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**PLANNING ENGINEERING AND PROJECT MANAGEMENT**

Lecture#08 PLANNING ENGINEERING AND PROJECT MANAGEMENT By Lec. Junaid Arshad DEPARTMENT OF ENGINEERING MANAGEMENT

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**Topics Covered CPM Calculations for AOA and AON Networks**

Slack Time / Float Critical Path, Critical Activity Practice Problems

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**CPM Calculations for AON Network**

Provides activity information Early start (ES) & late start (LS) Early finish (EF) & late finish (LF) Slack (S) / Float (FL) Identifies critical path This and the next several slides illustrate the definitions of terms appropriate to critical path analysis. There are many opportunities for good managers to truly manage a project once they have a PERT network established. For instance, sub-contractors know early start and late start times and the managers know the activities on the critical path upon which to focus effort.

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**Forward and Backward Pass**

Forward pass is a technique to move forward through network diagram. Backward pass is its opposite. Early Start (ES) and Early Finish (EF) use the forward pass technique. Late Start (LS) and Late Finish (LF) use the backward pass technique. Note: If the float of the activity is zero, the two starts (ES and LS) and the two finish (EF and LF) are the same. Hence, If float of activity is zero, ES = LS and EF = LF.

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**Early Start and Early Finish Steps**

Begin at starting event and work forward ES = 0 for starting activities ES is earliest start EF = ES + Activity time EF is earliest finish ES = Maximum EF of all predecessors for non- starting activities

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**Late Start and Late Finish Steps**

Begin at ending event and work backward LF = Maximum EF for ending activities LF is latest finish; EF is earliest finish LS = LF - Activity time LS is latest start LF = Minimum LS of all successors for non-ending activities

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**AON Network Calculations**

ES LS EF LF Earliest Finish Latest Start Earliest Start Activity Name Activity Duration Latest Finish

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**CPM Calculations for an AON Network**

Problem 04 Activity Preceding Activity Duration (days) A - 10 B 07 C 12 D 18 E 14 F 13 G 16 H D, E I F, G 06 CPM Calculations for an AON Network

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Slack Time/Float Slack Time is the amount of time an activity may be delayed without affecting the project deadline. This is also referred as float. Total Slack Time / Total Float: Time shared among more than one activity. Free Slack Time /Free Float: Time associated with a single activity.

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Critical Activity An activity having zero slack time is called critical activity. The concept of critical activities is that it draws the attention of the project manager to the activities that needs the closest monitoring. Any delay of a critical activity leads to an equivalent delay of the total project.

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Critical Path A path having longest duration (completion time) in the network is called critical path. Shortest time project can be completed Any delay on critical path activities, delays project Critical path activities have zero slack

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**Explanation of Total Float**

Total Float is valid for a chain and not for a single activity. In the under discussion example, C and G have a float of 06 days. This means that the sum of delays for C and G may run up to 06 days without affecting the project finish time. Analysis of float is a particularly neat tool for calculating consequences of schedule variance.

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**Assume the following data with respect to**

schedule (for problem 04) B will be delayed by 04 days D will be delayed by 01 day E will be delayed by 05 days G will be delayed by 03 days

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It is recognized that D is critical, hence a delay of at least one day to the overall project is unavoidable. Activity G has a float of 06 days. Since no other activity on that chain has a delay, the float will accommodate the 03 day delay of G.

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**Further, B and E are both on the same chain**

Further, B and E are both on the same chain. The float along the chain is 07 days and the total delay is 4+5=9 days. This means a 02 day delay of the project. In conclusion, the project will be delayed by 02 days and B-E-H will be the new critical path. A-D will have a float of one, and C-G a float of 04.

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**CPM Calculations for AON Network**

CPM calculation for AON Network is same as for AOA network, but the calculation of events is omitted.

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**Problem 05: General Hospital’s Activities and Predecessors**

Activity Immediate Predecessors Duration (days) A - 2 B 3 C D A, B 4 E F G D, E 5 H F, G

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**AON Network for General Hospital Includes Critical Path**

Start A B C D F G H 13 2 15 8 5 4 10 3 7 E 1 Slack=0 Slack=6 Slack=1 Slack=0

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**Critical Path for General Hospital**

Start H B D G

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**Explanation of Free Float**

Consider slack time of activity F. Delaying this activity decreases only its slack time and does not impact the slack time of any other activity. This type of slack time is referred as free slack / free float.

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**Gantt Chart for General Hospital Early Start and Finish**

A Build internal components B Modify roof and floor C Construct collection stack D Pour concrete and install frame E Build high-temperature burner F Install pollution control system G Install air pollution device H Inspect and test This and the following slide illustrate the translation of Early and Late Start and Finish time to Gantt charts.

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**Gantt Chart for General Hospital Late Start and Finish**

A Build internal components B Modify roof and floor C Construct collection stack D Pour concrete and install frame E Build high-temperature burner F Install pollution control system G Install air pollution device H Inspect and test GENERAL HOSPITAL This and the following slide illustrate the translation of Early and Late Start and Finish time to Gantt charts.

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**Table for Network Scheduling**

Problem 06 Table for Network Scheduling

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**Problem 06 Solution - AOA Method**

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Early Event Time (TE)

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Finding TE Values

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Late Event Time (TL)

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Finding TL Values

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Critical Path

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Activity Scheduling An activity’s early starting time equals the TE of its beginning event: ES = TE. An activity’s late finishing time equals the TL for its ending event: LF = TL. From these, Two times are computed using the expected activity completion time t: Early finishing time: EF = ES + t. Late starting time: LS = LF - t.

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**Problem 06 Solution - AOA Method**

Scheduled Times must fall between ES and LF and allow at least time t to complete.

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**CPM Calculations for an AOA Network**

Problem 07 Activity Preceding Activity Duration (weeks) A - 10 B 07 C 12 D 18 E 14 F 13 G 16 H D, E I F, G 06 CPM Calculations for an AOA Network

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**Predecessors (Dependencies) Table for Network Scheduling**

Problem 08 Activity Predecessors (Dependencies) Time (Weeks) A - 3 B 5 C 7 D 8 E F G 4 H I 6 J G - H Table for Network Scheduling

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Q&A

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