The standard deviation is the square root of the variance, which is 1.465 weeks.
Z = (Target Time - Expected Time) / Standard Deviation
= (42 - 40) / 1.465
= 1.37
Looking up 1.37 in the standard normal distribution table gives a probability of around 0.085 or 8.5% that the project will take longer than 42 days.
Network analysis techniques such as critical path method (CPM) and program evaluation and review technique (PERT) can be used to plan, manage, and control projects. CPM involves identifying all activities, their durations, and their logical sequence or precedence relationships using a network diagram of nodes and arrows. It allows determining the critical path that dictates the minimum project duration and identifying any activities that could delay the project if they slip. PERT extends CPM by using three time estimates per activity to model the uncertainty in activity durations through probability distributions.
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.
The document discusses the Gantt chart, a project management tool used to illustrate the timeline of project activities. It provides examples of how to create a basic Gantt chart, including determining the project start/end dates, listing activities with durations and dependencies, and using forward or backward scheduling to populate the chart. The Gantt chart provides a simple visual representation of a project schedule but has limitations like difficulty updating and lack of cost/resource information. Alternative project planning techniques like PERT and GERT are also discussed.
CPM and PERT are network analysis techniques used for project planning and scheduling. CPM was developed in the 1950s by DuPont for chemical plant projects and focuses on minimizing project duration. PERT was developed by the US Navy for the Polaris missile program and handles uncertain activity times using probability. Both techniques represent activities as nodes and their dependencies as arrows to build a network that identifies the critical path showing the shortest time to complete the 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.
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.
This document discusses project management techniques CPM and PERT. It begins by defining a project and project management. It then discusses network planning methods including CPM and PERT. The four steps to managing a project with these methods are described: describing the project, diagramming the network, estimating time of completion, and monitoring progress. Key concepts like activities, precedence relationships, and events are also defined. The document goes on to provide details on CPM and PERT, including estimating time, determining critical paths, and differences between the two methods.
Network analysis techniques such as critical path method (CPM) and program evaluation and review technique (PERT) can be used to plan, manage, and control projects. CPM involves identifying all activities, their durations, and their logical sequence or precedence relationships using a network diagram of nodes and arrows. It allows determining the critical path that dictates the minimum project duration and identifying any activities that could delay the project if they slip. PERT extends CPM by using three time estimates per activity to model the uncertainty in activity durations through probability distributions.
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.
The document discusses the Gantt chart, a project management tool used to illustrate the timeline of project activities. It provides examples of how to create a basic Gantt chart, including determining the project start/end dates, listing activities with durations and dependencies, and using forward or backward scheduling to populate the chart. The Gantt chart provides a simple visual representation of a project schedule but has limitations like difficulty updating and lack of cost/resource information. Alternative project planning techniques like PERT and GERT are also discussed.
CPM and PERT are network analysis techniques used for project planning and scheduling. CPM was developed in the 1950s by DuPont for chemical plant projects and focuses on minimizing project duration. PERT was developed by the US Navy for the Polaris missile program and handles uncertain activity times using probability. Both techniques represent activities as nodes and their dependencies as arrows to build a network that identifies the critical path showing the shortest time to complete the 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.
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.
This document discusses project management techniques CPM and PERT. It begins by defining a project and project management. It then discusses network planning methods including CPM and PERT. The four steps to managing a project with these methods are described: describing the project, diagramming the network, estimating time of completion, and monitoring progress. Key concepts like activities, precedence relationships, and events are also defined. The document goes on to provide details on CPM and PERT, including estimating time, determining critical paths, and differences between the two methods.
Project Management Tools and Techniques (PERT- Project Evaluation and Review ...Zulfiquer Ahmed Amin
Project management involves planning, executing, and controlling projects to achieve specific goals within defined time and resource constraints. It utilizes tools like PERT (Program Evaluation and Review Technique) to estimate activity times, determine critical paths, and update schedules as projects progress. PERT uses three time estimates - optimistic, most likely, and pessimistic - to calculate expected activity times and identify float and slack. The critical path determines the minimum project duration, and crashing or fast tracking can potentially shorten schedules at increased cost. Project management tools help make projects more efficient and effective.
Project planning involves carefully breaking down a project into logical components using tools like the work breakdown structure and network diagrams to identify dependencies between tasks. This allows project teams to develop accurate schedules, usually in the form of Gantt charts, to coordinate resources and activities to achieve goals on time and on budget. Production planning establishes production rates and resource usage to satisfy customer demand as expressed in sales forecasts, while balancing inventory levels and maintaining a stable workforce over a 6-18 month horizon. The process begins with a sales forecast and may incorporate desired inventory changes to determine the production plan.
A Gantt chart is a type of bar chart used to illustrate a project schedule. It was developed by Henry Gantt and shows the tasks, durations, and dependencies of activities within a project. The document outlines how to construct a Gantt chart by listing activities, estimating their time requirements, ordering them, and drawing the chart with start/end dates for each activity based on duration and dependencies. Gantt charts provide a simple visual representation of a project plan but can be limited in visualizing dependencies between tasks.
The document discusses network analysis and the critical path method (CPM). It explains that CPM can be used to determine the minimum time required to complete a project if activity durations are known. CPM was developed in the 1950s by researchers at DuPont and Sperry Rand. It also discusses the Program Evaluation and Review Technique (PERT) which can estimate project completion probabilities when durations are uncertain. Both CPM and PERT helped reduce the Polaris missile development time. The document provides examples of CPM and PERT applications and rules for constructing a project network diagram.
Project planning and scheduling techniquesShivangi Saini
The document discusses various project scheduling and analysis techniques including:
- Milestone charts, task lists, Gantt charts, and network diagrams for displaying project schedules.
- Critical path analysis, critical chain analysis, PERT, and resource leveling for analyzing project schedules.
- Buffer management, crashing, fast-tracking, split-to-phases, and mainline-offline scheduling for accelerating project schedules. Each technique is briefly described along with its risks and applications.
A project is defined as a temporary endeavor undertaken to create a unique product or service. Network analysis techniques like the Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) are used to plan and schedule complex projects. These methods involve identifying all activities, their durations, and logical relationships to construct a network diagram. The critical path is then determined by calculating the longest path of linked activities from start to finish, which must be carefully managed to ensure on-time project completion.
This document provides an overview of monitoring and evaluation (M&E) for programs and interventions. It discusses what M&E is, the differences between monitoring and evaluation, why M&E is important, how to develop an M&E plan, and key components of an M&E plan. Monitoring involves routine data collection to track progress towards objectives, while evaluation assesses overall impact by comparing outcomes between program and non-program groups. Developing a strong M&E plan from the beginning is essential to demonstrate accountability and guide effective implementation.
This document provides an overview of project monitoring and evaluation. It defines monitoring as the regular collection of information to track changes over time, and evaluation as analyzing the effectiveness and impact of a project. The key purposes of monitoring and evaluation are to assess results, improve management, promote learning, ensure accountability, and understand stakeholder perspectives. Effective monitoring and evaluation considers outputs, processes, outcomes, impact, and reach. Internal evaluation is done by project staff, while external evaluation involves independent evaluators assessing how funds were used. Distinctions are made between monitoring as an ongoing activity and evaluation as an in-depth assessment.
This document outlines the seven phases of the project life cycle: initiation, planning, execution, monitoring and control, and closeout. It describes the key activities and outputs for each phase. The initiation phase involves selecting a project manager and defining objectives. The planning phase develops detailed plans for tasks, schedule, budget, roles and communication. Execution involves executing the plans, and monitoring and control compares results to metrics and identifies variances. The closeout phase hands over the final product and archives lessons learned.
it includes 21 slides, having definition of project, project management, project management cycle.
it also explains all the phases of PMC.
it also includes characteristics, advantages and disadvantages of project management cycle.
This document discusses project auditing, including what a project audit is, its benefits, how to judge a project's success or failure, determining project objectives, the contents and format of a project audit, and the responsibilities of an auditor. A project audit is a formal inquiry into any aspect of a project that can help identify problems, improve performance, and evaluate the project team. Key factors in differentiating success from failure are objective design and scope, experienced personnel, appropriate authority, and clear accountability. Project audits should cover the current status, future status, critical tasks, risks, lessons for other projects, and audit limitations.
This document provides information about critical path method (CPM) including:
- An introduction to CPM and examples of projects where it can be applied.
- The differences between CPM and PERT.
- Key terms and definitions used in CPM like activity times, floats, and critical path.
- An example of calculating event times, activity times, floats, and determining the critical path for a sample CPM network diagram.
The document defines key project management concepts including what constitutes a project, project characteristics, the differences between project and program management, the six basic project functions, common pitfalls, and the triple constraints of time, cost and scope. It also outlines the nine knowledge areas that comprise the project management framework: integration management, scope management, time management, cost management, quality management, human resource management, communications management, risk management, and procurement management.
What is a Project and Project Management? This presentation helps you to gain more knowledge about how to manage a project and helps in understanding the Project Life Cycle.
The document provides an overview of key components for an effective project charter, including objectives, scope, deliverables, timelines, budgets, resources, risks, and measures of success. An effective charter clearly defines the project goals, how it fits strategically, what work will be done, when it will be completed, who will work on it, potential challenges, and how success will be determined. The charter establishes a shared understanding and provides essential information to ensure project alignment, buy-in, and successful delivery.
This document discusses various aspects of planning including definitions, types of planning processes, and differences between strategic and operational planning. It defines planning as "the management function that includes decisions and actions to insure future results." There are two main types of planning - strategic planning which establishes long-term direction and priorities, and operational planning which focuses on short-term goals and day-to-day activities. Strategic planning involves analyzing internal/external factors, setting goals and objectives, and identifying strategies, while operational planning develops detailed action plans and controls to implement strategic plans.
A Gantt chart is a bar chart that illustrates a project schedule and the phases and activities of a project work breakdown structure. It was introduced by Henry Gantt around 1910-1915. A Gantt chart shows the current schedule status, measures task duration in the project, and represents cost, time and scope. It is useful for planning, scheduling, and monitoring projects by laying out task order and allowing visualization of progress. The steps to construct a Gantt chart include scheduling critical and non-critical tasks based on precedence relationships and earliest start times.
PERT (Program Evaluation and Review Technique) is a project management tool developed by the US Navy to analyze complex projects by breaking them into tasks, estimating activity times, and identifying the critical path of tasks. It facilitates decision making by determining the earliest and latest start/finish times and calculating slack time to reduce project time and costs. PERT uses a network diagram and beta distribution to model activity times and account for uncertainty in complex, non-routine projects.
Project appraisal for financial marketskarangoyal972
This document discusses various financial techniques used for project appraisal, including net present value (NPV), internal rate of return (IRR), average rate of return (ARR), payback period, discounted payback period, and profitability index. It provides formulas for calculating each technique and discusses their advantages and disadvantages for assessing the viability and profitability of potential projects.
This document introduces earned value analysis (EVA), a project management technique that integrates scope, schedule, and cost to measure performance. It defines key EVA terms like budgeted cost of work performed, actual cost, earned value, and planned value. Metrics like cost variance, schedule variance, cost performance index, and estimate at completion are also explained. An example project is used to demonstrate how to calculate these metrics. The document proposes implementing EVA for ATCO projects by developing a module in their EIS system to track EVA parameters and metrics on a monthly basis. A plan is outlined to get feedback, train users, and start the new EVA process.
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.
Project Management Tools and Techniques (PERT- Project Evaluation and Review ...Zulfiquer Ahmed Amin
Project management involves planning, executing, and controlling projects to achieve specific goals within defined time and resource constraints. It utilizes tools like PERT (Program Evaluation and Review Technique) to estimate activity times, determine critical paths, and update schedules as projects progress. PERT uses three time estimates - optimistic, most likely, and pessimistic - to calculate expected activity times and identify float and slack. The critical path determines the minimum project duration, and crashing or fast tracking can potentially shorten schedules at increased cost. Project management tools help make projects more efficient and effective.
Project planning involves carefully breaking down a project into logical components using tools like the work breakdown structure and network diagrams to identify dependencies between tasks. This allows project teams to develop accurate schedules, usually in the form of Gantt charts, to coordinate resources and activities to achieve goals on time and on budget. Production planning establishes production rates and resource usage to satisfy customer demand as expressed in sales forecasts, while balancing inventory levels and maintaining a stable workforce over a 6-18 month horizon. The process begins with a sales forecast and may incorporate desired inventory changes to determine the production plan.
A Gantt chart is a type of bar chart used to illustrate a project schedule. It was developed by Henry Gantt and shows the tasks, durations, and dependencies of activities within a project. The document outlines how to construct a Gantt chart by listing activities, estimating their time requirements, ordering them, and drawing the chart with start/end dates for each activity based on duration and dependencies. Gantt charts provide a simple visual representation of a project plan but can be limited in visualizing dependencies between tasks.
The document discusses network analysis and the critical path method (CPM). It explains that CPM can be used to determine the minimum time required to complete a project if activity durations are known. CPM was developed in the 1950s by researchers at DuPont and Sperry Rand. It also discusses the Program Evaluation and Review Technique (PERT) which can estimate project completion probabilities when durations are uncertain. Both CPM and PERT helped reduce the Polaris missile development time. The document provides examples of CPM and PERT applications and rules for constructing a project network diagram.
Project planning and scheduling techniquesShivangi Saini
The document discusses various project scheduling and analysis techniques including:
- Milestone charts, task lists, Gantt charts, and network diagrams for displaying project schedules.
- Critical path analysis, critical chain analysis, PERT, and resource leveling for analyzing project schedules.
- Buffer management, crashing, fast-tracking, split-to-phases, and mainline-offline scheduling for accelerating project schedules. Each technique is briefly described along with its risks and applications.
A project is defined as a temporary endeavor undertaken to create a unique product or service. Network analysis techniques like the Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) are used to plan and schedule complex projects. These methods involve identifying all activities, their durations, and logical relationships to construct a network diagram. The critical path is then determined by calculating the longest path of linked activities from start to finish, which must be carefully managed to ensure on-time project completion.
This document provides an overview of monitoring and evaluation (M&E) for programs and interventions. It discusses what M&E is, the differences between monitoring and evaluation, why M&E is important, how to develop an M&E plan, and key components of an M&E plan. Monitoring involves routine data collection to track progress towards objectives, while evaluation assesses overall impact by comparing outcomes between program and non-program groups. Developing a strong M&E plan from the beginning is essential to demonstrate accountability and guide effective implementation.
This document provides an overview of project monitoring and evaluation. It defines monitoring as the regular collection of information to track changes over time, and evaluation as analyzing the effectiveness and impact of a project. The key purposes of monitoring and evaluation are to assess results, improve management, promote learning, ensure accountability, and understand stakeholder perspectives. Effective monitoring and evaluation considers outputs, processes, outcomes, impact, and reach. Internal evaluation is done by project staff, while external evaluation involves independent evaluators assessing how funds were used. Distinctions are made between monitoring as an ongoing activity and evaluation as an in-depth assessment.
This document outlines the seven phases of the project life cycle: initiation, planning, execution, monitoring and control, and closeout. It describes the key activities and outputs for each phase. The initiation phase involves selecting a project manager and defining objectives. The planning phase develops detailed plans for tasks, schedule, budget, roles and communication. Execution involves executing the plans, and monitoring and control compares results to metrics and identifies variances. The closeout phase hands over the final product and archives lessons learned.
it includes 21 slides, having definition of project, project management, project management cycle.
it also explains all the phases of PMC.
it also includes characteristics, advantages and disadvantages of project management cycle.
This document discusses project auditing, including what a project audit is, its benefits, how to judge a project's success or failure, determining project objectives, the contents and format of a project audit, and the responsibilities of an auditor. A project audit is a formal inquiry into any aspect of a project that can help identify problems, improve performance, and evaluate the project team. Key factors in differentiating success from failure are objective design and scope, experienced personnel, appropriate authority, and clear accountability. Project audits should cover the current status, future status, critical tasks, risks, lessons for other projects, and audit limitations.
This document provides information about critical path method (CPM) including:
- An introduction to CPM and examples of projects where it can be applied.
- The differences between CPM and PERT.
- Key terms and definitions used in CPM like activity times, floats, and critical path.
- An example of calculating event times, activity times, floats, and determining the critical path for a sample CPM network diagram.
The document defines key project management concepts including what constitutes a project, project characteristics, the differences between project and program management, the six basic project functions, common pitfalls, and the triple constraints of time, cost and scope. It also outlines the nine knowledge areas that comprise the project management framework: integration management, scope management, time management, cost management, quality management, human resource management, communications management, risk management, and procurement management.
What is a Project and Project Management? This presentation helps you to gain more knowledge about how to manage a project and helps in understanding the Project Life Cycle.
The document provides an overview of key components for an effective project charter, including objectives, scope, deliverables, timelines, budgets, resources, risks, and measures of success. An effective charter clearly defines the project goals, how it fits strategically, what work will be done, when it will be completed, who will work on it, potential challenges, and how success will be determined. The charter establishes a shared understanding and provides essential information to ensure project alignment, buy-in, and successful delivery.
This document discusses various aspects of planning including definitions, types of planning processes, and differences between strategic and operational planning. It defines planning as "the management function that includes decisions and actions to insure future results." There are two main types of planning - strategic planning which establishes long-term direction and priorities, and operational planning which focuses on short-term goals and day-to-day activities. Strategic planning involves analyzing internal/external factors, setting goals and objectives, and identifying strategies, while operational planning develops detailed action plans and controls to implement strategic plans.
A Gantt chart is a bar chart that illustrates a project schedule and the phases and activities of a project work breakdown structure. It was introduced by Henry Gantt around 1910-1915. A Gantt chart shows the current schedule status, measures task duration in the project, and represents cost, time and scope. It is useful for planning, scheduling, and monitoring projects by laying out task order and allowing visualization of progress. The steps to construct a Gantt chart include scheduling critical and non-critical tasks based on precedence relationships and earliest start times.
PERT (Program Evaluation and Review Technique) is a project management tool developed by the US Navy to analyze complex projects by breaking them into tasks, estimating activity times, and identifying the critical path of tasks. It facilitates decision making by determining the earliest and latest start/finish times and calculating slack time to reduce project time and costs. PERT uses a network diagram and beta distribution to model activity times and account for uncertainty in complex, non-routine projects.
Project appraisal for financial marketskarangoyal972
This document discusses various financial techniques used for project appraisal, including net present value (NPV), internal rate of return (IRR), average rate of return (ARR), payback period, discounted payback period, and profitability index. It provides formulas for calculating each technique and discusses their advantages and disadvantages for assessing the viability and profitability of potential projects.
This document introduces earned value analysis (EVA), a project management technique that integrates scope, schedule, and cost to measure performance. It defines key EVA terms like budgeted cost of work performed, actual cost, earned value, and planned value. Metrics like cost variance, schedule variance, cost performance index, and estimate at completion are also explained. An example project is used to demonstrate how to calculate these metrics. The document proposes implementing EVA for ATCO projects by developing a module in their EIS system to track EVA parameters and metrics on a monthly basis. A plan is outlined to get feedback, train users, and start the new EVA process.
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.
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.
Pert- program evaluation and review techniqueVinci Viveka
The Program Evaluation and Review Technique (PERT) is a statistical tool used in project management to analyze the tasks involved in completing a project. It involves defining tasks, organizing them into a network diagram, and estimating activity times and dependencies. This allows project managers to compute the minimum time needed to complete the project by identifying the critical path. PERT was developed for the U.S. Navy in the 1950s and facilitates decision making by making the dependencies and critical path of a project visible.
The document discusses critical path method for planning and scheduling a project. It includes a network diagram with activities labeled A through L and their dependencies. It then calculates the earliest and latest start and finish times and identifies the critical path with the least amount of slack time.
The document discusses a warehouse expansion project and provides information about its activities, including expected completion times, variances, and crashing options. It asks how to shorten the expected completion time to achieve an 80% chance of meeting a 40-week deadline. Calculating the necessary reduction using the normal distribution, the expected completion time would need to be shortened to 38 weeks. It also provides crashing costs and time reductions for each activity and asks to determine the optimal crashing decisions using linear programming to minimize total crashing costs.
The document outlines the activities and critical path required to build a new athletic complex on a university campus. It identifies 8 key activities - A through H - with their durations. Activity B through F and H make up the critical path of 14 weeks to complete the project. The summary also provides the activity schedule showing the earliest and latest start and finish times to ensure the project is completed on time.
Rowing Selection usiSeat racing by Duncan Holland: Seat racing examplesRebecca Caroe
Rowperfect Seminar 2006 Seat Racing as part of selection by Duncan Holland, head coach of Cambridge University Boat Club.
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The critical path method is used to analyze a project schedule network diagram to determine the longest path of activities. Key steps are:
1) Draw the network diagram of activities and dependencies
2) Perform forward and backward passes to calculate early and late start/finish times
3) Identify the critical path(s) with the longest total duration as the schedule cannot be shortened without changing these activities
4) Determine the float of non-critical activities which can be delayed without affecting the project completion date.
The document contains 5 practice problems related to project management:
1) Draw a network diagram for a construction project with 8 activities.
2) Find the critical path for a project with 5 activities and calculate the total variance.
3) Calculate the variance in completion time for the critical path.
4) Calculate probabilities for a project's completion time given its expected time and standard deviation.
5) Determine a software project's expected completion date, total normal cost, and cost to crash one activity by 1 week.
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Artificial Intelligence (AI) has revolutionized the creation of images and videos, enabling the generation of highly realistic and imaginative visual content. Utilizing advanced techniques like Generative Adversarial Networks (GANs) and neural style transfer, AI can transform simple sketches into detailed artwork or blend various styles into unique visual masterpieces. GANs, in particular, function by pitting two neural networks against each other, resulting in the production of remarkably lifelike images. AI's ability to analyze and learn from vast datasets allows it to create visuals that not only mimic human creativity but also push the boundaries of artistic expression, making it a powerful tool in digital media and entertainment industries.
2. Objective of the presentation
• To understand the formula , the use and
the benefits of Program , Evaluation ,and
Review Technic (PERT) analysis .
3. What is the PERT ?
Program (Project) Evaluation and Review Technique (PERT): is
a project management tool used to schedule, organize, and
coordinate tasks within a project. It is basically a method to
analyse the tasks involved in completing a given
project, especially the time needed to complete each task, and
to identify the minimum time needed to complete the total
project.
4. When we use PERT ?
• PERT is used when activity times are uncertain.
– Determine the duration of the project .
– Decision making under risk (“P” for probabilistic)
5. Determine the duration of the project
• OPTIMISTIC TIME: Best time if everything goes perfectly
• REALISTIC TIME: Most likely time
• PESSIMISTIC TIME: A worst-case situation
B + 4M + P
Expected Time = -------------------
6
6. Determine the duration of the project
• Example:
For excavation activity let :
B = 12 days
M = 18 days
P = 60
What is the expected time for this activity?
Sol :
12 + 4(18) + 60
Expected Time = -------------------------
6
= 24 days
7. Determine the duration of the project
Activity Predecessor Optimistic Normal Pessimistic Te
(B) (m) (P) (B+4m+P)/6
A --- 2 4 6 4.00
B --- 3 5 9 5.33
C A 4 5 7 5.17
D A 4 6 10 6.33
E B, C 4 5 7 5.17
F D 3 4 8 4.50
G E 3 5 8 5.17
f
9. Determine the duration of the project
D F
D:6.33 D:4.5
ES:4 ES:10.33
EF:10.33 EF:14.83
A
D:4
ES:0
EF:4
C
D:5.17 Finish
Start ES:4
ES:0 D:0
EF:9.17 ES:19.51
EF:0
EF:19.51
B E G
D:5.33 D:5.17 D:5.17
ES:0 ES:9.17 ES:14.34
EF:5.33 EF:14.34 EF:19.51
10. Determine the duration of the project
D F
D:6.33 D:4.5
ES:4 ES:10.33
EF:10.33 EF:14.83
LS:8.68 LS:15.01
LF:15.01 LF:19.51
A
D:4
ES:0
EF:4
LS:0
LF:4
C
D:5.17
Start Finish
ES:4
D:0 D:0
EF:9.17
ES:0 ES:19.51
LS:4
EF:0 EF:19.51
LF:9.17
LS:0 LS:19.51
LF:0 LF:19.51
B E G
D:5.33 D:5.17 D:5.17
ES:0 ES:9.17 ES:14.34
EF:5.33 EF:14.34 EF:19.51
LS:3.84 LS:9.17 LS:14.34
LF:9.17 LF:14.34 LF:19.51
11. Determine the duration of the project
Critical Path
Critical Path: A-C-E-G
• Path A-D-F = 14.83 work days
• Path A-C-E-G = 19.51 work days
• Path B-E-G = 15.67 work days
12. Determine the duration of the project
Critical Path
Activity LF-EF Total
A 4-4 0
B 9.17 – 5.33 3.84
C 9.17 – 9.17 0
D 15.01 – 10.33 4.68
E 14.34 – 14.34 0
F 19.51 – 14.83 4.68
G 19.51 – 19.51 0
13. Assessing Risks
• Risk is a measure of the probability (and
consequences) of not completing a project
on time.
• A major responsibility of the project
manager at the start of a project is to
develop a risk-management plan.
• A Risk-Management Plan identifies the
key risks to a project’s success and
prescribes ways to circumvent them.
14. Assessing Risks
• With PERT’s three time-estimates, we get a mean
(average) time and a variance for each activity and each
path.
– We also get a project mean time and variance.
• In order to compute probabilities (assuming a normal
distribution) we need the activity means and variances.
– Most computer packages calculate this for you.
15. Assessing Risks
Path Time (wks) 12
I 27
48 1563
A-I-K33 33
A-F-K28 28
A K
A-C-G-J-K 67 0 12 12 F 22 Latest 63 69 Latest
B-D-H-J-K 69 2 1214 53 1063 start 63 6 69
finish
B-E-J-K 43 time time
C
12 22 22 G 57
Start Finish
14 1024 24 59
35
0
B9 9
D19 19
H 59 59
J 63
0 9 9 9 1019 19 4059 59 4 63
9 E 33
35 2459
16. Assessing Risks
• What is the probability that our sample project
will finish in 69 weeks as scheduled?
100% (Why?)
– Because we used CPM!
• (This means we were certain of all of our activity times.)
– If we weren’t certain, we should have used PERT
• You can’t do risk analysis if you use CPM
17. Assessing Risks
• Calculate standard deviation
– Standard deviation- average deviation from the
estimated time
• SD=(TP-T0)/6
– higher the SD is the greater amount of uncertainty
exists
• Calculate variance
– reflects the spread of a value over a normal
distribution
• V=SD2
– a large variance indicates great uncertainty, a small
variance indicates a more accurate estimate
18. Assessing Risks
What is the Probability of it taking 72 weeks?
Critical Critical Path = B - D - H - J – K = 69 weeks
Path T = 72 weeks C = 69 weeks
Varianc T–C
e
2 = (variances of activities along critical path) =
z
2
2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89
z= 72 – 69
11.89 Look up Z value in normal distribution table
Z = 0.870 Pz = .8078 or 80.78%
(Probability of it taking 72 weeks)
19. Assessing Risks
Look up the Z value (0.870) in the table of normal distribution.
.8078 or 80.78% is the probability of the project taking up to 72 wks.
Going over 72 weeks would be 100 – 80.78 = 19.22%
20. Assessing Risks
Normal distribution:
Length of critical Mean = 69 weeks;
path is 69 weeks = 3.45 weeks
Probability of taking
72 weeks is 0.8078 Probability of
or 80.78% exceeding 72 weeks
is 0.1922 or 19.22%
69 72
Project duration (weeks)
21. Assessing Risks
• Assume a PERT project critical path takes 40 days, and that the
variance of this path is 2.147
– You wish to know the probability of the project going over 42 days.
• Compute the standard deviation of the critical path. (Take the square
root of the variance of 2.147) Std. Dev. = 1.465
– POM/QM software gives you the variance of the critical path.
• Compute the Z value: Z = (absolute time difference) / Std. Dev.
In this example, Z = (42 days - 40 days) / 1.465 = 1.365
• Look up the Z value of 1.365 in a Normal Distribution table to get the
probability of the project taking 42 days.
• Subtract it from 100% to get the probability of going over 42.
22. Assessing Risks
Look up the Z value (1.365) in the table of normal distribution.
(In this case you need to interpolate between the Z values of .9313 and .9147)
.9139 or 91.39% is the probability of the project taking up to 42 days.
Going over 42 days is thus 100 - 91.39 = 8.61%
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