The document discusses the Critical Path Method (CPM) for project scheduling, including how to develop a work breakdown structure, identify different types of activities, perform forward and backward pass calculations to determine early and late start/finish dates, and identify the critical path and float for activities. It also covers how to incorporate lags, determine event times in arrow networks, and the effects of an imposed finish date on the schedule.
The document discusses project scheduling techniques like PERT and CPM. It provides an example of using these methods to schedule the building of an elaborate parade float. Key activities, durations, and dependencies are laid out. Calculations are shown to determine the critical path, earliest and latest start/finish times, and project completion time. For activities with uncertain durations, a three-time estimate approach is described to model duration as a distribution and calculate the probability of on-time completion.
The document discusses project scheduling techniques PERT and CPM. It provides an example of using these methods to schedule the building of an elaborate parade float. Key activities, durations, and dependencies are laid out. Earliest and latest start/finish times are calculated. The critical path is identified as several critical activities that must be completed on schedule. The project completion time is estimated at 18 days based on the critical path. Uncertain activity times and calculating the probability of on-time project completion are also discussed.
Network analysis techniques like CPM and PERT are useful for planning, scheduling, and controlling projects. They define activities, durations, and dependencies using a network diagram. The critical path is identified as the longest sequence of activities to complete the project. Monitoring progress against the network allows managers to focus on critical tasks and adjust resources if needed to minimize delays. While useful for large projects, activity definitions and time estimates require care to apply these techniques accurately.
The document discusses graphs, networks, project scheduling, critical path method (CPM), program evaluation and review technique (PERT), activity-on-node (AON) and activity-on-arc (AOA) representations, activity slack, floats, crashing activities to reduce project duration, and performing time-cost tradeoffs to optimize project costs. It provides definitions of key terms like vertices, edges, predecessors, successors, critical and non-critical activities, earliest start times, latest completion times, total float and free float. It also includes an example problem demonstrating how to construct a network diagram, find the critical path, compute activity times, and determine the optimal crash time and costs to meet a deadline.
CPM and PERT are project management techniques that use network diagrams to analyze the tasks, schedule, and dependencies of a project. They determine the critical path, which is the longest sequence of tasks that determines the minimum time to complete the project. PERT further accounts for uncertainty in task durations by using three time estimates to calculate the expected duration and variance for each task. This allows calculating the probability of completing the project by a given date.
Critical Path Method (CPM) was developed in late 1950s and is used to identify task that are necessary for completion of project on time without delay.
Lecture - Project, Planning and Control.pdflucky141651
Geometric method impossible in higher dimensions
• Algebraical methods:
• Simplex method (George B. Dantzig 1949):
skim through the feasible solution polytope.
Similar to a "Gaussian elimination".
Very good in practice, but can take an
exponential time
Critical Path Method (CPM) is a network diagramming technique used to predict total project duration and identify the critical path. The critical path is the longest sequence of activities with zero float - it determines the earliest project completion date. In the example network diagram, the critical path is activities A, B, C, F with a total length of 15 time units. Calculating early and late start/finish dates using forward and backward passes identifies float, which indicates how much delay activities on the critical path can experience before delaying the overall project end date.
The document discusses project scheduling techniques like PERT and CPM. It provides an example of using these methods to schedule the building of an elaborate parade float. Key activities, durations, and dependencies are laid out. Calculations are shown to determine the critical path, earliest and latest start/finish times, and project completion time. For activities with uncertain durations, a three-time estimate approach is described to model duration as a distribution and calculate the probability of on-time completion.
The document discusses project scheduling techniques PERT and CPM. It provides an example of using these methods to schedule the building of an elaborate parade float. Key activities, durations, and dependencies are laid out. Earliest and latest start/finish times are calculated. The critical path is identified as several critical activities that must be completed on schedule. The project completion time is estimated at 18 days based on the critical path. Uncertain activity times and calculating the probability of on-time project completion are also discussed.
Network analysis techniques like CPM and PERT are useful for planning, scheduling, and controlling projects. They define activities, durations, and dependencies using a network diagram. The critical path is identified as the longest sequence of activities to complete the project. Monitoring progress against the network allows managers to focus on critical tasks and adjust resources if needed to minimize delays. While useful for large projects, activity definitions and time estimates require care to apply these techniques accurately.
The document discusses graphs, networks, project scheduling, critical path method (CPM), program evaluation and review technique (PERT), activity-on-node (AON) and activity-on-arc (AOA) representations, activity slack, floats, crashing activities to reduce project duration, and performing time-cost tradeoffs to optimize project costs. It provides definitions of key terms like vertices, edges, predecessors, successors, critical and non-critical activities, earliest start times, latest completion times, total float and free float. It also includes an example problem demonstrating how to construct a network diagram, find the critical path, compute activity times, and determine the optimal crash time and costs to meet a deadline.
CPM and PERT are project management techniques that use network diagrams to analyze the tasks, schedule, and dependencies of a project. They determine the critical path, which is the longest sequence of tasks that determines the minimum time to complete the project. PERT further accounts for uncertainty in task durations by using three time estimates to calculate the expected duration and variance for each task. This allows calculating the probability of completing the project by a given date.
Critical Path Method (CPM) was developed in late 1950s and is used to identify task that are necessary for completion of project on time without delay.
Lecture - Project, Planning and Control.pdflucky141651
Geometric method impossible in higher dimensions
• Algebraical methods:
• Simplex method (George B. Dantzig 1949):
skim through the feasible solution polytope.
Similar to a "Gaussian elimination".
Very good in practice, but can take an
exponential time
Critical Path Method (CPM) is a network diagramming technique used to predict total project duration and identify the critical path. The critical path is the longest sequence of activities with zero float - it determines the earliest project completion date. In the example network diagram, the critical path is activities A, B, C, F with a total length of 15 time units. Calculating early and late start/finish dates using forward and backward passes identifies float, which indicates how much delay activities on the critical path can experience before delaying the overall project end date.
Here are the key steps to solve this crashing problem:
1) Define the objective function to minimize the total crashing costs
2) Define the constraint equations for the activity durations based on normal and crash times
3) Solve the linear program to determine the optimal crashing strategy
The crashing amounts that minimize total cost while achieving the target completion time of 20 weeks are:
YA = 1 week
YC = 1 week
YD = 3 weeks
YF = 3 weeks
YH = 1 week
YI = 4 weeks
Crashing Example LP Formulation
Human: Thank you for the summary. Here is a document with more details on a project. Summarize it in 3 sentences or less
The document discusses project scheduling techniques like the Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT). It explains how a network diagram shows the logical dependencies and sequence of tasks in a project. Calculating earliest and latest start/finish times helps identify the critical path and float for activities. PERT is useful for projects with uncertain durations, using 3 time estimates. The critical path determines the minimum project duration, and monitoring it helps complete the project on schedule.
The document describes the steps to develop a project network using critical path method (CPM). It involves identifying activities, developing a network diagram, estimating time for each activity, calculating earliest and latest times, determining critical path, and analyzing floats. An example network is provided to illustrate determining earliest occurrence time, latest occurrence time, and floats like total float and free float. The document also discusses scheduling when resources are limited and bounding schedules. Finally, it provides an illustration of CPM analysis to minimize total project cost by crashing critical activities.
This document discusses key concepts in project management including:
1) How to construct a project network diagram representing activities and their dependencies.
2) How to determine a project's critical path which indicates its minimum duration.
3) How to calculate activity floats which provide flexibility in scheduling.
The document discusses pull systems for replenishing inventory using the example of purchasing milk. It also discusses the critical path method (CPM) for network analysis and project scheduling. CPM involves identifying the critical path of activities that determine the shortest project duration. An example CPM analysis is provided to find the earliest and latest event times for activities in a project.
The document discusses project scheduling models and the PERT/CPM approach. It uses the example of a project by KLONE Computers to design, manufacture, and market a new computer. The key steps are:
1. Identifying all activities and their precedence relationships for the KLONE project.
2. Calculating the earliest and latest start/finish times using forward and backward passes to determine the critical path.
3. Applying the probability approach by estimating optimistic, most likely, and pessimistic times to calculate the mean and variance of each activity's duration and the overall project.
This document covers project scheduling techniques like the Program Evaluation and Review Technique (PERT) and Critical Path Method (CPM). It provides examples of activity-on-node and activity-on-arrow network diagrams for a paper manufacturing project. It then demonstrates how to determine a project schedule by performing forward and backward passes on the network to calculate earliest and latest start/finish times, and identify the critical path and slack times.
This document provides a project management plan for setting up a new warehouse for Jigama Ltd. It identifies the key stages in the project lifecycle including define, plan, organize, execute and close. In the define stage, the report outlines functional specifications for the warehouse, develops scenarios to assess risks and alternatives, and recommends a cost-benefit analysis using net present value. The plan considers tasks, skills, leadership, administration and control needed to successfully manage the warehouse project on time and on budget.
The critical path method (CPM) network for the given project is constructed following these steps:
1) Determine the earliest start time (ES) using forward pass
2) Determine the latest completion time (LC) using backward pass
3) Identify the critical path as the longest path where ES = LC
The critical path is identified as activities B, D, H, K, N with a total project duration of 25 months. Non-critical activities are identified by having total float greater than zero.
The document discusses project scheduling and outlines the key steps and considerations for developing an effective project schedule. It begins by explaining that a project schedule communicates the work, resources, and timeframes needed to deliver a project on time. It then discusses developing a work breakdown structure (WBS) to break down all project work into deliverables. From there, it outlines how to describe each activity, identify precedence relationships between activities, and determine estimated completion times to develop a network diagram and precedence chart. The document also covers calculating earliest and latest start/finish times, identifying slack times and the critical path, and using Gantt charts to monitor project progress.
The document discusses PERT (Program Evaluation and Review Technique) and CPM (Critical Path Method), which are project management techniques developed in the 1950s to schedule, monitor, and control complex projects. It provides definitions of PERT and CPM, the six basic steps to use them, and their importance in answering questions about project timelines, resource needs, and costs. The techniques involve breaking a project into activities, determining their relationships and time estimates, and analyzing the network to identify the critical path requiring the closest monitoring. The document also reviews an example application of PERT and outlines advantages and limitations of the project management approaches.
The document discusses network models like CPM and PERT that are used for project management. CPM uses deterministic activity times to create a network and identify the critical path, while PERT uses probabilistic estimates. Both techniques can determine the project duration, start/finish dates, critical activities, float, and the effects of delays. The document also covers crashing the critical path to shorten a project's duration, including calculating activity costs and finding the minimum total project cost.
The document discusses project scheduling techniques PERT and CPM. It provides an overview of PERT which was developed for projects with uncertain activity times, and CPM which was developed for projects with known activity times. The document then discusses how project networks are constructed and how critical paths are determined. It provides an example of applying PERT/CPM to the project of building a parade float, determining the critical path and project duration.
This document provides a step-by-step solution to a project management problem involving determining the critical path of a project. It begins by constructing a network diagram of the project activities and their durations. It then calculates the earliest and latest start and finish times of each activity using forward and backward pass computations. This allows it to identify the critical path - the longest chain of activities where each activity finishes as late as possible. It also calculates the total float of each activity, which is the amount of time it can be delayed without delaying project completion. The critical path identified has a total project duration of 14 weeks.
The document discusses the Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) for project scheduling. CPM determines the minimum project duration when activity times are known with certainty, while PERT estimates the probability of completing on time when activity times are uncertain. Both methods represent projects as networks and identify critical paths that must be followed to complete on schedule.
Critical path presentation for timely project completionAniruddha Kulkarni
For the project management and timely completion of tasks Working on the critical path seems to be the best advantage since the path calculates the longest route of planned activities to the end of the task or project.
The Critical Path Method (CPM) is a technique for scheduling a set of project activities. It identifies the longest continuous chain of activities from start to finish required to complete the project on time. This longest chain is called the critical path. CPM calculates the earliest and latest times each activity can start and finish without making the project longer. Activities on the critical path have no scheduling flexibility, while other activities have "float" or slack time that can be used for scheduling flexibility. CPM is useful for determining the minimum project duration and identifying which activities must be carefully managed and monitored to avoid project delays.
The document provides an overview and examples of PERT/CPM (Program/Project Evaluation and Review Technique/Critical Path Method). It begins with an agenda and motivation for using PERT/CPM for project management. It then provides examples using a network diagram for a project at General Foundry, including calculating expected activity times and variances. It discusses determining the critical path and calculating the probability of project completion times. Finally, it demonstrates calculating early starts, early finishes, late starts, and late finishes for activities in a CPM network.
This document contains details of a project management analysis for a company developing a cordless vacuum cleaner. It includes a list of project activities and predecessors, a network diagram showing the critical path as 17 weeks, and calculations showing a 96% probability of completing the project within the 20 week deadline. It also includes budgets for each activity and monitoring of costs against budget.
This document provides an introduction to the Critical Path Method (CPM) project scheduling technique. It defines CPM and explains that it was developed in the 1950s to assist with scheduling complex projects. The document outlines the key steps in CPM, including constructing a network diagram of tasks, calculating early and late start/finish times, and identifying the critical path. An example is provided to demonstrate how to determine the critical path of a project using CPM. Benefits and limitations of the technique are also summarized.
Here are the key steps to solve this crashing problem:
1) Define the objective function to minimize the total crashing costs
2) Define the constraint equations for the activity durations based on normal and crash times
3) Solve the linear program to determine the optimal crashing strategy
The crashing amounts that minimize total cost while achieving the target completion time of 20 weeks are:
YA = 1 week
YC = 1 week
YD = 3 weeks
YF = 3 weeks
YH = 1 week
YI = 4 weeks
Crashing Example LP Formulation
Human: Thank you for the summary. Here is a document with more details on a project. Summarize it in 3 sentences or less
The document discusses project scheduling techniques like the Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT). It explains how a network diagram shows the logical dependencies and sequence of tasks in a project. Calculating earliest and latest start/finish times helps identify the critical path and float for activities. PERT is useful for projects with uncertain durations, using 3 time estimates. The critical path determines the minimum project duration, and monitoring it helps complete the project on schedule.
The document describes the steps to develop a project network using critical path method (CPM). It involves identifying activities, developing a network diagram, estimating time for each activity, calculating earliest and latest times, determining critical path, and analyzing floats. An example network is provided to illustrate determining earliest occurrence time, latest occurrence time, and floats like total float and free float. The document also discusses scheduling when resources are limited and bounding schedules. Finally, it provides an illustration of CPM analysis to minimize total project cost by crashing critical activities.
This document discusses key concepts in project management including:
1) How to construct a project network diagram representing activities and their dependencies.
2) How to determine a project's critical path which indicates its minimum duration.
3) How to calculate activity floats which provide flexibility in scheduling.
The document discusses pull systems for replenishing inventory using the example of purchasing milk. It also discusses the critical path method (CPM) for network analysis and project scheduling. CPM involves identifying the critical path of activities that determine the shortest project duration. An example CPM analysis is provided to find the earliest and latest event times for activities in a project.
The document discusses project scheduling models and the PERT/CPM approach. It uses the example of a project by KLONE Computers to design, manufacture, and market a new computer. The key steps are:
1. Identifying all activities and their precedence relationships for the KLONE project.
2. Calculating the earliest and latest start/finish times using forward and backward passes to determine the critical path.
3. Applying the probability approach by estimating optimistic, most likely, and pessimistic times to calculate the mean and variance of each activity's duration and the overall project.
This document covers project scheduling techniques like the Program Evaluation and Review Technique (PERT) and Critical Path Method (CPM). It provides examples of activity-on-node and activity-on-arrow network diagrams for a paper manufacturing project. It then demonstrates how to determine a project schedule by performing forward and backward passes on the network to calculate earliest and latest start/finish times, and identify the critical path and slack times.
This document provides a project management plan for setting up a new warehouse for Jigama Ltd. It identifies the key stages in the project lifecycle including define, plan, organize, execute and close. In the define stage, the report outlines functional specifications for the warehouse, develops scenarios to assess risks and alternatives, and recommends a cost-benefit analysis using net present value. The plan considers tasks, skills, leadership, administration and control needed to successfully manage the warehouse project on time and on budget.
The critical path method (CPM) network for the given project is constructed following these steps:
1) Determine the earliest start time (ES) using forward pass
2) Determine the latest completion time (LC) using backward pass
3) Identify the critical path as the longest path where ES = LC
The critical path is identified as activities B, D, H, K, N with a total project duration of 25 months. Non-critical activities are identified by having total float greater than zero.
The document discusses project scheduling and outlines the key steps and considerations for developing an effective project schedule. It begins by explaining that a project schedule communicates the work, resources, and timeframes needed to deliver a project on time. It then discusses developing a work breakdown structure (WBS) to break down all project work into deliverables. From there, it outlines how to describe each activity, identify precedence relationships between activities, and determine estimated completion times to develop a network diagram and precedence chart. The document also covers calculating earliest and latest start/finish times, identifying slack times and the critical path, and using Gantt charts to monitor project progress.
The document discusses PERT (Program Evaluation and Review Technique) and CPM (Critical Path Method), which are project management techniques developed in the 1950s to schedule, monitor, and control complex projects. It provides definitions of PERT and CPM, the six basic steps to use them, and their importance in answering questions about project timelines, resource needs, and costs. The techniques involve breaking a project into activities, determining their relationships and time estimates, and analyzing the network to identify the critical path requiring the closest monitoring. The document also reviews an example application of PERT and outlines advantages and limitations of the project management approaches.
The document discusses network models like CPM and PERT that are used for project management. CPM uses deterministic activity times to create a network and identify the critical path, while PERT uses probabilistic estimates. Both techniques can determine the project duration, start/finish dates, critical activities, float, and the effects of delays. The document also covers crashing the critical path to shorten a project's duration, including calculating activity costs and finding the minimum total project cost.
The document discusses project scheduling techniques PERT and CPM. It provides an overview of PERT which was developed for projects with uncertain activity times, and CPM which was developed for projects with known activity times. The document then discusses how project networks are constructed and how critical paths are determined. It provides an example of applying PERT/CPM to the project of building a parade float, determining the critical path and project duration.
This document provides a step-by-step solution to a project management problem involving determining the critical path of a project. It begins by constructing a network diagram of the project activities and their durations. It then calculates the earliest and latest start and finish times of each activity using forward and backward pass computations. This allows it to identify the critical path - the longest chain of activities where each activity finishes as late as possible. It also calculates the total float of each activity, which is the amount of time it can be delayed without delaying project completion. The critical path identified has a total project duration of 14 weeks.
The document discusses the Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) for project scheduling. CPM determines the minimum project duration when activity times are known with certainty, while PERT estimates the probability of completing on time when activity times are uncertain. Both methods represent projects as networks and identify critical paths that must be followed to complete on schedule.
Critical path presentation for timely project completionAniruddha Kulkarni
For the project management and timely completion of tasks Working on the critical path seems to be the best advantage since the path calculates the longest route of planned activities to the end of the task or project.
The Critical Path Method (CPM) is a technique for scheduling a set of project activities. It identifies the longest continuous chain of activities from start to finish required to complete the project on time. This longest chain is called the critical path. CPM calculates the earliest and latest times each activity can start and finish without making the project longer. Activities on the critical path have no scheduling flexibility, while other activities have "float" or slack time that can be used for scheduling flexibility. CPM is useful for determining the minimum project duration and identifying which activities must be carefully managed and monitored to avoid project delays.
The document provides an overview and examples of PERT/CPM (Program/Project Evaluation and Review Technique/Critical Path Method). It begins with an agenda and motivation for using PERT/CPM for project management. It then provides examples using a network diagram for a project at General Foundry, including calculating expected activity times and variances. It discusses determining the critical path and calculating the probability of project completion times. Finally, it demonstrates calculating early starts, early finishes, late starts, and late finishes for activities in a CPM network.
This document contains details of a project management analysis for a company developing a cordless vacuum cleaner. It includes a list of project activities and predecessors, a network diagram showing the critical path as 17 weeks, and calculations showing a 96% probability of completing the project within the 20 week deadline. It also includes budgets for each activity and monitoring of costs against budget.
This document provides an introduction to the Critical Path Method (CPM) project scheduling technique. It defines CPM and explains that it was developed in the 1950s to assist with scheduling complex projects. The document outlines the key steps in CPM, including constructing a network diagram of tasks, calculating early and late start/finish times, and identifying the critical path. An example is provided to demonstrate how to determine the critical path of a project using CPM. Benefits and limitations of the technique are also summarized.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
Thinking of getting a dog? Be aware that breeds like Pit Bulls, Rottweilers, and German Shepherds can be loyal and dangerous. Proper training and socialization are crucial to preventing aggressive behaviors. Ensure safety by understanding their needs and always supervising interactions. Stay safe, and enjoy your furry friends!
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Assessment and Planning in Educational technology.pptxKavitha Krishnan
In an education system, it is understood that assessment is only for the students, but on the other hand, the Assessment of teachers is also an important aspect of the education system that ensures teachers are providing high-quality instruction to students. The assessment process can be used to provide feedback and support for professional development, to inform decisions about teacher retention or promotion, or to evaluate teacher effectiveness for accountability purposes.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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3. 3
Who develops the WBS?
A WBS is developed by the A/E at the end of the design phase.
and/or by the bidders during the proposal (procurement phase).
4. 4
TYPES OF ACTIVITIES
1. Production Activities
Those that can be taken directly from plans and specifications
2. Procurement Activities
Procurement of material and equipment
3. Management Decision Activities
Activities that can be created by management to avoid certain situations
Delay Concrete
Company Vacation
5. 5
Example
Draw the logic network and perform the CPM calculations for the schedule shown next.
Duration
IPA
Activity
5
-
A
8
A
B
6
A
C
9
B
D
6
B,C
E
3
C
F
1
D,E,F
G
6. 6
In mathematical terms, the ES for activity j is as follows :
ESj =max( EFi )
where (EFi) represents the EF for all preceding activities.
Likewise, the EF time for activity j is as follows :
EF j= ESj + Dur j
where Dur j is the duration of activity j
Forward pass: The process of navigating through a network from start to end and calculating the
completion date for the project and the early dates for each activity
Forward pass calculations
8. 8
In mathematical terms, the late finish LF for activity j is as follows :
(
LFj =min(LSk
where (LSk) represents the late start date for all succeeding activities.
Likewise, the LS time for activity j (LS j) is as follows :
LS j= LFj - Dur j
where Dur j is the duration of activity
Backward pass: The process of navigating through a network from end to start and calculating the late dates for
each activity. The late dates (along with the early dates) determine the critical activities, the critical path, and the
amount of float each activity has.
Backward pass calculations
10. 10
Types Of Floats
There are several types of float. The simplest and most important type of float is
Total Float (TF)
Total float (TF): The maximum amount of time an activity can be delayed from its
early start without delaying the entire project.
TF = LS – ES
or
TF = LF - EF
or
TF = LF - Dur - ES
11. 11
Free Float: may be defined as the maximum amount of time an activity can be delayed
without delaying the early start of the succeeding activities
FFi = min(ESi+1) - EFi
where min (ESi+1) means the least (i.e., earliest) of the early start dates of succeeding activities
12. 12
In the previous example we can find the free float and total float for each activity as the following :
Activity C’s free float, FF = 11 - 11 = 0 days
And
Activity C’s total float, TF =16 - 11= 5 days …… and so on.
FF
TF
LF
LS
EF
ES
Duration
Activity
0
0
5
0
5
0
5
A
0
0
13
5
13
5
8
B
0
5
16
10
11
5
6
C
0
0
22
13
22
13
9
D
3
3
22
16
19
13
6
E
8
8
22
19
14
11
3
F
0
0
23
22
23
22
1
G
Critical activity
Note : We must always realize that FF ≤ TF
17. 17
Activity ES EF LS LF TF FF
A 0 5 0 5 0 0
B 5 11 5 11 0 0
C 5 10 6 11 1 1
D 5 8 8 11 3 0
E 11 14 12 15 1 1
F 11 15 11 15 0 0
G 8 12 11 15 3 0
H 12 19 15 22 3 0
I 15 23 15 23 0 0
J 15 17 20 22 5 2
K 19 22 22 25 3 3
L 23 25 23 25 0 0
Tabular Solution
18. 18
Comments on the Solution
Near-critical activities may be as important as critical activities
It is a good practice for the project manager not to give subordinates two sets of
dates
PM has to choose one set of dates within the range of Early – Late
Management may reserve a number of days as “management float” or “time contingency”
19. 19
Float Discussion
Total float –in general- belongs to a path rather than the activity itself
If an activity uses “its” float, successors may lose some or all of “their” float
Total float versus free float
20. 20
The question is: “who owns the float”?
Float distribution attempts
Review the contract – what if it is not mentioned?
Float with resource leveling
Shifting activities within their float may affect:
Start / finish dates of succeeding activities
Resource usage: Labor and equipment (crews)
Materials: delivery, storage
Cash flow
21. 21
Lags in Node Networks
A lag is a minimum compulsory waiting period between the start/finish of an
activity and the start/finish of the successor
A lead is a negative lag
The lag is added in the CPM’s forward pass calculations and subtracted in the
backward pass
22. 22
Examples:
Concrete curing (before formwork stripping or reshoring)
Asphalt curing (before striping)
Waiting for a permit to be issued
Waiting for the delivery of a custom material or equipment
25. 25
Activity ES EF LS LF TF FF
A 0 5 2 7 2 0
B 0 3 0 3 0 0
C 0 6 1 7 1 0
D 5 12 14 21 9 7
E 7 14 7 14 0 0
F 6 10 7 11 1 1
G 14 19 14 19 0 0
H 21 27 21 27 0 0
I 19 22 24 27 5 5
Tabular Solution
26. 26
Effect of Imposed Finish Date
Imposed Finish Date is the project’s completion date, as specified in the contract or
stipulated by the owner
When compared to the calculated finish date:
Calculated finish date < imposed finish date
• You are in good shape
• What happens if you enter the imposed date?
Calculated finish date > imposed finish date
• Negative float appears when you enter the imposed date
• You need to accelerate / crash the schedule
27. 27
Examples with Imposed Finish Dates
Repeat Example 3 with imposed finish date of 28 days
Repeat Example 3 with imposed finish date of 22 days
29. 29
Imposed Finish Date > Calculated Finish Date
A
5
D
3
B
6
C
5
G
4
E
3
F
4
H
7
I
8
J
2
K
3
L
2
PF
0, 5
3, 8
5, 11
5, 10
5, 8
11, 15
11, 14
8, 12
15, 17
15, 23
12, 19
23, 25
19, 22
25
28
26, 28
25, 28
18, 26
23, 25
18, 25
15, 18
14, 18
14, 18
8, 14
9, 14
11, 14
3 4
6 6 6 6
8
4
3 3
3
3
30. 30
A
5
D
3
B
6
C
5
G
4
E
3
F
4
H
7
I
8
J
2
K
3
L
2
PF
0, 5
-3, 2
5, 11
5, 10
5, 8
11, 15
11, 14
8, 12
15, 17
15, 23
12, 19
23, 25
19, 22
25
22
20, 22
19, 22
12, 20
17, 19
12, 19
9, 12
8, 12
8, 12
2, 8
3, 8
5, 8
-3
-3
-3
-2 -3
-3
-2 2
0 0 0 0
Imposed Finish Date < Calculated Finish Date
31. 31
Negative float is a situation that occurs when performing an activity even
on its early dates, fails to meet the project’s imposed finish date or other
constraint
It may occur in one of two cases:
Before construction starts
During construction (after normal start)
Negative Float
32. 32
Event Times in Arrow Networks
The early event time, TE, is the largest (latest) date obtained to reach an event (going from
start to finish).
The late event time, TL, is the smallest (earliest) date obtained to reach an event (going from
finish to start).
Example
Perform the CPM calculations, including the event times, for the arrow network shown below.
34. 34
The preceding logic is similar to that of the forward and backward passes: When you are going forward, pick
the largest number. When you are going backward, pick the smallest number.
i j
Act. Name
Dur.
TEi
TLi
TEj
TLj
CPM
36. 36
Definitions
Activity, or task: A basic unit of work as part of the total project that is easily measured and
controlled. It is time- and resource consuming.
Backward pass: The process of navigating through a network from end to start and calculating the
late dates for each activity. The late dates (along with the early dates) determine the critical
activities, the critical path, and the amount of float each activity has.
Critical activity: An activity on the critical path. Any delay in the start or finish of a critical activity will
result in a delay in the entire project.
Critical path: The longest path in a network, from start to finish, including lags and constraints.
.
37. 37
Early dates: The early start date and early finish date of an activity.
Early finish (EF): The earliest date on which an activity can finish within project constraints.
Early start (ES): The earliest date on which an activity can start within project constraints.
Event: A point in time marking a start or an end of an activity. In contrast to an activity, an event does not consume time or
resources.
Forward pass: The process of navigating through a network from start to end and calculating the completion date for the
project and the early dates for each activity.
Late dates: The late start date and late finish date of an activity.
Late finish (LF): The latest date on which an activity can finish without extending the project duration.
Late start (LS): The latest date on which an activity can start without extending the project duration.