculation Technical Specifications and Formula . . . . . . . . . . . . . 19III: How to Calculate EARLIEST FINISH . . . . . . . . . . . . . . . . . . . . . . . 20III.A: Condition EF|du: Earliest Finish thru Activity Duration . . . . . . . . . . . . . 21III.A.1: Date Calculation Process, in Plain English . . . . . . . . . . . . . . . . . . . . 21III.A.2: Date Calculation Technical Specifications and Formula . . . . . . . . . . . . . 21

III.B: Condition EF|fr: Earliest Finish thru Finish Restriction(s) . . . . . . . . . . . . 22III.B.1: Date Calculation Process, in Plain English . . . . . . . . . . . . . . . . . . . . 22III.B.2: Date Calculation Technical Specifications and Formula . . . . . . . . . . . . . 22

IV: How to Calculate LATEST START . . . . . . . . . . . . . . . . . . . . . . . . . 23IV.A: Condition LS|du: Latest Start thru Activity Duration . . . . . . . . . . . . . . . 24IV.A.1: Date Calculation Process, in Plain English . . . . . . . . . . . . . . . . . . . . 24IV.A.2: Date Calculation Technical Specifications and Formula . . . . . . . . . . . . . 24

IV.B: Condition LS|sr: Latest Start thru Start Restriction(s) . . . . . . . . . . . . . . . 25IV.B.1: Date Calculation Process, in Plain English . . . . . . . . . . . . . . . . . . . . 25IV.B.2: Date Calculation Technical Specifications and Formula . . . . . . . . . . . . . 25

V: How to Calculate LATEST FINISH . . . . . . . . . . . . . . . . . . . . . . . . . 26V.A: Condition LF|dr: Latest Finish thru Default Restriction(s) . . . . . . . . . . . . 27V.A.1: Date Calculation Process, in Plain English . . . . . . . . . . . . . . . . . . . . 27V.A.2: Date Calculation Technical Specifications and Formula . . . . . . . . . . . . . 27

V.B: Condition LF|fr: Latest Finish thru Finish Restriction(s) . . . . . . . . . . . . . 28V.B.1: Date Calculation Process, in Plain English . . . . . . . . . . . . . . . . . . . . 28V.B.2: Date Calculation Technical Specifications and Formula . . . . . . . . . . . . . 28

V.C: Condition LF|mx: Latest Finish thru Restriction Type Mixture . . . . . . . . . 29V.C.1: Date Calculation Process, in Plain English . . . . . . . . . . . . . . . . . . . . 29V.C.2: Date Calculation Technical Specifications and Formula . . . . . . . . . . . . . 29

V.D: Condition LF|no: Latest Finish with No Restriction Linkages . . . . . . . . . . 30V.D.1: Date Calculation Process, in Plain English . . . . . . . . . . . . . . . . . . . . 30V.D.2: Date Calculation Technical Specifications and Formula . . . . . . . . . . . . . 30

VI: Date Calculation Computational Rules . . . . . . . . . . . . . . . . . . . . . . . 31VI.A: Computational Rules for Computing Earliest Start . . . . . . . . . . . . . . . . . 31VI.B: Computational Rules for Computing Earliest Finish . . . . . . . . . . . . . . . . 33

WPB-KI-13 Calculating Dates in the Critical Path Method

Page 5Copyright, 2012 International Center for Scheduling, Inc. (ICS-Global) All rights reserved.

VI.C: Computational Rules for Computing Latest Start . . . . . . . . . . . . . . . . . . 34VI.D: Computational Rules for Computing Latest Finish . . . . . . . . . . . . . . . . . 35

VII: Convenient Reference Information . . . . . . . . . . . . . . . . . . . . . . . . . 37VII.A: Dominant/Cognitive Terminology Conversions . . . . . . . . . . . . . . . . . . 37

VIII: Summary of Date Calculation Formulas . . . . . . . . . . . . . . . . . . . . . . 39VIII.A: Arithmetic Formulas: Start-of-Day or End-of-Day Perspectives . . . . . . . . . 39VIII.B: Arithmetic Formulas: Point-of-Day Perspective . . . . . . . . . . . . . . . . . . 40

IX: Definitions of Terms Used in this White Paper . . . . . . . . . . . . . . . . . . 41


WPB-KI-13How to Calculate Dates in the Critical Path Method

Including “The Ten Essential Formulas”

This White Paper explains the Ten Essential Formulas that are used to determine the Four Basic Calculated Dates associated with every Activity [1] in a Critical Path Method (CPM) Schedule. For the following discussion, see Figure F001.

1 That is, every Activity with a non-zero Duration.

Ten Essential FormulasEarliest

StartLatestStart

LatestFinish

Four Basic Calculated Dates >> EarliestFinish

Two

Calc

ulat

ion

Vari

able

s

Rest

rictio

n Li

nkag

es

Activity Duration EF|du LS|du -na--na-

No Restrictions ES|no LF|no-na--na-

(Finish-to-Start)Default Restriction(s) ES|dr LF|dr-na--na-

(Start-to-Start)Start Restriction(s) ES|sr -na- LS|sr -na-

(Finish-to-Finish)Finish Restriction(s) EF|fr -na- LF|fr-na-

F001: CPM Date Calculations: Table of Dates, Variables, and Formulas



� Figure F001 offers a helpful guide to knowing which Date Calculation Formulas to apply under which circumstances. While one should read this White Paper in its entirety to fully understand the above table, a more focused discussion appears under Date Calculation Variables, on page 11.

� To learn more about Date Calculation Perspectives, read ICS-WHITE PAPER WPB-KJ-28, “UNDERSTANDING THE POINT-OF-DAY PERSPECITVES.”

I: Overview: Date Calculation ConceptsBefore we immerse ourselves in the specifi cs of the Ten Essential Formulas, we need to establish a common frame of reference for such discussions. Specifi cally, we need to reach a common understanding as to:

Four Basic Calculated Dates: Just what are the Four Basic Calculated Dates that are central to every Activity in a Critical Path Method Schedule?

Date Calculation Processes: What Date Calculation processes are employed when determining the specific values of Calculated Dates?

Date Calculation Procedures: What inherent procedures are used with each distinct Date Calculation Process?

Date Calculation Variables: What Date Calculation Variables, inherent in basic CPM Logic Diagram content, should be taken into consideration when performing Date Calculations?

Date Calculation Arithmetic Formulas: What Arithmetic Formulas should be employed, based on whichever Date Calculation Variables happen to be present in any particular instance?

Date Calculation Computational Rules: What helpful Computational Rules might one consider when performing Forward Pass and Backward Pass Processes?

I.A: Date Calculation Specifi cationsThese six topics are intertwined with one another. Each of the Four Basic Calculated Dates has its own set of Arithmetic Formulas and Computational Rules. These Arithmetic Formulas and Computational Rules, even for just one Calculated Date, differ depending on the Date Calculation Variables that dictate which Date Calculation Procedures to be followed. All of this will make more sense as you read on. Let's take them one at a time.



I.B: Four Basic Calculated DatesWithin the Critical Path Method, as a method of modeling Project Execution Strategy, every Activity in the Project Schedule has FOUR BASIC CALCULATED DATES associated with it. Here is how the ICS-Dictionary defi nes them:

Earliest Start: An estimate of the earliest possible Calculated Date by which an Activity can be reasonably expected to start, assuming the fl awless performance of all prior Activities to which the Activity is Logically connected in a Progressive Relationship.

Earliest Finish: An estimate of the earliest possible Calculated Date by which an Activity can be reasonably expected to fi nish, assuming the fl awless performance of all prior Activities to which the Activity is Logically connected in a Progressive Relationship.

Latest Start: An estimate of the latest plausible date to which an start may be postponed without rendering as unachievable the required completion of any downstream Deadline Milestones to which the Activity is Logically connected in a Progressive Relationship.

Latest Finish: An estimate of the latest plausible date to which an fi nish may be postponed without rendering as unachievable the required completion of any downstream Deadline Milestones to which the Activity is Logically connected in a Progressive Relationship.

I.C: Date Calculation ProcessesIt is well explained throughout Dominant Project Management literature that Earliest Start and Earliest Finish Dates are determined through a process called a Forward Pass. Likewise, Latest Start and Latest Finish Dates are determined through a Backward Pass Process. We wish to embellish on this general understanding by further distinguishing between processes and procedures, seemingly synonymous terms.

To be clear, Date Calculation Processes are comprised of Date Calculation Procedures, Arithmetic Formulas, Computational Rules, and Date Calculation Variables, as clarifi ed by the following ICS-Dictionary defi nitions:

Forward Pass Process: Used to determine the Earliest Start and Earliest Finish Dates of a series of Progressively-related Activities in a CPM Network Diagram, the Forward Pass Process is a combination of (a) Computational Procedures that utilize



(b) Arithmetic Formulas in accordance with (c) condition-specifi c Computational Rules that are mandated by particular (d) Date Calculation Variables.

Backward Pass Process: Used to determine the Latest Start and Latest Finish Dates of a series of Progressively-related Activities in a CPM Network Diagram, the Backward Pass Process is a combination of (a) Computational Procedures that utilize (b) Arithmetic Formulas in accordance with (c) condition-specifi c Computational Rules that are mandated by particular (d) Date Calculation Variables.

From these defi nitions we learn that both the Forward Pass and the Backward Pass are processes, not procedures. According to Dictionary.com, a process is:

Process: A set or series of actions directed to some end or a natural series of changes.

I.D: Date Calculation ProceduresContrast this with a procedure, which the same source defi nes as:

Procedure: A series of actions conducted in a certain manner, an established way of doing something.

These defi nitions help us to better understand why the two terms are so often used interchangeably: they both deal with a “series of actions.”

But when we look closer, we see that the distinguishing characteristic of a process is that it is “directed to some end,” whereas a procedure's primary distinguishing characteristic is the “certain manner” in which a series of actions are performed.

Now let us think about the Forward Pass Process which is a set of actions that lead to the determination of Earliest Dates. The Backward Pass must be a process too, for it leads to the determination of Latest Dates. They are both processes because they are both “directed to some end.”

Almost without exception, Dominant Project Management literature refers to the Forward Pass and Backward Pass as an arithmetic exercises that one performs in order to determine Earliest Dates and Latest Dates, respectively. To their credit, these authorities take pains to note that the Forward Pass and Backward Pass differ in some rather basic ways. For instance:

In a Forward Pass, one uses addition to interpolate the logic and calculate the Early Dates; in a Backward Pass, subtraction is used.



In a Forward Pass, when there are multiple predecessor Activities feeding into a successor Activity, one uses the latest/largest date among the predecessors to determine the Earliest Dates of the successor Activity. Yet, in a Backward Pass, however, one uses the earliest/smallest of the successor dates to determine the Latest Dates of the predecessor Activity. (All of this is explained below.)

But to their discredit, almost without exception these same authorities fail to correlate the different Computational Rules and Arithmetic Formulas to the presence or absence of particular Date Calculation Variables.

I.E: Date Calculation VariablesCognitive Project Management has identifi ed Two Date Calculation Variables that are key factors in the determination of Earliest Dates and Latest Dates. Said differently, determination of each of the previously mentioned Four Basic Calculated Dates requires consideration of some combination of these Two Date Calculation Variables, which in turn mandates which Computational Rules and Arithmetic Formulas to apply in any given circumstance.

Here is the ICS-Dictionary for this term:

Date Calculation Variables: Inherent in the raw content of the CPM Network Diagram are Date Calculation Variables that determine the Arithmetic Formulas and Computational Rules to be used during performance of Forward Pass and Backward Pass Procedures. The two Date Calculation Variables are Performance Restrictions and Activity Durations.

As the above defi nition clarifi es, and Figure F001 indicates as well, Date Calculation Variables are comprised of two elements: Activity Durations and Performance Restrictions. So that you are clear on what these two Date Calculation Variables are all about, here are their defi nitions, from the ICS-Dictionary.

Activity Duration: Expressed in Continuous Crew Days, the Activity Duration represents an estimate of the amount of time required by an assumed Crew Confi guration to perform the Scope of Work of an Activity, as briefl y described by the Activity Description. An Activity Duration is one of two Date Calculation Variables used to determine the appropriate Date Calculation Procedures, Computational Rules, and Arithmetic Formulas.



Performance Restriction: Performance Restriction is the name that Cognitive Project Management has given to the four possible ways that Activities can be dependently linked to one another in Progressive Relationships within the Critical Path Method. Each distinct confi guration is called a Restriction Linkage. The four Restriction Linkages of Cognitive Project Management correspond to the four Dependency Types (or Relationship Types) of Dominant Project Management: Default Restriction (Finish-to-Start Dependency), Start Restriction (Start-to-Start Dependency), Finish Restriction (Finish-to-Finish Dependency), and Holdback Restriction (Start-to-Finish Dependency).

From Figure F001 we can make a few immediate observations: Activity Durations: Only two Calculated Dates (Earliest Finish and Latest Start)

require consideration of the Activity Duration. That is, the Activity Duration has no bearing on the determination of the other two Calculated Dates (Earliest Start and Latest Finish).

Restriction Linkages: We can make several observations about how the combination of Restriction Linkages affect the determination of an Activity's Four Basic Calculated Dates.

Two Calculated Dates, Earliest Start and Latest Finish, can have one or two different types of Restriction Linkages affecting them simultaneously.

Two other Calculated Dates, Earliest Finish and Latest Start, are never affected by more than one type of Restriction Linkage.

� Although No Restrictions is included as a Restriction Linkage, it is really not a Restriction Linkage at all, but instead a Performance Restriction condition of there not being any Restriction Linkages affecting the subject Calculated Date.

It is listed however because an underlying principle of both Forward Pass and Backward Pass Date Calculations is that every progressively-related Activity is connected to other Immediately-Restricting Activities by way of zero, one, or two Restriction Linkages.

I.F: Date Calculation Arithmetic FormulasAs noted at the outset of this White Paper, there are Ten Essential Formulas that are the basis for all Forward Pass and Backward Pass Date Calculations. The role of Computational Rules is to help you determine which Arithmetic Formulas to apply under which circumstances, as defi ned by different combinations of calculation variables. We



discuss Computational Rules after this current section on Arithmetic Formulas.

� These Arithmetic Formulas are applicable for either the End-of-Day Perspective or the Start-of-Day Perspective. For those using the Point-of-Day Perspective, a modified set of Arithmetic Formulas is required. For your convenience, we have included the set of modified Point-of-Day formulas at the end of this White Paper.

I.G: Arithmetic Formulas Identifi ersTo ease communications, each Arithmetic Formula has its own Arithmetic Formula Identifi er. An Arithmetic Formula Identifi er has two parts, separated by a vertical bar. For example, consider, LF|dr.

The left-most two characters identify the Calculated Date that the Arithmetic Formula solves for. In this case, the LF value tells is that we are solving for the Latest Finish.

The right-most two characters tell us about the controlling Date Calculation Variable. In the above example, dr value tells that the Activity Pair is connected by way of a Default Restriction (Finish-to-Start) Restriction Linkage.



I.H: Arithmetic Formulas AbbreviationsActivity Roles that describe how connecting Activities relate to the Subject Activity are coded as follows:

X = Restricting Activity; Y = Subject Activity; Z = Restricted Activity Restriction Linkages are coded as follows:

Abbreviation Full Namedr Default Restriction (Finish-to-Start)sr Start Restriction (Start-to-Start)fr Finish Restriction (Finish-to-Finish)

mx Mixture of Performance Restriction Linkages

|dr = Default Restriction (Finish-to-Start) |sr = Start Restriction (Start-to-Start) |fr = Finish Restriction (Finish-to-Finish) |no = No Restriction (that drives the Subject Activity desired date)

The FOUR BASIC CALCULATED DATES are abbreviated as: ES = Earliest Start; EF = Earliest Finish LS = Latest Start; LF = Latest Finish

The DATE CALCULATION VARIABLES are abbreviated as: DU = Activity Duration DLdr = Restriction Delay through Default Restriction DLsr = Restriction Delay through Start Restriction DLfr = Restriction Delay through Finish Restriction

Project-level codes are as follows: PS = Project Start; PF = Project Finish; DD = Data Date



II: How to Calculate EARLIEST STARTThere are four possible Date Calculation conditions that might affect Earliest Start determination:

ES|dr : When one or more Default Restrictions are the only logic ties connected to the start of the Subject Activity.

ES|sr : When one or more Start Restrictions are the only logic ties connected to the start of the Subject Activity.

ES|mx : When one or more Default Restriction and one or more Start Restrictions are connected to the start of the Subject Activity.

ES|no : Used when neither Default Restrictions nor Start Restrictions are connected to the start of the Subject Activity.

� Even if the Subject Activity is preceded by activities linked by way of Finish Restrictions, Finish Restrictions do not affect Earliest Start dates.



II.A: Condition ES|dr: Earliest Start thru Default Restriction(s)This condition exists when one or more Default Restrictions are the only logic ties connected to the start of the Subject Activity. Under this condition, a Computed Choice for the Subject Activity’s Earliest Start is determined by whichever Restricting Activity yields the chronologically latest date – when its Default Restriction Delay is added to its Earliest Finish. See Figure F002.

II.A.1: Date Calculation Process, in Plain English

Follow these steps:1. Identify all Restricting Activities

tied to the Subject Activity by way of a Default Restriction. (e.g. Activity X1, )

2. For each Restricting Activity, determine its Earliest Finish and (EFX1

) and any corresponding Restriction Delay (DLdrX1

). 3. For each Restricting Activity, add

to the Earliest Finish whatever, if any, Restriction Delay may be imposed on the Restriction Linkage. The resultant date is called a Computed Choice.

4. From all Computed Choices, identify the chronologically latest date, which then becomes the Subject Activity’s Earliest Start.

II.A.2: Date Calculation Technical Specifi cations and Formula Formula Identifier: ES|dr Formula Solves For: Earliest Start (ES) Calculation Variable: Default Restriction (dr) Dependency Type: Finish-to-Start Role of Subject Activity: Restricted Activity Formula: ESY = max [ (EFX1

+ DLdrX1), (EFX2

+ DLdrX2) ... (EFXn

+ DLdrXn) ]

EF

ESY

EF

DLdrRestrictingActivity X1

RestrictingActivity X2

SubjectActivity Y

X2DLdr

X1

X1

X2

F002: Earliest Start thru Default Restriction(s)



II.B: Condition ES|sr: Earliest Start thru Start Restriction(s)This condition exists when one or more Start Restrictions are the only logic ties connected to the start of the Subject Activity. Under this condition, a Computed Choice for the Subject Activity’s Earliest Start is determined by whichever Restricting Activity yields the chronologically latest date – when its Start Restriction Delay is added to its Earliest Start. See Figure F003.

II.B.1: Date Calculation Process, in Plain English

Follow these steps:1. Identify all Restricting

Activities tied to the Subject Activity by way of a Start Restriction. (e.g. Activity X1, )

2. For each Restricting Activity, determine its Earliest Start and (ESX1

) and any corresponding Restriction Delay (DLsrX1

). 3. For each Restricting Activity,

add to the Earliest Start whatever, if any, Restriction Delay may be imposed on the Restriction Linkage. The resultant date is called a Computed Choice.

4. From all Computed Choices, identify the chronologically latest date, which then becomes the Subject Activity’s Earliest Start.

II.B.2: Date Calculation Technical Specifi cations and Formula Formula Identifier: ES|sr Formula Solves For: Earliest Start (ES) Calculation Variable: Start Restriction (sr) Dependency Type: Start-to-Start Role of Subject Activity: Restricted Activity Formula: ESY = max [ (ESX1

+ DLsrX1), (ESX2

+ DLsrX2) ... (ESXn

+ DLsrXn) ]

X1

X2

ESY

ES

ES

SubjectActivity Y

DLsrX1

DLsrX2



F003: Earliest Start thru Start Restriction(s)



II.C: Condition ES|mx: Earliest Start thru Restriction Type MixtureThis condition exists when the start of the Subject Activity is restricted by one or more Default Restrictions and by one or more Start Restrictions. Under this condition, the Subject Activity’s Earliest Start is determined by the chronologically latest date among all Computed Choices derived from all of the Subject Activity's Restricting Activities.See Figure F004.

II.C.1: Date Calculation Process, in Plain English

Follow these steps:1. Perform the Date Calculation

Process for the Earliest Start thru Default Restriction(s) condition. See instructions for Condition ES|dr.

2. Find the ES|dr Computed Choice.

3. Perform the Date Calculation Process for the Earliest Start thru Start Restriction(s) condition. See instructions for Condition ES|sr.

4. Find the ES|sr Computed Choice.

5. Determine the chronologically latest date between these two Computed Choices. This becomes the Subject Activity's Earliest Start.

II.C.2: Date Calculation Technical Specifi cations and Formula Formula Identifier: ES|mx Formula Solves For: Earliest Start (ES) Calculation Variable: Default Restriction (dr) and Start Restriction (sr) Dependency Type: Finish-to-Start and Start-to-Start Role of Subject Activity: Restricted Formula: ES|mx = max (ES|dr, ES|sr)

X1

X2

ESY

ES

ES

SubjectActivity Y

DLsrX1

DLdrX2



X1EF

X2EF

YEF

F004: Earliest Start thru Restriction Mixture



II.D: Condition ES|no: Earliest Start with No Restriction Linkages

This condition exists when the start of the Subject Activity is not restricted by either a Default Restriction or a Start Restriction. Under this condition, the Subject Activity’s Earliest Start is determined by the current Data Date. See Figure F005.

� Note: Even if the Subject Activity is preceded by Activities linked by way of Finish Restrictions, Finish Restrictions do not affect Earliest Start dates.

� Note: In a Baseline Schedule (also known as an As-Planned Schedule) where the project has not yet begun, the Data Date is set to Day 0 (End-of-Day Perspective) or Day 1(Start-of-Day Perspective). [2]

II.D.1: Date Calculation Process, in Plain English

Follow these steps:1. Determine the Project Start Date.2. Determine the current Data Date.3. Whichever is chronologically later becomes the Subject Activity's Earliest Start.

II.D.2: Date Calculation Technical Specifi cations and Formula Formula Identifier: ES|no Formula Solves For: Earliest Start (ES) Calculation Variable: Project Start (PS) or Data Date (DD) Restriction Linkage/Dependency Type: None Role of Subject Activity: Restricted Formula: ESM = max (PS, DD)

2 For more about Point-of-Day Perspectives, see ICS-White Paper WPB-KJ-28, "Understanding the Point-of-Day Perspectives."

SubjectActivity Y

ESY



PS/DD

F005: Earliest Start thru No Restriction(s)



III: How to Calculate EARLIEST FINISHThere are two possible Date Calculation conditions that might affect Earliest Finish determination:

EF|du : Always used, whether Finish Restrictions terminate into the Subject Activity, or not. The Activity Duration, added to the Activity's Earliest Start, is always a factor in determining the Subject Activity's Earliest Finish.

EF|fr : When one or more Finish Restrictions terminate into the Subject Activity.

� Start Restrictions do not affect Earliest Finish dates.



III.A: Condition EF|du: Earliest Finish thru Activity DurationThis condition exists in every Activity within a CPM Schedule. Under this condition, a Computed Choice for the Subject Activity’s Earliest Finish is determined by aggregating the Subject Activity's Earliest Start by the amount of the Activity Duration. See Figure F006.

III.A.1: Date Calculation Process, in Plain English

Follow these steps:1. Determine the Subject

Activity's Earliest Start. 2. Determine the Subject

Activity's Duration.3. The Earliest Start date,

aggregated by the Activity Duration, yields the Subject Activity’s Earliest Finish Computed Choice as calculated through the Activity Duration.

4. If there are no Finish Restrictions connected to the Subject Activity, then this Computed Choice becomes the Earliest Finish for the Subject Activity.

� Start Restrictions do not affect Earliest Finish dates.

III.A.2: Date Calculation Technical Specifi cations and Formula Formula Identifier: EF|du Formula Solves For: Earliest Finish (EF) Calculation Variable: Activity Duration Restriction Linkage/Dependency Type: None Role of Subject Activity: Restricted Activity Formula: EFY = (ESY+ DUY)

EFYES

DU

SubjectActivity Y

Y



Y

F006: Earliest Finish thru Duration



III.B: Condition EF|fr: Earliest Finish thru Finish Restriction(s)This condition exists when one or more Finish Restrictions are logically connected to the Subject Activity. Under this condition, a Computed Choice for the Subject Activity’s Earliest Finish is determined by whichever Restricting Activity yields the chronologically latest date – when its Finish Restriction Delay is added to its Earliest Finish. See Figure F007.

III.B.1: Date Calculation Process, in Plain English

Follow these steps:1. Identify all Restricting

Activities tied to the Subject Activity by way of a Finish Restriction. (e.g. Activity X1, )

2. For each Restricting Activity, add to the Earliest Finish (EFX1

) whatever, if any, Finish Restriction Delay (DLfrX1

) may be imposed on the Restriction Linkage. The resultant date is called a Computed Choice.

3. From all such Computed Choices, determine the chronologically latest date, which then becomes the Subject Activity’s Earliest Finish Computed Choice as calculated through the Finish Restriction(s).

4. Whichever Earliest Finish Computed Choice (through Duration or Finish Restriction) is chronologically later, determines the Subject Activity's Earliest Finish.

III.B.2: Date Calculation Technical Specifi cations and Formula Formula Identifier: EF|fr Formula Solves For: Earliest Finish (EF) Calculation Variable: Finish Restriction (fr) Dependency Type: Finish-to-Finish Role of Subject Activity: Restricted Activity Formula: EFY = max [ (EFX1

+ DLfrX1), (EFX2

+ DLfrX2) ... (EFXn

+ DLfrXn); (ESY+ DUY)]

EFY

SubjectActivity Y

X1EF

DLfrX2



X2EF

DLfrX1

F007: Earliest Finish thru Finish Restriction(s)



IV: How to Calculate LATEST STARTThere are two possible Date Calculation conditions that might affect Latest Start determination:

LS|du : Always used, whether Start Restrictions sprout from the Subject Activity, or not. The Activity Duration, subtracted from the Activity's Latest Finish, is always a factor in determining the Subject Activity's Latest Start.

LS|sr : When one or more Start Restrictions sprout from the Subject Activity.

� Finish Restrictions do not affect Latest Start dates.



IV.A: Condition LS|du: Latest Start thru Activity DurationThis condition exists in every Activity within a CPM Schedule. Under this condition, a Computed Choice for the Subject Activity’s Latest Start is determined by subtracting its Activity Duration from its Latest Finish. See Figure F008.

IV.A.1: Date Calculation Process, in Plain English

Follow these steps:1. Determine the Subject

Activity's Latest Finish. 2. Determine the Subject

Activity's Duration.3. The Latest Finish date, reduced

by the Activity Duration, yields the Subject Activity’s Latest Start Computed Choice as calculated through the Activity Duration.

4. If there are no Start Restrictions sprouting from the Subject Activity, then this Computed Choice becomes the Latest Start for the Subject Activity.

� Default Restrictions and Finish Restrictions do not affect Latest Start dates.

IV.A.2: Date Calculation Technical Specifi cations and Formula Formula Identifier: LS|du Formula Solves For: Latest Start (LS) Calculation Variable: Activity Duration Restriction Linkage/Dependency Type: None Role of Subject Activity: Restricting Activity Formula: LSY = (LFY - DUY)

LFYLSY DUY

SubjectActivity Y

RestrictedActivity Z1


F008: Latest Start thru Duration



IV.B: Condition LS|sr: Latest Start thru Start Restriction(s)This condition exists when one or more Start Restrictions sprout from the Subject Activity. Under this condition, a Computed Choice for the Subject Activity’s Latest Start is determined by whichever Restricted Activity establishes the chronologically earliest date – resulting from its Start Restriction Delay being subtracted from its Latest Start. See Figure F009.

IV.B.1: Date Calculation Process, in Plain EnglishFollow these steps:

1. Identify all Restricted Activities tied to the Subject Activity by way of a Start Restriction. (e.g. Activity Z1, )

2. For each Restricted Activity, subtract from the Latest Start (LSZ1

) whatever, if any, Start Restriction Delay (DLsrZ1

) may be imposed on the Restriction Linkage. The resultant date is called a Computed Choice.

3. From all such Computed Choices, determine the chronologically earliest date, which then becomes the Subject Activity’s Latest Start Computed Choice as calculated through the Start Restriction(s).

4. Whichever Latest Start Computed Choice (through Duration or Start Restriction) is chronologically earlier, determines the Subject Activity's Latest Start.

IV.B.2: Date Calculation Technical Specifi cations and Formula Formula Identifier: LS|sr Formula Solves For: Latest Start (LS) Calculation Variable: Start Restriction (sr) Dependency Type: Start-to-Start Role of Subject Activity: Restricting Activity Formula: LSY = min [ (LSZ1

- DLsrZ1), (LSZ2

- DLsrZ2) ... (LSZn

- DLsrZn); (LFY - DUY)]

SubjectActivity Y

LSY

Z1LS

DLsrZ1



Z2LS

DLsrZ2

F009: Latest Start thru Start Restriction(s)



V: How to Calculate LATEST FINISHThere are four possible Date Calculation conditions that might affect Latest Finish determination:

LF|dr : When one or more Default Restrictions are the only logic ties sprouting from the end of the Subject Activity.

LF|fr : When one or more Finish Restrictions are the only logic ties sprouting from the end of the Subject Activity.

LF|mx : When one or more Default Restriction and one or more Finish Restrictions are sprouting from the end of the Subject Activity.

LF|no : When neither Default Restrictions nor Finish Restrictions sprout from the end of the Subject Activity.

� Even if the Subject Activity is succeeded by Activities linked by way of Start Restrictions, Start Restrictions do not affect Latest Finish dates.



V.A: Condition LF|dr: Latest Finish thru Default Restriction(s)This condition exists when one or more Default Restrictions are the only logic ties sprouting from the end of the Subject Activity. Under this condition, a Computed Choice for the Subject Activity’s Latest Finish is determined by whichever Restricted Activity yields the chronologically earliest date – when its Default Restriction Delay is subtracted from its Latest Start. See Figure F010.

V.A.1: Date Calculation Process, in Plain English

Follow these steps:1. Identify all Restricted Activities

tied to the Subject Activity by way of a Default Restriction. (e.g. Activity Z1, )

2. For each Restricted Activity, determine its Latest Start (LSZ1

) and any corresponding Restriction Delay (DLdrZ1

). 3. For each Restricted Activity,

subtract from the Latest Start whatever, if any, Restriction Delay may be imposed on the Restriction Linkage. The resultant date is called a Computed Choice.

4. From all Computed Choices, identify the chronologically earliest date, which then becomes the Subject Activity’s Latest Finish.

V.A.2: Date Calculation Technical Specifi cations and Formula Formula Identifier: LF|dr Formula Solves For: Latest Finish (LF) Calculation Variable: Default Restriction (dr) Dependency Type: Finish-to-Start Role of Subject Activity: Restricting Activity Formula: LFY = min [ (LSZ1

- DLdrZ1), (LSZ2

- DLdrZ2) ... (LSZn

- DLdrZn) ]

SubjectActivity Y

LFY

Z1LS

DLdrZ1 RestrictedActivity Z1


Z2LS

DLdrZ2

F010: Latest Finish thru Default Restriction(s)



V.B: Condition LF|fr: Latest Finish thru Finish Restriction(s)This condition exists when one or more Finish Restrictions are the only logic ties sprouting from the end of the Subject Activity. Under this condition, a Computed Choice for the Subject Activity’s Latest Finish is determined by whichever Restricted Activity yields the chronologically earliest date – when its Finish Restriction Delay is subtracted from its Latest Finish. See Figure F0011.

V.B.1: Date Calculation Process, in Plain English

Follow these steps:1. Identify all Restricted Activities

tied to the Subject Activity by way of a Finish Restriction. (e.g. Activity Z1, )

2. For each Restricted Activity, determine its Latest Finish (LFZ1

) and any corresponding Restriction Delay (DLfrZ1

). 3. For each Restricted Activity,

subtract from the Latest Finish whatever, if any, Restriction Delay may be imposed on the Restriction Linkage. The resultant date is called a Computed Choice.

4. From all Computed Choices, identify the chronologically earliest date, which then becomes the Subject Activity’s Latest Finish.

V.B.2: Date Calculation Technical Specifi cations and Formula Formula Identifier: LF|fr

Formula Solves For: Latest Finish (LF)

Calculation Variable: Finish Restriction (fr)

Dependency Type: Finish-to-Finish

Role of Subject Activity: Restricting Activity Formula: LFY = min [ (LFZ1

- DLfrZ1), (LFZ2

- DLfrZ2) ... (LFZn

- DLfrZn) ]

LFY

SubjectActivity Y

Z1LFDLfr Z1



Z2LF

DLfr Z2

F011: Latest Finish thru Finish Restriction(s)



V.C: Condition LF|mx: Latest Finish thru Restriction Type MixtureThis condition exists when the fi nish of the Subject Activity is linked to downstream Activities by one or more Default Restrictions and by one or more Finish Restrictions. Under this condition, the Subject Activity’s Latest Finish is determined by the chronologically earliest date among all Computed Choices derived from all of the Subject Activity's Restricted Activities. See Figure F012.

V.C.1: Date Calculation Process, in Plain English

Follow these steps:1. Perform the Date Calculation

Process for the Latest Finish thru Default Restriction(s) condition. See instructions for Condition LF|dr.

2. Find the LF|dr Computed Choice.3. Perform the Date Calculation

Process for the Latest Finish thru Finish Restriction(s) condition. See instructions for Condition LF|fr.

4. Find the LF|fr Computed Choice.5. Determine the chronologically

earliest date between the two Computed Choices. This becomes the Subject Activity's Latest Finish .

V.C.2: Date Calculation Technical Specifi cations and Formula Formula Identifier: LF|mx Formula Solves For: Latest Finish (LF) Calculation Variable: Default Restriction (dr) and Finish Restriction (fr) Dependency Type: Finish-to-Start and Finish-to-Finish Role of Subject Activity: Restricting Formula: LF|mx = min (LF|dr, LF|fr)

LFY

SubjectActivity Y

Z1LFDLfr Z1



Z2LF

Y

LSZ2

DLdrZ2LS

F012: Latest Finish thru Restriction Mixture



V.D: Condition LF|no: Latest Finish with No Restriction Linkages

This condition exists when the fi nish of the Subject Activity does not restrict any other downstream Activity by way of either a Default Restriction or a Finish Restriction. Under this condition, the Subject Activity’s Latest Finish is determined by the Latest Finish for the entire Project (Schedule). See Figure F013.

� Note: Even if the Subject Activity is succeeded by Activities linked by way of Start Restrictions, Start Restrictions do not affect Latest Finish dates.

V.D.1: Date Calculation Process, in Plain EnglishFollow these steps:

1. Determine the Project Completion Milestone.2. This becomes the Subject Activity's Latest Finish.

V.D.2: Date Calculation Technical Specifi cations and Formula Formula Identifier: LF|no Formula Solves For: Latest Finish (LF) Calculation Variable: Project Finish (PF) Restriction Linkage/Dependency Type: None Role of Subject Activity: Restricting Formula: LF|mx = min (LF|dr, LF|fr)

LFY

SubjectActivity Y



PF

F013: Latest Finish thru No Restriction(s)

� Note: Even if the Subject Activity is succeeded by Activities linked by way of Start Restrictions, Start Restrictions do not affect Latest Finish dates.



VI: Date Calculation Computational RulesIt is not enough simply to know about the Arithmetic Formulas for calculating the Four Basic Calculated Dates. One must also know which Arithmetic Formulas to use in each particular circumstance, The following process maps should be fairly self- explanatory. Nevertheless, we will provide limited commentary, in addition.

VI.A: Computational Rules for Computing Earliest StartAs shown in Figure F014, the Earliest Start Date will be derived from one of four culminating Arithmetic Formulas: ES|dr, ES|sr, ES|mx, or ES|no.

Solid Black Line: Since the Default Restriction is the most common Performance Restriction in the Critical Path Method, we test for it first.

If there are one or more Default Restrictions, then the fi rst computation is ES|dr, to find the maximum Earliest Start from all incoming Default

Formula ES|dr

AnyIncoming

dr?

ES = ES|mx

AnyIncoming

sr?Any

Incomingsr?

Formula ES|sr

Formula ES|mx

Formula ES|sr Formula ES|no

ES = ES|noES = ES|srES = ES|dr

Yes No

Yes

No

Yes

No

F014: Process Map for Computing Earliest Start



Restrictions. This becomes the Computed Choice through the Default Restriction.

Next, we check for the presence of one or more incoming Start Restrictions. If they exist, then we perform computation ES|sr to fi nd the maximum Earliest Start from all incoming Start Restrictions. This becomes the Computed Choice through the Start Restrictions.

Given that we have two different Computed Choices at play, we must now determine which Computed Choice yields the larger/latest Earliest Start. We apply ES|mx = max (ES|dr, ES|sr).

Finally, we conclude that the Earliest Start for Subject Activity is ES|mx.

Dashed Red Line: The Dashed Red Line branches from the Solid Black Line at the point at which we have already confirmed that one or more Default Restrictions exist and we have performed the ES|dr computation.

We test for the presence of at least one incoming Start Restriction, but fi nd none.

Since the only Date Calculation Variable at play is one or more Default Restrictions, we conclude that the Earliest Start for Subject Activity is ES|dr.

Broken Green Line: The Broken Green Line reflects a situation wherein the Subject Activity has no incoming Default Restrictions.

We test for incoming Start Restrictions and fi nd one or more. We perform computation ES|sr to fi nd the maximum Earliest Start from all incoming Start Restrictions. This becomes the Computed Choice through the Start Restrictions.

Since the only Date Calculation Variable at play is one or more Start Restrictions, we conclude that the Earliest Start for Subject Activity is ES|sr.

Dotted Blue Line: The Dotted Blue Line reflects a situation wherein the Subject Activity has no incoming Performance Restrictions of any kind. As a result, we apply ES|no, which we conclude must be the Earliest Start for Subject Activity.



VI.B: Computational Rules for Computing Earliest Finish

As shown in Figure F015, the Earliest Finish date will be derived from one of two culminating Arithmetic Formulas: EF|du, EF|mx.

Solid Black Line: Every Activity has an Activity Duration and so, at a minimum, the Earliest Finish must always be computed through the Activity Duration. This becomes the Computed Choice through the Activity Duration. The only remaining question is whether the Subject Activity is also linked by way of one or more Finish Restrictions.

If there are one or more Finish Restrictions, then it is necessary to perform Arithmetic Formula EF|fr, to fi nd the maximum Earliest Finish from all incoming Finish Restrictions.This becomes the Computed Choice through the Finish Restrictions.

Given that we have two different Computed Choices at play, we must now determine which Computed Choice yields the larger/latest Earliest Finish. We apply EF|mx = max (EF|du, EF|fr).

Finally, we conclude that the Earliest Finish for Subject Activity is EF|mx.

AnyIncoming

fr?

EF = EF|mx

Formula EF|fr

Formula EF|mx

EF = EF|du

Yes No

Formula EF|du

F015: Process Map for Computing Earliest Finish



Broken Green Line: The Broken Green Line reflects a situation wherein the Subject Activity has no incoming Finish Restrictions.

Since the only Date Calculation Variable at play is the Activity Duration, we conclude that the Earliest Finish for Subject Activity is EF|du.

VI.C: Computational Rules for Computing Latest StartAs shown in Figure F016, the Latest Start date will be derived from one of two culminating Arithmetic Formulas: LS|du, LS|mx.

Solid Black Line: Every Activity has an Activity Duration and so, at a minimum, the Latest Start must always be computed through the Activity Duration. This becomes the Computed Choice through the Activity Duration. The only remaining question is whether the Subject Activity is also linked by way of one or more outgoing Start Restrictions.

If there are one or more outgoing Start Restrictions, then the necessary Arithmetic Formula is LS|sr, to find the minimum Latest Start from all outgoing Start Restrictions. This becomes the Computed Choice through the Start Restrictions.

AnyOutgoing

sr?

LS = LS|mx

Formula LS|sr

Formula LS|mx

LS = LS|du

Yes No

Formula LS|du

F016: Process Map for Computing Latest Start



Given that we have two different Computed Choices at play, we must now determine which Computed Choice yields the smaller/earliest Latest Start. We apply LS|mx = min (LS|du, LS|sr).

Finally, we conclude that the Latest Start for Subject Activity is LS|mx.

Broken Green Line: The Broken Green Line reflects a situation wherein the Subject Activity has no outgoing Start Restrictions.

Since the only Date Calculation Variable at play is the Activity Duration, we conclude that the Latest Start for Subject Activity is LS|du.

VI.D: Computational Rules for Computing Latest FinishAs shown in Figure F017, the Latest Finish date will be derived from one of four culminating Arithmetic Formulas: LF|dr, LF|fr, LF|mx, or LF|no.

Formula LF|dr

AnyOutgoing

dr?

LF = LF|mx

AnyOutgoing

fr?Any

Outgoingfr?

Formula LF|fr

Formula LF|mx

Formula LF|fr Formula LF|no

LF = LF|noLF = LF|frLF = LF|dr

Yes No

Yes

No

Yes

No

F017: Process Map for Computing Latest Finish



Solid Black Line: Since the Default Restriction is the most common Performance Restriction in the Critical Path Method, we test for it first.

If there are one or more Default Restrictions, then the first Arithmetic Formula is LF|dr, to find the maximum Latest Finish from all outgoing Default Restrictions. This becomes the Computed Choice through the Default Restrictions.

Next, we check for the presence of one or more outgoing Finish Restrictions. If they exist, then we perform Arithmetic Formula LF|fr to fi nd the maximum Latest Finish from all outgoing Finish Restrictions. This becomes the Computed Choice through the Finish Restrictions.

Given that we have two different Computed Choices at play, we must now determine which Computed Choice yields the smaller/earliest Latest Finish . We apply LF|mx = min (LF|dr, ES|fr).

Finally, we conclude that the Latest Finish for Subject Activity is LF|mx.

Dashed Red Line: The Dashed Red Line branches from the Solid Black Line at the point at which we have already confirmed that one or more Default Restrictions exist and we have performed the LF|dr Arithmetic Formula.

We test for the presence of at least one outgoing Finish Restriction, but fi nd none.

Since the only Date Calculation Variable at play is one or more Default Restrictions, we conclude that the Latest Finish for Subject Activity is LF|dr.

Broken Green Line: The Broken Green Line reflects a situation wherein the Subject Activity has no outgoing Default Restrictions.

We test for outgoing Finish Restrictions and fi nd one or more. We perform Arithmetic Formula LF|fr to find the maximum Latest Finish from all outgoing Finish Restrictions. This becomes the Computed Choice through the Finish Restrictions.

Since the only Date Calculation Variable at play is one or more Finish Restrictions, we conclude that the Latest Finish for Subject Activity is LF|fr.

Dotted Blue Line: The Dotted Blue Line reflects a situation wherein the Subject Activity has no outgoing Performance Restrictions of any kind. As a result, we apply Arithmetic Formula LF|no, which we conclude must be the Latest Finish for Subject Activity.



VII: Convenient Reference InformationRealizing that we have introduced and used quite a few terms that are not commonplace in Dominant Project Management circles, we include this closing section to help the reader correlate terms used in Dominant Project Management with those used in Cognitive Project Management.

VII.A: Dominant/Cognitive Terminology ConversionsMost readers of this White Paper are familiar with the common terminology of Dominant Project Management. This White Paper, however, uses many terms that were coined by Cognitive Project Management. The following table and diagram, hopefully self-explanatory, should assist the reader in making the conversion from one lexicon to the other. The following table provides equivalents for other common terms:

Cognitive Project Management Terms Dominant Project Management TermsCommunal Relationships No equivalentSymbiotic Relationships No equivalentProgressive Relationships No equivalentEventually-Impacting Relationships No equivalentImmediately-Restricting Relationships No equivalentPerformance Restrictions Relationship or DependencyRestrictions Linkages Relationship Type or Dependency Type Default Restriction Linkage (dr) Finish-to-Start Relationship/Dependency (FS)Start Restriction Linkage (sr) Start-to-Start Relationship/Dependency (SS)Finish Restriction Linkage (fr) Finish-to-Finish Relationship/Dependency (FF)Holdback Restriction Linkage (not used) (hr) Start-to-Finish Relationship/Dependency (SF)

Restriction Delay Leads and/or LagsRestriction Flow No equivalent

Figure F018 explains some of the primary terms associated with Activities that are linked together in Progressive Relationships:

Subject Activity: In any Activity Pair in a Progressive Relationship, one Activity is considered the Subject Activity, and the other Activity is described as either restricting it, or restricted by it.

Restricting Activity: In an Immediately-Restricting Progressive Relationship, the Activity in an Activity-Pair that is causing the restriction is called the Restricting Activity. Dominant Project Management calls this the Predecessor Activity.



Restricted Activity: In an Immediately-Restricting Progressive Relationship, the Activity in an Activity-Pair that is being restricted is called the Restricted Activity. Dominant Project Management calls this the Successor Activity.

Immediately-Restricting Progressive Relationship: Two Activities that are connected to one another through Logic Ties, but have no other Activities coming between them — that is, they are touching — are said to be in an Immediately-Restricting Progressive Relationship.

Eventually-Impacting Progressive Relationship: Two Activities that are connected to one another through Logic Ties, but do have other Activities coming between them — that is, they are not directly touching one another — are said to be in an Eventually-Impacting Progressive Relationship.

SubjectActivity

RestrictedActivity

RestrictingActivity

SS:4

FF:2

Logic Tie

Logic Code

(predecessor)

(successor)

These two activities are in anEventually-Impacting Relationship

These two activities are in anImmediately-Restricting Relationship

Progressive Relationship Category

F018: Primary Terms of Progressive Relationships



VIII: Summary of Date Calculation FormulasAs a convenience to the reader, we have gathered together all of the formulas discussed in this White Paper. In addition, we have modifi ed them for the particular Point-of-Day Perspective being used. Subsection VIII.A contains the formulas one would use for either Start-of-Day or End-of-Day Perspectives. Subsection VIII.B contains the formulas one would use for Point-of-Day Perspectives. If you desire a primer on Point-of-Day Perspectives, see ICS-White PaperWPB-KJ-28, “Understanding the Point-of-Day Perspectives.”

VIII.A: Arithmetic Formulas: Start-of-Day or End-of-Day Perspectives

ES|dr: ESY = max [ (EFX1+ DLdrX1

), (EFX2+ DLdrX2

) ... (EFXn+ DLdrXn

) ]

ES|sr: ESY = max [ (ESX1+ DLsrX1

), (ESX2+ DLsrX2

) ... (ESXn+ DLsrXn

) ]

ES|no: ESY = max (PS, DD)

ES|mx = max (ES|dr, ES|sr)

EF|du: EFY = (ESY+ DUY)

EF|fr: EFY = max [ (EFX1+ DLfrX1

), (EFX2+ DLfrX2

) ... (EFXn+ DLfrXn

) ]

EF|mx = max (EF|du, ES|fr)

LS|du: LSY = (LFY- DUY)

LS|sr: LSY = min [ (LSZ1- DLsrZ1

), (LSZ2- DLsrZ2

) ... (LSZn- DLsrZn

) ]

LS|mx = min (LS|du, LS|sr)

LF|dr: LFY = min [ (LSZ1- DLdrZ1

), (LSZ2- DLdrZ2

) ... (LSZn- DLdrZn

) ]

LF|fr: LFY = min [ (LFZ1- DLfrZ1

), (LFZ2- DLfrZ2

) ... (LFZn- DLfrZn

) ]

LF|no: LFY = (PF)

LF|mx = min (LF|dr, LF|fr)



IX: Definitions of Terms Used in this White PaperThe following defi nitions, for technical or unusual terms used in this White Paper, are excerpted from the ICS-Dictionary. You may wish to consult the ICS-Dictionary for additional terms not defi ned in the following glossary.

Activity Duration: Expressed in Continuous Crew Days, the Activity Duration represents an estimate of the amount of time required by an assumed Crew Confi guration to perform the Scope of Work of an Activity, as briefl y described by the Activity Description. An Activity Duration is one of two Date Calculation Variables used to determine the appropriate Date Calculation Procedures, Computational Rules, and Arithmetic Formulas.

Backward Pass Process: Used to determine the Latest Start and Latest Finish Dates of a series of Progressively-related Activities in a CPM Network Diagram, the Backward Pass Process is a combination of (a) Computational Procedures that utilize (b) Arithmetic Formulas in accordance with (c) condition-specifi c Computational Rules that are mandated by particular (d) Date Calculation Variables.

Cognitive Project Management: The ICS-Compendium advocates Cognitive Project Management as a superior alternative, designed specifi cally for Construction Project Management as practiced in North America. Conversely, the ICS-Compendium uses the term Dominant Project Management to refer to the broadest grouping of contemporary literature, dogma, standards, best practices, and other formal writings and teachings on Project Management topics. In a word, Dominant Project Management refers to today’s “conventional wisdom” on Project Management topics.

Communal Relationship: A Communal Relationship is formed between two Activities if they share one or more common, Project Performance Determinants. A Progressive Relationship is one of three Relationship Categories found in a CPM Schedule.

Crew Confi guration: The compositional make-up of a work crew: both the number of workers and type of workers.

Date Calculation Variables: Inherent in the raw content of the CPM Network Diagram are Date Calculation Variables that determine the Arithmetic Formulas and Computational Rules to be used during performance of Forward Pass and Backward Pass Procedures. The two Date Calculation Variables are Performance Restrictions and Activity Durations.



Default Restriction: A Performance Restriction in which the commencement of a Restricted Activity is constrained by the prior completion of the Restricting Activity. The extent of a Default Restriction is expressed as a Restriction Delay, an amount of Time by which the start of the Restricted Activity is constrained by the completion of the Restricting Activity. According to Cognitive Project Management, the Restriction Delay of a Default Restriction represents a passage of time. The Default Restriction corresponds to the Finish-to-Start Relationship Type of Dominant Project Management. Its Restriction Abbreviation is "FS."

Dominant Project Management: The term Dominant Project Management is used throughout the ICS-Compendium to refer to the broadest grouping of contemporary literature, dogma, standards, best practices, and other formal writings and teachings on Project Management topics. In a word, Dominant Project Management refers to today’s “conventional wisdom” on Project Management topics. In contrast, the ICS-Compendium advocates Cognitive Project Management as a superior alternative, designed specifi cally for Construction Project Management as practiced in North America.

Earliest Dates: The two “earliest possible” Calculated Dates by which an Activity can be reasonably expected to start or fi nish, assuming the fl awless performance of all prior Activities to which the Activity is logically connected, Earliest Start and Earliest Finish are calculated through a Date Calculation Procedure known as a Forward Pass.

Earliest Finish: An estimate of the earliest possible Calculated Date by which an Activity can be reasonably expected to fi nish, assuming the fl awless performance of all prior Activities to which the Activity is Logically connected in a Progressive Relationship.

Earliest Start: An estimate of the earliest possible Calculated Date by which an Activity can be reasonably expected to start, assuming the fl awless performance of all prior Activities to which the Activity is Logically connected in a Progressive Relationship.

Finish Restriction: A Performance Restriction in which the completion of a Restricted Activity is constrained by the prior completion of its Restricting Activity. The extent of a Finish Restriction is expressed as a Restriction Delay, an amount of time required by the Restricted Activity to perform the fi nal portion of its work. According to Cognitive Project Management, the Restriction Delay of a Finish Restriction represents work performance time (contained in the duration of the Restricted Activity) — as opposed to the mere passage of time. The Finish



Restriction corresponds to the Finish-to-Finish Relationship Type of Dominant Project Management. Its Restriction Abbreviation is "FF."

Forward Pass Process: Used to determine the Earliest Start and Earliest Finish Dates of a series of Progressively-related Activities in a CPM Network Diagram, the Forward Pass Process is a combination of (a) Computational Procedures that utilize (b) Arithmetic Formulas in accordance with (c) condition-specifi c Computational Rules that are mandated by particular (d) Date Calculation Variables.

Holdback Restriction: The Holdback Restriction corresponds to the Start-to-Finish Relationship Type of Dominant Project Management. Its Restriction Abbreviation is "SF." Throughout Dominant Project Management circles there is no consistent or universal understanding as to how this Performance Restriction works. As best as we can tell, a Holdback Restriction seems to be a hybrid combination of both a Start Restriction and a Finish Restriction. That is, in a Holdback Restriction, a fi nal portion of the Restricted Activity cannot be performed until the Restricting Activity has both commenced and progressed to a certain extent. While Cognitive Project Management does not encourage the use of the Holdback Restriction, it provides a name for it (Holdback Restriction) in the interest of thoroughness.

Latest Dates: The two “latest plausible” Calculated Dates by which an Activity’s start or fi nish may be postponed without rendering as unachievable the required completion of any downstream Finish Date Constraints to which the Activity is logically connected, Latest Start and Latest Finish are calculated through a Date Calculation Procedure known as a Backward Pass.

Latest Finish: An estimate of the latest plausible date to which an fi nish may be postponed without rendering as unachievable the required completion of any downstream Deadline Milestones to which the Activity is Logically connected in a Progressive Relationship.

Latest Dates: The two “latest plausible” Calculated Dates by which an Activity’s start or fi nish may be postponed without rendering as unachievable the required completion of any downstream Finish Date Constraints to which the Activity is logically connected, Latest Start and Latest Finish are calculated through a Date Calculation Procedure known as a Backward Pass.

Performance Determinant: A Performance Determinant is a Project Performance Variable that is shared by Activities in a Communal Relationship. Examples of Project Determinants include information (e.g., timely answer to an RFI), participants (e.g., access to Owner, PM, etc), work space (e.g., access to job site or limited



work area), and resources (e.g., labor, materials, equipment).

Performance Restriction: Performance Restriction is the name that Cognitive Project Management has given to the four possible ways that Activities can be dependently linked to one another in Progressive Relationships within the Critical Path Method. Each distinct confi guration is called a Restriction Linkage. The four Restriction Linkages of Cognitive Project Management correspond to the four Dependency Types (or Relationship Types) of Dominant Project Management: Default Restriction (Finish-to-Start Dependency), Start Restriction (Start-to-Start Dependency), Finish Restriction (Finish-to-Finish Dependency), and Holdback Restriction (Start-to-Finish Dependency).

Procedure: A series of actions conducted in a certain manner, an established way of doing something.

Process: A set or series of actions directed to some end or a natural series of changes.

Progressive Relationship: A Progressive Relationship exists between two Activities that are linked together by way of Performance Restrictions (and possibly additional intervening Activities). In a Progressive Relationship, the timing of a downstream Activity is or will be affected by the timely performance of one or more upstream Activities.

Restriction Delay: What Cognitive Project Management refers to as a Restriction Delay, Dominant Project Management somewhat interchangeably calls Leads and Lags. A Restriction Delay is a numeric value that expresses the delaying effect of an Immediately-Restricting Progressive Relationship. Restriction Delay is one of fi ve components of a Restriction Statement.

Restriction Linkage: What Cognitive Project Management refers to as a Restriction Linkage, Dominant Project Management calls a Relationship/Dependency Type. In an Immediately-Restricting Progressive Relationship where a Performance Restriction exists between two Activities, there are four possible Restriction Linkages: Default Restriction (Finish-to-Start Dependency), Start Restriction (Start-to-Start Dependency), Finish Restriction (Finish-to-Finish Dependency), and Holdback Restriction (Start-to-Finish) Dependency. Restriction Linkage is one of fi ve components of a Restriction Statement.

Start Restriction: A Performance Restriction in which the commencement of a Restricted Activity is constrained by both (a) the commencement and (b) partial performance of a Restricting Activity. The extent of a Start Restriction is expressed as a Restriction Delay, an amount of time required by the Restricting Activity to



perform an opening portion of its work as a prerequisite to commencement of the Restricted Activity. According to Cognitive Project Management, the Restriction Delay of a Start Restriction represents work performance time (contained in the duration of the Restricting Activity) — as opposed to the mere passage of time. The Start Restriction corresponds to the Start-to-Start Relationship Type of Dominant Project Management. Its Restriction Abbreviation is "SS."

Symbiotic Relationship: A Symbiotic Relationship between two Activities is one in which the performance of each Activity may (or may not) have an impact/effect on the conditions under which the other Activity must perform. The potential to impact or affect the other Activity's operational conditions exists in both directions – but need not necessarily ever occur. A Symbiotic Relationship is one of three Relationship Categories that may be found in a CPM Schedule.

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