1 ARCH 435 PROJECT MANAGEMENT Lecture 3: Project Time Planning (Arrow Diagramming Technique) Activity on Arrow (AOA)

1.Each activity (task) is portrayed or presented by an arrow. 2.The tail and head of the arrow denote the start and finis h of the activity whilst its duration is shown in brackets below. 3.The length of the arrow has no significance neither has its orientation.  ARROW DIAGRAM Activity ] Duration] Site Preparation ] 30]

 As means of further defining the point in time, when an activ ity starts or finishes, start and finish events are added.  An event (= node = connector), unlike an activity, does not con sume time or resources, it merely represents a point in time at which something happens.  Numbers are given to the events to provide a unique iden tity to each activity.  The first event in a project schedule is the start of the proje ct. The last event in a project schedule is the end of the proje ct.  ARROW DIAGRAM

2010 Activity [Duration] Start EventFinish Event Activity identification numbers called event numbers  Activity Identification

 i-j Numbers of Events The node at the tail of an arrow is the i-node. The node at the head of an arrow is the j-node. i j Activity Duration

 The network (the graphical representation of a project plan) must hav e definite points of beginning and finish. (The accuracy and usefulness of a network is dependent mainly upon intimate knowledge of the project itself, and upon the general qua lities of judgment and skill of the planning personnel.) 2)The arrows originate at the right side of a node and terminate at the l eft side of a node. 3)Any two events may be directly connected by no more than one activ ity. 4)Use symbols to indicate crossovers to avoid misunderstanding.  Rules of Making Arrow Diagram

AB  Logical Relationships Node “20” is the j-node for activity “A” and it is also the i-no de for activity “B”. Therefore, activity “A” is a predecessor to activity “B”. In other words activity “B” is a successor to activity “A”. Activity B depends on activity A.

Succeeding activities Event numbers must not be duplicated in a network. j-node number is always greater than i-node number.  Logical Relationships

Concurrent activities (happens at the same time)  Logical Relationships

5)The network must be a logical representation of all the activ ities. Dummy Activities are used, where necessary for: Unique numbering, and Logical sequencing. Dummy activity is an arrow that represents merely a de pendency of one activity upon another. A dummy activity h as a zero time. It is also called dependency arrow.  Rules of Making Arrow Diagram

The following network shows incorrect activity numbering A B  Dummy Activities

For unique numbering, use a dummy activity A B 75  Dummy Activities

For representing logical relationships, you may need dummy activities.  Dummy Activities A B C D In this diagram: Activity C depends on Activities A, B. Activity D depends on Activities A, B. LETS SAY, Activity C depends on Activity A ONLY, and Activity D depends on Activities A, B. How can we represent this relationship?

In this case, use a dummy activity to indicate the correct relationship.  Dummy Activities A B C D Now, Activity C depends on Activities A ONLY. Activity D depends on Activities A, B. 35

6)There must be no "looping" in the network. The loop is an indi cation of faulty logic. The definition of one or more of the depe ndency relationships is not valid.  Rules of Making Arrow Diagram

7)The network must be continuous (without unconnected activities)  Rules of Making Arrow Diagram

8)Networks should have only one initial event and only one terminal eve nt  Rules of Making Arrow Diagram

9)Before an activity may begin, all activities preceding it must be completed (the logical relationship betwe en activities is (finish to start).  Rules of Making Arrow Diagram

Standard layout for recording data  Network Analysis (Computation) 1.Occurrence times of Events = Early and late timings of event occurrence = Early and late event times Earliest Event Time Latest Event Time Event Label Activity Tail Head Activity

 Early Event Time (EET = E =T E ) Forward Pass for Computing EET Each activity starts as soon as possible, i.e., as soon as all of its pred ecessor activities are completed. 1.Direction: Left to right, from the beginning to the end of the project 2.Set: EET of the initial node = 0 3.Add: EET j = EET i + D ij 4.Take the maximum The estimated project duration = EET of the last node. Early Event Time (Earliest occurrence time for event) is the earliest time at w hich an event can occur, considering the duration of precedent activities. j i EETj EETi Activity Dij

AB C  Early Event Times (EET = E =T E )

 Early Event Times (T E ) K L M

 Early Event Times (T E ) Example:

 Early Event Times (T E )

 Late Event Time (LET = L =T L ) Backward Pass for Computing LET 1.Direction: Right to left, from the end to the beginning of the project 2.Set: LET of the last (terminal) node = EET. 3.Subtract: LET i = LET j - D ij 4.Take the minimum Late Event Time (Latest occurrence time of event) is the latest time a t which an event can occur, if the project is to be completed on sched ule. j i LETi EETj LETj EET i Activity Dij

 Late Event Times (T L )

 Late Event Times (T L ), Example:

 Late Event Times (T L ), Example:

1.Early Start (ES): The earliest time at which an activity can be started. ES ij = EET i 2.Early Finish (EF): The earliest time at which an activity can be completed. EFij = ESij + Dij 3.Late Finish (LF): The latest time at which an activity can be co mpleted without delaying project completion. LFij = LETj 4.Late Start (LS): The latest time at which an activity can be sta rted. LSij = LFij  Dij 2.Activity Times (Schedule)  Network Analysis (Computation)

 Example: Activity Times ES = EET 20 = 2 EF = ES + D = = 5 LF = LET 50 = 13 LS = LF – D = 13 – 3 = 10

1.Total Float (TF) Total float or path float is the amount of time that an activity’s completion may be delayed without exten ding project completion time. Total float or path float is the amount of time that an a ctivity’s completion may be delayed without affecting the earliest start of any activity on the network critical path. Activity Floats  Network Analysis (Computation)

1.Total Float (TF)  Total path float time for activity (i-j) is the total float ass ociated with a path.  For arbitrary activity (i  j), the total float can be writte n as: Path Float =Total Float (TF ij ) = LS ij  ES ij = LF ij  EF ij = LET j – EET i  D ij Activity Floats  Network Analysis (Computation)

 Example: Total Float Times TF = LS ES TF = 10 – 2 = 8 TF = LF EF TF = 13 – 5 = 8 TF = LET 50 – EET 20 - D TF = 13 – 2 – 3 =

 Network Analysis (Computation) 2.Free Float (FF) Free float or activity float is the amount of time that an activi ty’s completion time may be delayed without affecting the earli est start of succeeding activity. Activity float is “owned” by an individual activity, whereas path or total float is shared by all activities along a slack path. Total float always equals or exceeds free float (TF ≥ FF). For arbitrary activity (i  j), the free float can be written as: Activity Float = Free Float (FF ij ) = ES jk  EF ij = EET j – EET i  D ij Activity Floats

FF = ES – EF FF = 8 – 5 = 3 FF = EET 50 – EET 20 - D FF = 8 – 2 – 3 = 3  Example: Free Float Times

 Network Analysis (Computation)  Interfering Float (ITF)  Interfering float is the difference between TF and FF.  If ITF of an activity is used, the start of some succeeding activi ties will be delayed beyond its ES.  In other words, if the activity uses its ITF, it “interferes” by this amount with the early times for the down path activity.  For arbitrary activity (i  j), the Interfering float can be written as : Interfering Float (ITF ij ) = TF ij  FF ij = LET j  EET j 3.Activity Floats

ITF = TF FF IFF = 8 – 3 = 5 ITF = LET 50 – EET 50 ITF = 13 – 8 = 5  Example: Interfering Float Times

 Network Analysis (Computation)  Independent Float (IDF)  It is the amount of float which an activity will always possess n o matter how early or late it or its predecessors and successor s are.  The activity has this float “independent” of any slippage of pre decessors and any allowable start time of successors. Assumi ng all predecessors end as late as possible and successors st art as early as possible.  IDF is “owned” by one activity.  In all cases, independent float is always less than or equal to f ree float (IDF ≤ FF). 3.Activity Floats

 Network Analysis (Computation)  Independent Float (IDF)  For arbitrary activity (i  j), the Independent Float can be written as: Independent Float (IDF ij ) = Max (0, EET j  LET i – D ij ) = Max (0, Min (ES jk ) - Max (LF li )  D ij ) 3.Activity Floats

 Example: Independent Float Times IDF = Max. (0, [EET 50 – LET 20 - D ]) IDF = Max. (0, [8 – 10 – 3]) =