The document discusses project management techniques like CPM and PERT. It provides 3 examples of projects: 1) construction of a retail complex, 2) clinical trials of a new drug, and 3) introduction of multimedia resources at a teacher's college. It then defines what a project is, noting that it is a unique endeavor with a defined start and end, undertaken to achieve specific objectives within time and resource constraints. The document discusses key aspects of project management like work breakdown structure, network diagrams, critical path method (CPM), and program evaluation and review technique (PERT).
Project Management: NETWORK ANALYSIS - CPM and PERTS.Vijaya Bhaskar
This document provides information about project management techniques including network analysis using Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT). It defines what a project and network are, and describes the basic steps and concepts involved in CPM and PERT. These include drawing networks, identifying critical paths, calculating expected durations and variances of activities, and determining the probability of completing projects within given timeframes. Examples are provided to illustrate key concepts like crashing project durations and calculating associated costs. The document is intended as a teaching aid for understanding fundamental aspects of project network analysis.
The document discusses project management techniques CPM/PERT. It provides examples of 3 different project managers and their roles overseeing construction of a retail complex, clinical trials for a new drug, and introducing new teaching resources at a college. It then defines key characteristics of projects, examples of project types, and an overview of what project management entails. The document proceeds to describe the project management process and techniques used in CPM and PERT including network diagrams, critical path analysis, and probability calculations for assessing project completion time.
Project Management Techniques ( CPM & PERT Techniques )
A revised PPT from other shared PPT available
Project management is a scientific way of planning, implementing, monitoring & controlling the various aspects of a project such as time, money, materials, manpower & other resources.
By,
Mr. AKARESH JOSE
Kerala Agricultural University
akareshjose@gmail.com
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.
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.
This document discusses the significance and uses of S-curves in project management. It begins by defining an S-curve as a graph that tracks project metrics like cost, hours, or deliverables against time. It then describes the different types of S-curves including target, cost, hours, baseline, and actual curves. Finally, it outlines several ways S-curves can help interpret a project's health, such as evaluating progress, forecasting cash flow, comparing outputs to plans, and determining growth or slippage from the baseline.
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.
Project Management: NETWORK ANALYSIS - CPM and PERTS.Vijaya Bhaskar
This document provides information about project management techniques including network analysis using Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT). It defines what a project and network are, and describes the basic steps and concepts involved in CPM and PERT. These include drawing networks, identifying critical paths, calculating expected durations and variances of activities, and determining the probability of completing projects within given timeframes. Examples are provided to illustrate key concepts like crashing project durations and calculating associated costs. The document is intended as a teaching aid for understanding fundamental aspects of project network analysis.
The document discusses project management techniques CPM/PERT. It provides examples of 3 different project managers and their roles overseeing construction of a retail complex, clinical trials for a new drug, and introducing new teaching resources at a college. It then defines key characteristics of projects, examples of project types, and an overview of what project management entails. The document proceeds to describe the project management process and techniques used in CPM and PERT including network diagrams, critical path analysis, and probability calculations for assessing project completion time.
Project Management Techniques ( CPM & PERT Techniques )
A revised PPT from other shared PPT available
Project management is a scientific way of planning, implementing, monitoring & controlling the various aspects of a project such as time, money, materials, manpower & other resources.
By,
Mr. AKARESH JOSE
Kerala Agricultural University
akareshjose@gmail.com
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.
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.
This document discusses the significance and uses of S-curves in project management. It begins by defining an S-curve as a graph that tracks project metrics like cost, hours, or deliverables against time. It then describes the different types of S-curves including target, cost, hours, baseline, and actual curves. Finally, it outlines several ways S-curves can help interpret a project's health, such as evaluating progress, forecasting cash flow, comparing outputs to plans, and determining growth or slippage from the baseline.
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 summarizes the key steps in project scheduling including identifying activities, determining precedence relationships, calculating earliest and latest start/finish times, determining slack times, identifying the critical path, and considering probabilistic approaches using PERT analysis. Specifically, it provides an example of scheduling a project for a computer manufacturing company, identifying 10 activities, calculating their earliest/latest times, determining the critical path, and finding the mean and variance of activity times and the overall project using three-point estimates.
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.
The document discusses the Program Evaluation and Review Technique (PERT) which is a management tool used to define and integrate project events. PERT uses optimistic, pessimistic, and most likely time estimates to calculate the expected time for tasks. It is event-oriented and models the logical order and dependencies of activities. Variance and standard deviation are also calculated to measure uncertainty. An example project is provided showing how to determine activity times, critical paths, and the probability of meeting a deadline.
Resource leveling and resource smoothing are techniques used to optimize resource use. Resource leveling focuses on moving resources between activities, which can change the critical path. Resource smoothing adjusts activity start and finish dates within their total float to avoid over-allocating resources, keeping the critical path unchanged. The key difference is that resource leveling may alter the critical path, while resource smoothing does not.
A Stream of Construction Management which covers Time Value of Money and Equivalence of Alternatives by Various Methods also includes basic idea of Benefit to Cost Ratio.
Resource levelling is a technique in project management that overlooks resource allocation and resolves possible conflict arising from over-allocation. When project managers undertake a project, they need to plan their resources accordingly.
This will benefit the organization without having to face conflicts and not being able to deliver on time. Resource levelling is considered one of the key elements to resource management in the organization.
An organization starts to face problems if resources are not allocated properly i.e., some resource may be over-allocated whilst others will be under-allocated. Both will bring about a financial risk to the organization.
Resource levelling is required when there is a demand for resources more compared to the available supply.
Resource levelling helps an organization to make use of the available resources to the maximum. The idea behind resource levelling is to reduce wastage of resources i.e., to stop over-allocation of resources.
Project manager will identify time that is unused by a resource and will take measures to prevent it or making an advantage out of it.
By resource conflicts, there are numerous disadvantages suffered by the organization, such as:
Delay in certain tasks being completed
Difficulty in assigning a different resource
Unable to change task dependencies
To remove certain tasks
To add more tasks
Overall delays and budget overruns of projects
The document discusses network construction for planning and scheduling large projects. It defines key terms like activities, events, precedence relationships. It describes activity on arrow and activity on node diagrams and provides rules for constructing networks without errors. Examples show how to build networks from descriptions of activities and their relationships. Dummy activities are introduced to properly represent connections when needed. Events are numbered according to flow to uniquely identify activities.
Project scheduling and resource levelling_Construction Management A Makwana
At the time of preparing the network of any project, usually it is assumed that all resources needed for its execution are available in plenty and no consideration of resource constraints is taken into account.
In such situations the duration of the project may increase escalating the cost of the project.
This document provides an overview of PERT/CPM (Program/Project Evaluation and Review Technique/Critical Path Method). It describes PERT/CPM as methods used to plan, schedule, and control projects involving complex sequences of interdependent activities. The document outlines the history, framework, basic terms, and differences between PERT and CPM. It also discusses the advantages and disadvantages of using PERT/CPM for project management.
This document provides information on the project management techniques of PERT and CPM. It defines PERT as dealing with uncertain project activities, using three time estimates and a probabilistic model. CPM is described as handling well-defined activities with fixed durations, using a deterministic model and focusing on time-cost tradeoffs. The document also outlines key elements of each technique such as events and activities, the critical path, and float.
The document discusses three examples of project managers and their responsibilities on different projects:
1) Construction of a retail development with 26 units and a supermarket. Responsible for coordinating contractors to ensure on-time and on-budget completion.
2) Directing trials of a new analgesic drug. Responsible for designing experiments and ensuring proper scientific and legal procedures are followed.
3) Introducing multimedia resources at a teacher training college in New Delhi. Responsible for purchasing and developing resources as well as encouraging acceptance by lecturers and students.
Program (Project) Evaluation and Review Technique (PERT): is a project management tool used to schedule, organize, and coordinate tasks within a project.
PERT is a scheduling method used to plan, schedule, and control projects. It employs a network of interrelated activities and coordinates costs and time criteria. The example project involves building a parade float over 26 weeks. PERT is used to identify the project's critical path of activities, calculate the probability of completing on time, and determine which path has the highest likelihood of completion within the deadline. The critical path is identified as A-C-F-I-K at 23 weeks, and there is a 98.30% probability of completing the entire project within the 26 week deadline.
1) Total float refers to the amount of time an activity can be delayed without delaying the project's estimated completion time. It assumes all preceding activities finish as early as possible and all succeeding activities start as late as possible. Total float can be calculated using the late start and early start or late finish and early finish of an activity.
2) Free float is the amount of time an activity can be delayed without impacting the project's estimated completion time or delaying succeeding activities. It is calculated using the early finish of an activity and the minimum early start of its successor activities.
3) Interfering float allows delaying an activity without impacting the project's completion, but it could delay one or more
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.
Project crashing refers to shortening the duration of project activities by using additional resources like overtime or temporary staff. This allows the project to finish earlier but increases costs. The optimal strategy is to crash activities on the critical path until their duration matches that of the non-critical path with the lowest duration, as crashing further would not reduce the overall project duration but would increase costs unnecessarily. The amount each activity can be crashed is determined, and activities on the critical path are crashed in a way that equalizes the completion time of all paths at the minimum possible overall cost.
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.
Chapter 09 of ICT Project Management based on IOE Engineering syllabus. This chapter mainly focuses on cost and project, cost management, cost estimating and more related to cost and project. Provided by Project Management Sir of KU
The document discusses the Critical Path Method (CPM) for project management. CPM determines the total calendar time required for a project by adding the times for activities in each sequence. The critical path is made up of activities where any delay will delay the whole project. Non-critical activities can be delayed within their slack time without impacting the project duration. Dummy activities with zero duration are sometimes added to networks to maintain clear precedence relationships between tasks that share start and end nodes.
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 document discusses project management techniques like CPM and PERT. It provides 3 examples of projects: 1) construction of a retail complex, 2) clinical trials of a new drug, and 3) introduction of multimedia resources at a teacher's college. It then defines what constitutes a project and lists some key project characteristics. The next sections describe tools used for project scheduling like work breakdown structure, Gantt charts, CPM and PERT networks. It provides examples of activity networks and calculations for critical path method.
The document discusses project management techniques like CPM and PERT. It provides 3 examples of projects to illustrate what constitutes a project. It then defines key aspects of project management like the work breakdown structure, network diagrams, and critical path method. The critical path method is explained through an example network diagram that is analyzed to find the earliest and latest start/finish times, critical path and project duration.
The document summarizes the key steps in project scheduling including identifying activities, determining precedence relationships, calculating earliest and latest start/finish times, determining slack times, identifying the critical path, and considering probabilistic approaches using PERT analysis. Specifically, it provides an example of scheduling a project for a computer manufacturing company, identifying 10 activities, calculating their earliest/latest times, determining the critical path, and finding the mean and variance of activity times and the overall project using three-point estimates.
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.
The document discusses the Program Evaluation and Review Technique (PERT) which is a management tool used to define and integrate project events. PERT uses optimistic, pessimistic, and most likely time estimates to calculate the expected time for tasks. It is event-oriented and models the logical order and dependencies of activities. Variance and standard deviation are also calculated to measure uncertainty. An example project is provided showing how to determine activity times, critical paths, and the probability of meeting a deadline.
Resource leveling and resource smoothing are techniques used to optimize resource use. Resource leveling focuses on moving resources between activities, which can change the critical path. Resource smoothing adjusts activity start and finish dates within their total float to avoid over-allocating resources, keeping the critical path unchanged. The key difference is that resource leveling may alter the critical path, while resource smoothing does not.
A Stream of Construction Management which covers Time Value of Money and Equivalence of Alternatives by Various Methods also includes basic idea of Benefit to Cost Ratio.
Resource levelling is a technique in project management that overlooks resource allocation and resolves possible conflict arising from over-allocation. When project managers undertake a project, they need to plan their resources accordingly.
This will benefit the organization without having to face conflicts and not being able to deliver on time. Resource levelling is considered one of the key elements to resource management in the organization.
An organization starts to face problems if resources are not allocated properly i.e., some resource may be over-allocated whilst others will be under-allocated. Both will bring about a financial risk to the organization.
Resource levelling is required when there is a demand for resources more compared to the available supply.
Resource levelling helps an organization to make use of the available resources to the maximum. The idea behind resource levelling is to reduce wastage of resources i.e., to stop over-allocation of resources.
Project manager will identify time that is unused by a resource and will take measures to prevent it or making an advantage out of it.
By resource conflicts, there are numerous disadvantages suffered by the organization, such as:
Delay in certain tasks being completed
Difficulty in assigning a different resource
Unable to change task dependencies
To remove certain tasks
To add more tasks
Overall delays and budget overruns of projects
The document discusses network construction for planning and scheduling large projects. It defines key terms like activities, events, precedence relationships. It describes activity on arrow and activity on node diagrams and provides rules for constructing networks without errors. Examples show how to build networks from descriptions of activities and their relationships. Dummy activities are introduced to properly represent connections when needed. Events are numbered according to flow to uniquely identify activities.
Project scheduling and resource levelling_Construction Management A Makwana
At the time of preparing the network of any project, usually it is assumed that all resources needed for its execution are available in plenty and no consideration of resource constraints is taken into account.
In such situations the duration of the project may increase escalating the cost of the project.
This document provides an overview of PERT/CPM (Program/Project Evaluation and Review Technique/Critical Path Method). It describes PERT/CPM as methods used to plan, schedule, and control projects involving complex sequences of interdependent activities. The document outlines the history, framework, basic terms, and differences between PERT and CPM. It also discusses the advantages and disadvantages of using PERT/CPM for project management.
This document provides information on the project management techniques of PERT and CPM. It defines PERT as dealing with uncertain project activities, using three time estimates and a probabilistic model. CPM is described as handling well-defined activities with fixed durations, using a deterministic model and focusing on time-cost tradeoffs. The document also outlines key elements of each technique such as events and activities, the critical path, and float.
The document discusses three examples of project managers and their responsibilities on different projects:
1) Construction of a retail development with 26 units and a supermarket. Responsible for coordinating contractors to ensure on-time and on-budget completion.
2) Directing trials of a new analgesic drug. Responsible for designing experiments and ensuring proper scientific and legal procedures are followed.
3) Introducing multimedia resources at a teacher training college in New Delhi. Responsible for purchasing and developing resources as well as encouraging acceptance by lecturers and students.
Program (Project) Evaluation and Review Technique (PERT): is a project management tool used to schedule, organize, and coordinate tasks within a project.
PERT is a scheduling method used to plan, schedule, and control projects. It employs a network of interrelated activities and coordinates costs and time criteria. The example project involves building a parade float over 26 weeks. PERT is used to identify the project's critical path of activities, calculate the probability of completing on time, and determine which path has the highest likelihood of completion within the deadline. The critical path is identified as A-C-F-I-K at 23 weeks, and there is a 98.30% probability of completing the entire project within the 26 week deadline.
1) Total float refers to the amount of time an activity can be delayed without delaying the project's estimated completion time. It assumes all preceding activities finish as early as possible and all succeeding activities start as late as possible. Total float can be calculated using the late start and early start or late finish and early finish of an activity.
2) Free float is the amount of time an activity can be delayed without impacting the project's estimated completion time or delaying succeeding activities. It is calculated using the early finish of an activity and the minimum early start of its successor activities.
3) Interfering float allows delaying an activity without impacting the project's completion, but it could delay one or more
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.
Project crashing refers to shortening the duration of project activities by using additional resources like overtime or temporary staff. This allows the project to finish earlier but increases costs. The optimal strategy is to crash activities on the critical path until their duration matches that of the non-critical path with the lowest duration, as crashing further would not reduce the overall project duration but would increase costs unnecessarily. The amount each activity can be crashed is determined, and activities on the critical path are crashed in a way that equalizes the completion time of all paths at the minimum possible overall cost.
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.
Chapter 09 of ICT Project Management based on IOE Engineering syllabus. This chapter mainly focuses on cost and project, cost management, cost estimating and more related to cost and project. Provided by Project Management Sir of KU
The document discusses the Critical Path Method (CPM) for project management. CPM determines the total calendar time required for a project by adding the times for activities in each sequence. The critical path is made up of activities where any delay will delay the whole project. Non-critical activities can be delayed within their slack time without impacting the project duration. Dummy activities with zero duration are sometimes added to networks to maintain clear precedence relationships between tasks that share start and end nodes.
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 document discusses project management techniques like CPM and PERT. It provides 3 examples of projects: 1) construction of a retail complex, 2) clinical trials of a new drug, and 3) introduction of multimedia resources at a teacher's college. It then defines what constitutes a project and lists some key project characteristics. The next sections describe tools used for project scheduling like work breakdown structure, Gantt charts, CPM and PERT networks. It provides examples of activity networks and calculations for critical path method.
The document discusses project management techniques like CPM and PERT. It provides 3 examples of projects to illustrate what constitutes a project. It then defines key aspects of project management like the work breakdown structure, network diagrams, and critical path method. The critical path method is explained through an example network diagram that is analyzed to find the earliest and latest start/finish times, critical path and project duration.
The document discusses project management and defines what constitutes a project. It provides examples of projects such as constructing buildings, developing new products, and implementing computer systems. It also summarizes some key aspects of project management including establishing a work breakdown structure, planning activities and schedules, and using techniques like critical path method (CPM) and program evaluation and review technique (PERT) to analyze networks and determine project duration.
PM 2 is directing a team of research scientists running trials on a new analgesic drug. Their responsibility is to design experiments, follow scientific and legal procedures, and have results analyzed independently.
PM 3 is being sent to New Delhi by an international aid agency to organize introducing multimedia resources at a teachers' college. Their role is complex, ensuring appropriate resources are purchased and developed within the college, and encouraging acceptance by lecturers and students.
PM 1 is in charge of constructing a retail development with 26 units and a supermarket. Their main responsibilities are coordinating contractors to complete the project on specification, within budget and on time.
The document discusses various project management methodologies including Waterfall, Agile, Scrum, Kanban, and Critical Path Method (CPM). It provides descriptions of how each methodology works, when it should be used, advantages and disadvantages. The Critical Path Method in particular aims to identify the longest sequence of dependent tasks in a project in order to minimize the overall project duration.
This document discusses approaches for maximizing the benefits of timesheets. It provides an overview of timesheets and analyzes survey results on timesheet usage. A case study of the Sustainable Water Resources Research Center is presented which implemented detailed timesheet tracking. The document also discusses integrating timesheets into project management systems and important human factors to consider for timesheet adoption, such as different personality types and managing organizational change. A recommended daily/weekly timesheet template with approvals is presented.
TIME & RESOURCE PLANNING,MANAGEMENT SOFTWAREKHUSHBU SHAH
The document discusses time planning and resource management for construction projects. It describes the key stages of time planning as project work breakdown, network modeling and analysis, and scheduling work programs. It also covers forecasting resource needs, the four M's of resource planning (manpower, machinery, material, money), resource allocation and leveling techniques, and the purpose of management software in optimizing operations and controlling projects.
The document discusses construction project planning. It defines construction planning as the first stage of construction management that takes a project from conception to completion. It includes scheduling, organizing, staffing, directing, and monitoring. The key steps in construction planning are defining the scope of work, generating a work breakdown structure (WBS) and organization breakdown structure (OBS), determining activity relationships, estimating activity details, and developing a project network. Other types of planning discussed include strategic planning, operational planning, scheduling, site planning, financial planning, resource planning, quality planning, risk planning, and communication planning. Metrics and references are also provided.
This document outlines the stages and concepts of project management. It discusses the introduction to projects and project management, including the definition of a project, characteristics of projects, and challenges of project management. It also describes common problems that can occur in software projects if not properly managed. Additionally, it covers key areas of project management knowledge and frameworks, such as integration management, scope management, and risk management. Finally, it discusses the typical stages a project goes through, including initiation and planning, execution, monitoring and control, and closing.
The document outlines a chapter on project management. It discusses key project management concepts like work breakdown structures, critical paths, PERT and CPM techniques. These techniques help schedule project activities, determine precedence relationships, identify critical paths, and calculate activity time estimates. The chapter also covers topics like project planning, scheduling, controlling, and the roles of project managers. An example case study on a large project by Bechtel is provided to illustrate real-world project management.
This document discusses project management and the Program Evaluation and Review Technique (PERT). It begins with introductions to project management and PERT. PERT is a statistical tool used to analyze tasks in a project and determine the minimum time needed. Key PERT concepts discussed include critical path, float, expected and normal times. The document provides a theoretical example and then applies PERT to an industrial example of assembling a switch board. Key steps of PERT execution are outlined. Questions about project management responsibilities are also addressed.
The document outlines a chapter on project management. It discusses key aspects of project management including project planning, scheduling, and controlling. It provides an overview of techniques like PERT and CPM which are network-based approaches to scheduling projects. Specific topics covered include defining the work breakdown structure, determining activity relationships and time/cost estimates, identifying the critical path, and using the network to plan and monitor the project. The learning objectives are to understand concepts like the critical path, network diagrams, and how to apply PERT/CPM for project scheduling.
This document discusses project planning and scheduling. It begins by defining project planning as breaking down a project into definable tasks, establishing logical relationships between tasks, and estimating resources, time and costs required. The document then discusses several key aspects of project planning and scheduling including work breakdown structures, network diagrams, critical path analysis and scheduling techniques. It also discusses factors that affect project scheduling such as time, manpower and materials. The document concludes by emphasizing the importance of planning for successfully completing projects on time and within budget while meeting quality requirements.
PROJECT CHARTER TEMPLATE GENERAL PROJECT INFORMATIONProject Na.docxwkyra78
PROJECT CHARTER TEMPLATE
GENERAL PROJECT INFORMATION
Project Name:
Project Sponsor:
Project Manager:
Email Address:
Phone Number:
Organizational Unit:
Process Impacted:
Expected Start Date:
Expected Completion Date:
Expected Savings:
Estimated Costs:
Green Belts Assigned:
Black Belts Assigned:
PROBLEM, ISSUE, GOALS, OBJECTIVES, DELIVERABLES
Problem or Issue:
Purpose of Project:
Business Case:
Goals/Metrics:
Expected Deliverables:
PROJECT SCOPE & SCHEDULE
Within Scope
Outside of Scope
PROJECT RESOURCES & COSTS
Project Team
Support Resources
Special Needs
PROJECT BENEFITS & CUSTOMERS
Process Owner
Key Stakeholders
Final Customers
Expected Benefits
PROJECT RISKS, CONSTRAINTS, ASSUMPTIONS
Risks:
Constraints:
Assumptions:
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Test for Understanding Study Guide
PSYC 3003 Week 6
This test contains 45 items with a time limit of 60 minutes. Because there is not a written Application Assignment covering quasi-experimental designs this week, approximately 2/3 of the test items are drawn from Chapter 14, and 1/3 are drawn from Chapter 7.
This study guide is available to help you organize your focus and preparation as you prepare to take the Test for Understanding on the content presented in the Learning Resources assigned for this week. Read the assigned chapters and take notes as needed on the topics listed within this guide.
Please note:The Course Instructor is available throughout the courseto assist you in your achievement of a better understanding of the course content; however, the Instructor will not provideyou with the answers to the study guide.
Chapter 7 – Naturalistic Methods
1. Be able to distinguish among examples of the following naturalistic research designs and corresponding methodology:
a. Observational
b. Case studies
c. Archival
2. Be familiar with how the following sampling methods are conducted:
a. Time
b. Event
c. Individual
3. What is systematic observation? Which of the above listed sampling methods involves this approach?
4. Be able to identify examples of methodology that involves the use of behavioral categories.
5. Be able to distinguish among the differences, and identify examples of, the following terms:
a. Acknowledged participant
b. Unacknowledged participant
c. Acknowledged observer
d. Unacknowledged observer
6. Why is interrater reliability important when collecting naturalistic observation data? How is interrater reliability conducted?
7. What is a ...
The document discusses the lifecycle management approach for projects. It describes the typical stages in a project's lifecycle including project selection, planning, implementation, completion and review. Specifically, it covers key aspects of each stage such as identifying projects, evaluating them, developing work breakdown structures and schedules, implementing as planned, and conducting post-project reviews. It also discusses common challenges in managing projects and emphasizes the importance of communication throughout the project lifecycle.
This document provides an overview of time management and project scheduling concepts. It discusses common scheduling mistakes, the importance of scheduling, and strategies for effective time management. It also covers key project scheduling processes from the PMBOK Guide, including defining activities, sequencing activities, estimating durations, developing the schedule, and controlling the schedule. Methods like critical path analysis, resource leveling, crashing, and float are explained. The document concludes with definitions of important scheduling terms.
This document provides an overview of project management concepts that will be covered in an operations management course. It discusses what constitutes a project and project management. The key aspects of project management include having a limited time frame, specific objectives, and metrics of time and cost. The document outlines the typical project life cycle phases of initiating, planning, executing, monitoring/controlling, and closing. It also discusses topics like work breakdown structure, network diagrams, scheduling techniques like Gantt charts, critical path method, and tools for project managers.
This document discusses project time management and provides details on the seven processes involved: plan schedule management, define activities, sequence activities, estimate activity resources, estimate activity durations, develop schedule, and control schedule. It defines key aspects of each process such as inputs, tools and techniques, and outputs. It also provides examples and explanations of techniques for sequencing activities, estimating durations, developing the project schedule, and identifying critical paths.
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Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024Sinan KOZAK
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TIME DIVISION MULTIPLEXING TECHNIQUE FOR COMMUNICATION SYSTEMHODECEDSIET
Time Division Multiplexing (TDM) is a method of transmitting multiple signals over a single communication channel by dividing the signal into many segments, each having a very short duration of time. These time slots are then allocated to different data streams, allowing multiple signals to share the same transmission medium efficiently. TDM is widely used in telecommunications and data communication systems.
### How TDM Works
1. **Time Slots Allocation**: The core principle of TDM is to assign distinct time slots to each signal. During each time slot, the respective signal is transmitted, and then the process repeats cyclically. For example, if there are four signals to be transmitted, the TDM cycle will divide time into four slots, each assigned to one signal.
2. **Synchronization**: Synchronization is crucial in TDM systems to ensure that the signals are correctly aligned with their respective time slots. Both the transmitter and receiver must be synchronized to avoid any overlap or loss of data. This synchronization is typically maintained by a clock signal that ensures time slots are accurately aligned.
3. **Frame Structure**: TDM data is organized into frames, where each frame consists of a set of time slots. Each frame is repeated at regular intervals, ensuring continuous transmission of data streams. The frame structure helps in managing the data streams and maintaining the synchronization between the transmitter and receiver.
4. **Multiplexer and Demultiplexer**: At the transmitting end, a multiplexer combines multiple input signals into a single composite signal by assigning each signal to a specific time slot. At the receiving end, a demultiplexer separates the composite signal back into individual signals based on their respective time slots.
### Types of TDM
1. **Synchronous TDM**: In synchronous TDM, time slots are pre-assigned to each signal, regardless of whether the signal has data to transmit or not. This can lead to inefficiencies if some time slots remain empty due to the absence of data.
2. **Asynchronous TDM (or Statistical TDM)**: Asynchronous TDM addresses the inefficiencies of synchronous TDM by allocating time slots dynamically based on the presence of data. Time slots are assigned only when there is data to transmit, which optimizes the use of the communication channel.
### Applications of TDM
- **Telecommunications**: TDM is extensively used in telecommunication systems, such as in T1 and E1 lines, where multiple telephone calls are transmitted over a single line by assigning each call to a specific time slot.
- **Digital Audio and Video Broadcasting**: TDM is used in broadcasting systems to transmit multiple audio or video streams over a single channel, ensuring efficient use of bandwidth.
- **Computer Networks**: TDM is used in network protocols and systems to manage the transmission of data from multiple sources over a single network medium.
### Advantages of TDM
- **Efficient Use of Bandwidth**: TDM all
1. Project Management - CPM/PERT
Dr. M Varaprasada Rao
DEAN - ACADEMICS
GIET RAJAHMUNDRY
2. Dr. Varaprasada Rao GGSESTC 2
What exactly is a project?
PM 1 – A building supervisor is in-charge for construction of a retail
development in the centre of Rajahmundry. There are 26 retail units
and a super market in the complex. The main responsibilities are to co-
ordinate the work of the various contractors to ensure that the project is
completed to specification, within budget and on time.
PM 2 – Dr. Rao directing a team of research scientists. They are
running trials on a new analgesic drug on behalf of a pharmaceutical
company. It is the responsibility to design the experiments and make
sure that proper scientific and legal procedures are followed, so that the
results can be subjected to independent statistical analysis.
PM 3- The international aid agency which employs me is sending me to
New Delhi to organize the introduction of multimedia resources at a
teachers’ training college. My role is quite complex. I have to make
sure that appropriate resources are purchased- and in some cases
developed within the college. I also have to encourage the acceptance
of these resources by lecturers and students within the college.03/13/18
3. Dr. Varaprasada Rao GGSESTC 3
Project is not defined by the type of outcome it is set up to achieve
PM 1 – A building supervisor is in-charge for construction of a retail
development in the centre of Rajahmundry. There are 26 retail units
and a super market in the complex. The main responsibilities are to co-
ordinate the work of the various contractors to ensure that the project is
completed to specification, within budget and on time.
PM 2 – Dr. Rao directing a team of research scientists. They are
running trials on a new analgesic drug on behalf of a pharmaceutical
company. It is the responsibility to design the experiments and make
sure that proper scientific and legal procedures are followed, so that the
results can be subjected to independent statistical analysis.
PM 3- The international aid agency which employs me is sending me to
New Delhi to organize the introduction of multimedia resources at a
teachers’ training college. My role is quite complex. I have to make
sure that appropriate resources are purchased- and in some cases
developed within the college. I also have to encourage the acceptance
of these resources by lecturers and students within the college.03/13/18
A shopping complex
A new drug
A new method of teaching students
4. Dr. Varaprasada Rao GIET 4
Characteristic of a project
A project is an endeavour involving a connected sequence of
activities and a range of resources, which is designed to achieve
a specific outcome and which operates within a time frame,
cost and quality constraints and which is often used to
introduce change.
A unique, one-time operational activity or effort
Requires the completion of a large number of
interrelated activities
Established to achieve specific objective
Resources, such as time and/or money, are limited
Typically has its own management structure
Need leadership
Project
03/13/18
5. Dr. Varaprasada Rao GIET 5
Examples
– constructing houses, factories, shopping malls,
athletic stadiums or arenas
– developing military weapons systems, aircrafts,
new ships
– launching satellite systems
– constructing oil pipelines
– developing and implementing new computer
systems
– planning concert, football games, or basketball
tournaments our National Event ‘Mythri’
– introducing new products into market
03/13/18
6. LET US LEARN THE TECHNIQUES
• My dear Students please look at the following
links at home and try to understand the basic
information and we will proceed further in the
next session on Monday.
• https://www.youtube.com/watch?v=vUMGvpsb8dc
(Only up to 11.58 Minutes)
• https://www.slideshare.net/annaprasad/project-mana
(Only 36 slides out of 145 slides)
03/13/18 Dr. Varaprasada Rao GIET 6
7. Dr. Varaprasada Rao GGSESTC 7
What is project management
• The application of a collection of tools and
techniques to direct the use of diverse resources
towards the accomplishment of a unique,
complex, one time task within time, cost and
quality constraints.
• Its origins lie in World War II, when the
military authorities used the techniques of
operational research to plan the optimum use
of resources.
• One of these techniques was the use of networks
to represent a system of related activities
03/13/18
8. Dr. Varaprasada Rao GGSESTC 8
Project Management Process
• Project planning - Project scheduling - Project control
• Project team
– made up of individuals from various areas and departments within a
company
• Matrix organization
– a team structure with members from functional areas, depending on skills
required
• Project Manager
– most important member of project team
• Scope statement
– a document that provides an understanding, justification, and expected result
of a project
• Statement of work
– written description of objectives of a project
• Organizational Breakdown Structure
– a chart that shows which organizational units are responsible for work items
• Responsibility Assignment Matrix
– shows who is responsible for work in a project
03/13/18
9. Dr. Varaprasada Rao GGSESTC 9
Work breakdown structure
• A method of breaking down a project into individual
elements ( components, subcomponents, activities and
tasks) in a hierarchical structure which can be scheduled
and cost
• It defines tasks that can be completed independently of
other tasks, facilitating resource allocation, assignment
of responsibilities and measurement and control of the
project
• It is foundation of project planning
• It is developed before identification of dependencies and
estimation of activity durations
• It can be used to identity the tasks in the CPM and PERT
03/13/18
10. Dr. Varaprasada Rao GGSESTC 10
Work Breakdown Structure for Computer Order
Processing System Project
Work Breakdown Structure for Computer Order
Processing System Project
03/13/18
11. Dr. Varaprasada Rao GGSESTC 11
Project Planning
• Resource Availability and/or Limits
– Due date, late penalties, early completion
incentives
– Budget
• Activity Information
– Identify all required activities
– Estimate the resources required (time) to complete
each activity
– Immediate predecessor(s) to each activity needed
to create interrelationships
03/13/18
12. Dr. Varaprasada Rao GGSESTC 12
Project Scheduling and Control Techniques
Gantt Chart
Critical Path Method (CPM)
Program Evaluation and Review Technique (PERT)
03/13/18
13. Dr. Varaprasada Rao GGSESTC 13
Graph or bar chart with a bar for each project activity that shows
passage of time
Provides visual display of project scheduleProvides visual display of project schedule
Gantt Chart
03/13/18
14. Dr. Varaprasada Rao GGSESTC 14
History of CPM/PERT
• Critical Path Method (CPM)
– E I Du Pont de Nemours & Co. (1957) for construction of new
chemical plant and maintenance shut-down
– Deterministic task times
– Activity-on-node network construction
– Repetitive nature of jobs
• Project Evaluation and Review Technique (PERT)
– U S Navy (1958) for the POLARIS missile program
– Multiple task time estimates (probabilistic nature)
– Activity-on-arrow network construction
– Non-repetitive jobs (R & D work)
03/13/18
15. Dr. Varaprasada Rao GGSESTC 15
• Event
– Signals the beginning or ending of an activity
– Designates a point in time
– Represented by a circle (node)
• Network
– Shows the sequential relationships among activities using nodes
and arrows
Activity-on-node (AON)
nodes represent activities, and arrows show precedence
relationships
Activity-on-arrow (AOA)
arrows represent activities and nodes are events for points in
time
Project Network
03/13/18
16. Dr. Varaprasada Rao GGSESTC 16
Project Network
• Network analysis is the general name given to certain specific
techniques which can be used for the planning, management and
control of projects
• Use of nodes and arrows
Arrows An arrow leads from tail to head directionally
– Indicate ACTIVITY, a time consuming effort that is required to perform a
part of the work.
Nodes A node is represented by a circle
- Indicate EVENT, a point in time where one or more activities start and/or
finish.
• Activity
– A task or a certain amount of work required in the project
– Requires time to complete
– Represented by an arrow
• Dummy Activity
– Indicates only precedence relationships
– Does not require any time of effort
03/13/18
25. Dr. Varaprasada Rao GGSESTC 25
AOA Project Network for House
3
2 0
1
3
1 1
1
1 2 4 6 7
3
5
Lay
foundation
Design house
and obtain
financing
Order and
receive
materials
Dummy
Finish
work
Select
carpet
Select
paint
Build
house
AON Project Network for House
1
3
2
2
4
3
3
1 5
1
6
1
7
1Start
Design house and
obtain financing
Order and receive
materials
Select paint
Select carpet
Lay foundations Build house
Finish work
03/13/18
26. Dr. Varaprasada Rao GGSESTC 26
Situations in network diagram
A
B
C
A must finish before either B or C can start
A
B
C both A and B must finish before C can start
D
C
B
A
both A and C must finish before either of
B or D can start
A
C
B
D
Dummy
A must finish before B can start
both A and C must finish before D can start
03/13/18
27. Dr. Varaprasada Rao GGSESTC 27
Concurrent Activities
2 3
Lay foundationLay foundation
Order materialOrder material
(a)(a) Incorrect precedenceIncorrect precedence
relationshiprelationship
(b)(b) Correct precedenceCorrect precedence
relationshiprelationship
3
42
DummyDummy
LayLay
foundationfoundation
Order materialOrder material
11
22 00
03/13/18
28. Dr. Varaprasada Rao GGSESTC 28
Network example
Illustration of network analysis of a minor redesign of a product and
its associated packaging.
The key question is: How long will it take to complete this project ?
03/13/18
29. Dr. Varaprasada Rao GGSESTC 29
For clarity, this list is kept to a minimum by specifying only
immediate relationships, that is relationships involving activities
that "occur near to each other in time".
03/13/18
30. Dr. Varaprasada Rao GGSESTC 30
Questions to prepare activity network
• Is this a Start Activity?
• Is this a Finish Activity?
• What Activity Precedes this?
• What Activity Follows this?
• What Activity is Concurrent with this?
03/13/18
31. Dr. Varaprasada Rao GGSESTC 31
CPM calculation
• Path
– A connected sequence of activities leading from
the starting event to the ending event
• Critical Path
– The longest path (time); determines the project
duration
• Critical Activities
– All of the activities that make up the critical path
03/13/18
32. Dr. Varaprasada Rao GGSESTC 32
Forward Pass
• Earliest Start Time (ES)
– earliest time an activity can start
– ES = maximum EF of immediate predecessors
• Earliest finish time (EF)
– earliest time an activity can finish
– earliest start time plus activity time
EF= ES + t
Latest Start Time (LS)
Latest time an activity can start without delaying critical path
time
LS= LF - t
Latest finish time (LF)
latest time an activity can be completed without delaying
critical path time
LS = minimum LS of immediate predecessors
Backward Pass
03/13/18
33. Dr. Varaprasada Rao GGSESTC 33
CPM analysis
• Draw the CPM network
• Analyze the paths through the network
• Determine the float for each activity
– Compute the activity’s float
float = LS - ES = LF - EF
– Float is the maximum amount of time that this activity can be
delay in its completion before it becomes a critical activity,
i.e., delays completion of the project
• Find the critical path is that the sequence of activities and events
where there is no “slack” i.e.. Zero slack
– Longest path through a network
• Find the project duration is minimum project completion time
03/13/18
41. Dr. Varaprasada Rao GGSESTC 41
CPM Example
• Critical Path
a, 6a, 6
f, 15f, 15
b, 8b, 8
c, 5c, 5
e, 9e, 9
d, 13d, 13
g, 17g, 17 h, 9h, 9
i, 6i, 6
j, 12j, 12
03/13/18
42. Dr. Varaprasada Rao GGSESTC 42
PERT
• PERT is based on the assumption that an activity’s duration
follows a probability distribution instead of being a single value
• Three time estimates are required to compute the parameters of
an activity’s duration distribution:
– pessimistic time (tp) - the time the activity would take if
things did not go well
– most likely time (tm) - the consensus best estimate of the
activity’s duration
– optimistic time (to) - the time the activity would take if things
did go well
Mean (expected time): te =
tp + 4 tm + to
6
Variance: Vt =σ 2
=
tp - to
6
2
03/13/18
43. Dr. Varaprasada Rao GGSESTC 43
PERT analysis
• Draw the network.
• Analyze the paths through the network and find the critical path.
• The length of the critical path is the mean of the project duration
probability distribution which is assumed to be normal
• The standard deviation of the project duration probability
distribution is computed by adding the variances of the critical
activities (all of the activities that make up the critical path) and
taking the square root of that sum
• Probability computations can now be made using the normal
distribution table.
03/13/18
44. Dr. Varaprasada Rao GGSESTC 44
Probability computation
Determine probability that project is completed within specified
time
Z =
x - µ
σ
where µ = tp = project mean time
σ = project standard mean time
x = (proposed ) specified time
03/13/18
45. Dr. Varaprasada Rao GGSESTC 45
Normal Distribution of Project Time
µ = tp Timex
Zσ
Probability
03/13/18
46. Dr. Varaprasada Rao GGSESTC 46
PERT Example
Immed. Optimistic Most Likely Pessimistic
Activity Predec. Time (Hr.) Time (Hr.) Time (Hr.)
A -- 4 6 8
B -- 1 4.5 5
C A 3 3 3
D A 4 5 6
E A 0.5 1 1.5
F B,C 3 4 5
G B,C 1 1.5 5
H E,F 5 6 7
I E,F 2 5 8
J D,H 2.5 2.75 4.5
K G,I 3 5 703/13/18
47. Dr. Varaprasada Rao GGSESTC 47
PERT Example
AA
DD
CC
BB
FF
EE
GG
II
HH
KK
JJ
PERT Network
03/13/18
48. Dr. Varaprasada Rao GGSESTC 48
PERT Example
Activity Expected Time Variance
A 6 4/9
B 4 4/9
C 3 0
D 5 1/9
E 1 1/36
F 4 1/9
G 2 4/9
H 6 1/9
I 5 1
J 3 1/9
K 5 4/9
03/13/18
49. Dr. Varaprasada Rao GGSESTC 49
PERT Example
Activity ES EF LS LF Slack
A 0 6 0 6 0 *critical
B 0 4 5 9 5
C 6 9 6 9 0 *
D 6 11 15 20 9
E 6 7 12 13 6
F 9 13 9 13 0 *
G 9 11 16 18 7
H 13 19 14 20 1
I 13 18 13 18 0 *
J 19 22 20 23 1
K 18 23 18 23 0 *
03/13/18
50. Dr. Varaprasada Rao GGSESTC 50
PERT Example
Vpath = VA + VC + VF + VI + VK
= 4/9 + 0 + 1/9 + 1 + 4/9
= 2
σpath = 1.414
z = (24 - 23)/σ = (24-23)/1.414 = .71
From the Standard Normal Distribution table:
P(z < .71) = .5 + .2612 = .7612
03/13/18
52. Dr. Varaprasada Rao GGSESTC 52
Cost consideration in project
• Project managers may have the option or requirement to crash the
project, or accelerate the completion of the project.
• This is accomplished by reducing the length of the critical
path(s).
• The length of the critical path is reduced by reducing the duration
of the activities on the critical path.
• If each activity requires the expenditure of an amount of money
to reduce its duration by one unit of time, then the project
manager selects the least cost critical activity, reduces it by one
time unit, and traces that change through the remainder of the
network.
• As a result of a reduction in an activity’s time, a new critical path
may be created.
• When there is more than one critical path, each of the critical
paths must be reduced.
• If the length of the project needs to be reduced further, the03/13/18
53. Dr. Varaprasada Rao GGSESTC 53
Project Crashing
• Crashing
– reducing project time by expending additional resources
• Crash time
– an amount of time an activity is reduced
• Crash cost
– cost of reducing activity time
• Goal
– reduce project duration at minimum cost
03/13/18
54. Dr. Varaprasada Rao GGSESTC 54
Activity crashingActivitycost
Activity time
Crashing activity
Crash
time
Crash
cost
Normal Activity
Normal
time
Normal
cost
Slope = crash cost per unit time
03/13/18
55. Dr. Varaprasada Rao GGSESTC 55
Time-Cost Relationship
Crashing costs increase as project duration decreases
Indirect costs increase as project duration increases
Reduce project length as long as crashing costs are less than
indirect costs
Time-Cost Tradeoff
cost
time
Direct cost
Indirect
cost
Total project costMin total cost =
optimal project
time
03/13/18
59. Dr. Varaprasada Rao GGSESTC 59
Benefits of CPM/PERT
• Useful at many stages of project management
• Mathematically simple
• Give critical path and slack time
• Provide project documentation
• Useful in monitoring costs
•How long will the entire project take to be completed? What are the
risks involved?
•Which are the critical activities or tasks in the project which could
delay the entire project if they were not completed on time?
•Is the project on schedule, behind schedule or ahead of schedule?
•If the project has to be finished earlier than planned, what is the best
way to do this at the least cost?
CPM/PERT can answer the following important
questions:
03/13/18
60. Dr. Varaprasada Rao GGSESTC 60
Limitations to CPM/PERT
• Clearly defined, independent and stable activities
• Specified precedence relationships
• Over emphasis on critical paths
• Deterministic CPM model
• Activity time estimates are subjective and depend on judgment
• PERT assumes a beta distribution for these time estimates, but
the actual distribution may be different
• PERT consistently underestimates the expected project
completion time due to alternate paths becoming critical
To overcome the limitation, Monte Carlo simulations can be
performed on the network to eliminate the optimistic bias
03/13/18
62. Dr. Varaprasada Rao GGSESTC 62
Practice Example
A social project manager is faced with a project with the following
activities:
Activity Description Duration
Social work team to live in village 5w
Social research team to do survey 12w
Analyse results of survey 5w
Establish mother & child health program 14w
Establish rural credit programme 15w
Carry out immunization of under fives 4w
Draw network diagram and show the critical path.
Calculate project duration.03/13/18
63. Dr. Varaprasada Rao GGSESTC 63
Practice problem
Activity Description Duration
1-2 Social work team to live in village 5w
1-3 Social research team to do survey 12w
3-4 Analyse results of survey 5w
2-4 Establish mother & child health program 14w
3-5 Establish rural credit programme 15w
4-5 Carry out immunization of under fives 4w
3
1
2
4
5
03/13/18
64. Re-cap
Please try to understand various systems now
03/13/18 Dr. Varaprasada Rao GGSESTC 64
66. Dr. Varaprasada Rao GGSESTC
Step 1-Define the Project: Cables By ITD is bringing a new product on line to be
manufactured in their current facility in existing space. The owners have identified 11
activities and their precedence relationships. Develop an AON for the project.
Activity Description
Immediate
Predecessor
Duration
(weeks)
A Develop product specifications None 4
B Design manufacturing process A 6
C Source & purchase materials A 3
D Source & purchase tooling & equipment B 6
E Receive & install tooling & equipment D 14
F Receive materials C 5
G Pilot production run E & F 2
H Evaluate product design G 2
I Evaluate process performance G 3
J Write documentation report H & I 4
K Transition to manufacturing J 203/13/18 66
67. Dr. Varaprasada Rao GGSESTC
Step 2- Diagram the Network for
Cables By ITD
03/13/18 67
68. Dr. Varaprasada Rao GGSESTC
Step 3 (a)- Add Deterministic Time Estimates
and Connected Paths
03/13/18 68
69. Dr. Varaprasada Rao GGSESTC
Step 3 (a) (Con’t): Calculate the
Project Completion Times
• The longest path (ABDEGIJK) limits the
project’s duration (project cannot finish in less
time than its longest path)
• ABDEGIJK is the project’s critical path
Paths Path duration
ABDEGHJK 40
ABDEGIJK 41
ACFGHJK 22
ACFGIJK 23
03/13/18 69
75. Dr. Varaprasada Rao GGSESTC
Revisiting Cables By ITD Using Probabilistic Time
Estimates
Activity Description
Optimistic
time
Most likely
time
Pessimistic
time
A Develop product specifications 2 4 6
B Design manufacturing process 3 7 10
C Source & purchase materials 2 3 5
D Source & purchase tooling & equipment 4 7 9
E Receive & install tooling & equipment 12 16 20
F Receive materials 2 5 8
G Pilot production run 2 2 2
H Evaluate product design 2 3 4
I Evaluate process performance 2 3 5
J Write documentation report 2 4 6
K Transition to manufacturing 2 2 203/13/18 75
76. Dr. Varaprasada Rao GGSESTC
Using Beta Probability Distribution to
Calculate Expected Time Durations
• A typical beta distribution is shown below, note that it has
definite end points
• The expected time for finishing each activity is a weighted
average
( )
6
cpessimistilikelymost4optimistic
timeExp.
++
=03/13/18 76
77. Dr. Varaprasada Rao GGSESTC
Calculating Expected Task Times
Activity
Optimistic
time
Most likely
time
Pessimistic
time
Expected
time
A 2 4 6 4
B 3 7 10 6.83
C 2 3 5 3.17
D 4 7 9 6.83
E 12 16 20 16
F 2 5 8 5
G 2 2 2 2
H 2 3 4 3
I 2 3 5 3.17
J 2 4 6 4
K 2 2 2 2
( )
6
4 cpessimistilikelymostoptimistic
timeExpected
++
=
03/13/18 77
78. Dr. Varaprasada Rao GGSESTC
Network Diagram with Expected
Activity Times
03/13/18 78
79. Dr. Varaprasada Rao GGSESTC
Estimated Path Durations through the
Network
• ABDEGIJK is the expected critical path &
the project has an expected duration of 44.83
weeks
Activities on paths Expected duration
ABDEGHJK 44.66
ABDEGIJK 44.83
ACFGHJK 23.17
ACFGIJK 23.34
03/13/18 79
81. Dr. Varaprasada Rao GGSESTC
Estimating the Probability of
Completion Dates
• Using probabilistic time estimates offers the advantage of predicting the
probability of project completion dates
• We have already calculated the expected time for each activity by making
three time estimates
• Now we need to calculate the variance for each activity
• The variance of the beta probability distribution is:
– where p=pessimistic activity time estimate
o=optimistic activity time estimate
2
2
6
op
σ
−
=
03/13/18 81
82. Dr. Varaprasada Rao GGSESTC
Project Activity Variance
Activity Optimistic Most Likely Pessimistic Variance
A 2 4 6 0.44
B 3 7 10 1.36
C 2 3 5 0.25
D 4 7 9 0.69
E 12 16 20 1.78
F 2 5 8 1.00
G 2 2 2 0.00
H 2 3 4 0.11
I 2 3 5 0.25
J 2 4 6 0.44
K 2 2 2 0.00
03/13/18 82
83. Dr. Varaprasada Rao GGSESTC
Variances of Each Path through the
Network
Path
Number
Activities on
Path
Path Variance
(weeks)
1 A,B,D,E,G,H,J,
k
4.82
2 A,B,D,E,G,I,J,K 4.96
3 A,C,F,G,H,J,K 2.24
4 A,C,F,G,I,J,K 2.38
03/13/18 83
84. Dr. Varaprasada Rao GGSESTC
Calculating the Probability of Completing the
Project in Less Than a Specified Time
• When you know:
– The expected completion time
– Its variance
• You can calculate the probability of completing the project in “X”
weeks with the following formula:
Where DT = the specified completion date
EFPath = the expected completion time of the path
−
=
−
= 2
Pσ
EFD
timestandardpath
timeexpectedpathtimespecified
z
PT
pathofvarianceσ 2
Path =
03/13/18 84
85. Dr. Varaprasada Rao GGSESTC
Example: Calculating the probability of
finishing the project in 48 weeks
• Use the z values in Appendix B to determine probabilities
• e.g. probability for path 1 is
Path
Number
Activities on
Path
Path Variance
(weeks)
z-value Probability of
Completion
1 A,B,D,E,G,H,J,k 4.82 1.5216 0.9357
2 A,B,D,E,G,I,J,K 4.96 1.4215 0.9222
3 A,C,F,G,H,J,K 2.24 16.5898 1.000
4 A,C,F,G,I,J,K 2.38 15.9847 1.000
1.52
4.82
weeks44.66weeks48
z =
−
=
03/13/18 85
86. Dr. Varaprasada Rao GGSESTC
Reducing Project Completion
Time
• Project completion times may need to be
shortened because:
– Different deadlines
– Penalty clauses
– Need to put resources on a new project
– Promised completion dates
• Reduced project completion time is
“crashing”
03/13/18 86
87. Dr. Varaprasada Rao GGSESTC
Reducing Project Completion Time
–
• Crashing a project needs to balance
– Shorten a project duration
– Cost to shorten the project duration
• Crashing a project requires you to know
– Crash time of each activity
– Crash cost of each activity
Crash cost/duration = (crash cost-normal cost)/(normal time – crash time)
03/13/18 87
88. Dr. Varaprasada Rao GGSESTC
Reducing the Time of a Project (crashing)
Activity Normal
Time (wk)
Normal
Cost
Crash
Time
Crash
Cost
Max. weeks
of reduction
Reduce
cost per
week
A 4 8,000 3 11,000 1 3,000
B 6 30,000 5 35,000 1 5,000
C 3 6,000 3 6,000 0 0
D 6 24,000 4 28,000 2 2,000
E 14 60,000 12 72,000 2 6,000
F 5 5,000 4 6,500 1 1500
G 2 6,000 2 6,000 0 0
H 2 4,000 2 4,000 0 0
I 3 4,000 2 5,000 1 1,000
J 4 4,000 2 6,400 2 1,20003/13/18 88
89. Dr. Varaprasada Rao GGSESTC
Crashing Example: Suppose the Cables By ITD project
manager wants to reduce the new product project from 41
to 36 weeks.
• Crashing Costs are considered to be linear
• Look to crash activities on the critical path
• Crash the least expensive activities on the critical path first
(based on cost per week)
– Crash activity I from 3 weeks to 2 weeks 1000
– Crash activity J from 4 weeks to 2 weeks 2400
– Crash activity D from 6 weeks to 4 weeks 4000
– Recommend Crash Cost 7400
03/13/18 89
90. A convenient analytical and visual technique of PERT and
CPM prove extremely valuable in assisting the managers in
managing the projects.
PERT stands for Project Evaluation and Review
Technique developed during 1950’s. The technique
was developed and used in conjunction with the planning
and designing of the Polaris missile project.
CPM stands for Critical Path Method which was
developed by DuPont Company and applied first to the
construction projects in the chemical industry.
Though both PERT and CPM techniques have similarity in terms of
concepts, the basic difference is; CPM has single time estimate and PERT
has three time estimates for activities and uses probability theory to find
the chance of reaching the scheduled time.
03/13/18 90Dr. Varaprasada Rao GGSESTC
91. Project management generally consists of three phases.
Planning:
Planning involves setting the objectives of the project. Identifying
various activities to be performed and determining the requirement of
resources such as men, materials, machines, etc.
The cost and time for all the activities are estimated, and a network diagram is
developed showing sequential interrelationships (predecessor and successor)
between various activities during the planning stage.
Scheduling:
Based on the time estimates, the start and finish times for each
activity are worked out by applying forward and backward pass
techniques, critical path is identified, along with the slack and float for
the non-critical paths.
Controlling:
Controlling refers to analyzing and evaluating the actual
progress against the plan. Reallocation of resources, crashing and
review of projects with periodical reports are carried out.
03/13/18 91Dr. Varaprasada Rao GGSESTC
92. COMPONENTS of PERT/CPM NETWORK
PERT / CPM networks contain two major components
i. Activities, and
ii. Events
Activity: An activity represents an action and consumption of
resources (time, money, energy) required to complete a portion of a
project. Activity is represented by an arrow, (Figure 8.1).
Event: An event (or node) will always occur at the
beginning and end of an activity. The event has no
resources and is represented by a circle. The ith event and
jth event are the tail event and head event respectively,
(Figure 8.2).
03/13/18 92Dr. Varaprasada Rao GGSESTC
93. Merge and Burst Events
One or more activities can start and end simultaneously at an
event (Figure 8.3 a, b).
Preceding and Succeeding Activities
Activities performed before given events are known as
preceding activities (Figure 8.4), and activities performed after
a given event are known as succeeding activities.
Activities A and B precede activities C and D
respectively.
03/13/18 93Dr. Varaprasada Rao GGSESTC
94. Dummy Activity
An imaginary activity which does not consume any resource and
time is called a dummy activity. Dummy activities are
simply used to represent a connection between events in
order to maintain a logic in the network. It is represented by a
dotted line in a network, see Figure 8.5.
03/13/18 94Dr. Varaprasada Rao GGSESTC
95. ERRORS TO BE AVOIDED IN CONSTRUCTING A
NETWORK
a. Two activities starting from a tail event
must not have a same end event. To ensure
this, it is absolutely necessary to introduce a
dummy activity, as shown in Figure 8.6.
b. Looping error should not be formed in a
network, as it represents performance of
activities repeatedly in a cyclic manner, as
shown below in Figure 8.7.
c. In a network, there should be only one
start event and one ending event as shown
below, in Figure 8.8.
d. The direction of arrows should
flow from left to right avoiding
mixing of direction as shown in
Figure 8.9.
03/13/18 95Dr. Varaprasada Rao GGSESTC
96. RULES IN CONSTRUCTING A NETWORK
1. No single activity can be represented more than once in a network. The
length of an arrow has no significance.
2. The event numbered 1 is the start event and an event with highest number is
the end event. Before an activity can be undertaken, all activities preceding
it must be completed. That is, the activities must follow a logical sequence
(or – interrelationship) between activities.
3. In assigning numbers to events, there should not be any duplication of event
numbers in a network.
4. Dummy activities must be used only if it is necessary to reduce the
complexity of a network.
5. A network should have only one start event and one end event.
03/13/18 96Dr. Varaprasada Rao GGSESTC
97. Some conventions of network diagram are shown in Figure 8.10
(a), (b), (c), (d) below:
03/13/18 97Dr. Varaprasada Rao GGSESTC
98. PROCEDURE FOR NUMBERING THE EVENTS
USING FULKERSON'S RULE
Step1: Number the start or initial event as 1.
Step2: From event 1, strike off all outgoing activities. This would have
made one or more events as initial events (event which do not have
incoming activities). Number that event as 2.
Step3: Repeat step 2 for event 2, event 3 and till the end event. The end
event must have the highest number
Example 1:
Draw a network for a house construction project. The sequence of
activities with their predecessors are given in Table 8.1, below.
03/13/18 98Dr. Varaprasada Rao GGSESTC
99. CRITICAL PATH ANALYSIS
The critical path for any network is the longest path through the entire
network.
Since all activities must be completed to complete the entire project,
the length of the critical path is also the shortest time allowable for
completion of the project.
Thus if the project is to be completed in that shortest time, all
activities on the critical path must be started as soon as possible.
These activities are called critical activities.
If the project has to be completed ahead of the schedule, then the time
required for at least one of the critical activity must be reduced.
Further, any delay in completing the critical activities will increase the
project duration.
03/13/18 99Dr. Varaprasada Rao GGSESTC
100. The activity, which does not lie on the critical path, is called non-critical
activity.
These non-critical activities may have some slack time.
The slack is the amount of time by which the start of an activity may be
delayed without affecting the overall completion time of the project.
But a critical activity has no slack.
To reduce the overall project time, it would require more resources (at
extra cost) to reduce the time taken by the critical activities to complete.
03/13/18 100Dr. Varaprasada Rao GGSESTC
101. Scheduling of Activities: Earliest Time (TE) and Latest
Time(TL)
Before the critical path in a network is determined, it is necessary to
find the earliest and latest time of each event to know the earliest
expected time (TE) at which the activities originating from the event
can be started and to know the latest allowable time (TL) at which
activities terminating at the event can be completed.
Forward Pass Computations (to calculate Earliest, Time TE)
Step 1: Begin from the start event and move towards the end
event.
Step 2: Put TE = 0 for the start event.
Step 3: Go to the next event (i.e node 2) if there is an incoming activity for
event 2, add calculate TE of previous event (i.e event 1) and activity time.
Note: If there are more than one incoming activities, calculate TE for all incoming
activities and take the maximum value. This value is the TE for event 2.
Step 4: Repeat the same procedure from step 3 till the end event.
03/13/18 101Dr. Varaprasada Rao GGSESTC
102. Backward Pass Computations (to calculate Latest Time TL)
Procedure :
Step 1: Begin from end event and move towards the start
event. Assume that the direction of arrows is reversed.
Step 2: Latest Time TL for the last event is the earliest
time. TE of the last event.
Step 3: Go to the next event, if there is an incoming activity,
subtract the value of TL of previous event from the activity duration
time. The arrived value is TL for that event. If there are more than
one incoming activities, take the minimum TE value.
Step 4: Repeat the same procedure from step 2 till the
start event.
03/13/18 102Dr. Varaprasada Rao GGSESTC
103. DETERMINATION OF FLOAT AND SLACK
TIMES
As discussed earlier, the non – critical activities have some slack
or float. The float of an activity is the amount of time available
by which it is possible to delay its completion time without
extending the overall project completion time.
tij = duration of activity
TE = earliest expected time
TL = latest allowable time
ESij = earliest start time of the activity
EFij = earliest finish time of the activity
LSij = latest start time of the activity
LFij = latest finish time of the activity
Total Float TFij: The total float of an activity is the difference between
the latest start time and the earliest start time of that activity.
TFij = LS ij – ESij ....................(1)
or
TFij = (TL – TE) – tij …………..(ii)03/13/18 103Dr. Varaprasada Rao GGSESTC
104. Free Float FFij: The time by which the completion of an activity can
be delayed from its earliest finish time without affecting the
earliest start time of the succeeding activity is called free float.
FF ij = (Ej – Ei) – tij ....................(3)
FFij = Total float – Head event
slack
Independent Float IFij: The amount of time by which the start of an
activity can be delayed without affecting the earliest start time of
any immediately following activities, assuming that the preceding
activity has finished at its latest finish time.
IF ij = (Ej – Li) – tij ....................
(4)
IFij = Free float – Tail event slack
Where tail event slack = Li – Ei
The negative value of independent float is considered to be zero.
03/13/18 104Dr. Varaprasada Rao GGSESTC
105. Critical Path:
After determining the earliest and the latest scheduled times for various
activities, the minimum time required to complete the project is
calculated. In a network, among various paths, the longest path which
determines the total time duration of the project is called the critical
path. The following conditions must be satisfied in locating the critical
path of a network.
An activity is said to be critical only if both the conditions are satisfied.
1. TL – TE = 0
2. TLj – tij – TEj = 0
Example :
A project schedule has the following characteristics as shown in Table
i. Construct PERT network.
ii. Compute TE and TL for
each activity.
iii. Find the critical path.
03/13/18 105Dr. Varaprasada Rao GGSESTC
106. (i) From the data given in the problem, the activity network is
constructed as shown in Figure given below
03/13/18 106Dr. Varaprasada Rao GGSESTC
107. (ii) To determine the critical path, compute the earliest time TE
and latest time TL for each of the activity of the project. The
calculations of TE and TL are as follows:,
To calculate TE for all activities
TE1 = 0
TE2 = TE1 + t1, 2 = 0 + 4 = 4
TE3 = TE1 + t1, 3 = 0 + 1 =1
TE4 = max (TE2 + t2, 4 and TE3 + t3, 4)
= max (4 + 1 and 1 + 1) = max (5, 2)
= 5 days
TE5 = TE3 + t3, 6 = 1 + 6 = 7
TE6 = TE5 + t5, 6 = 7 + 4 = 11
TE7 = TE5 + t5, 7 = 7 + 8 = 15
TE8 = max (TE6 + t6, 8 and TE7 + t7, 8)
= max (11 + 1 and 15 + 2) = max (12, 17)
= 17 days
TE9 = TE4 + t4, 9 = 5 + 5 = 10
TE10 = max (TE9 + t9, 10 and TE8 + t8, 10)
= max (10 + 7 and 17 + 5) = max (17, 22)
= 22 days
To calculate TL for all activities
TL10 = TE10 = 22
TL9 = TE10 – t9,10 = 22 – 7 = 15
TL8 = TE10 – t8, 10 = 22 – 5 = 17
TL7 = TE8 – t7, 8 = 17 – 2 = 15
TL6 = TE8 – t6, 8 = 17 – 1 = 16
TL5 = min (TE6 – t5, 6 and TE7 – t5, 7)
= min (16 – 4 and 15 –8) = min (12, 7)
= 7 days
TL4 = TL9 – t4, 9 = 15 – 5 =10
TL3 = min (TL4 – t3, 4 and TL5 – t3, 5 )
= min (10 – 1 and 7 – 6) = min (9, 1)
= 1 day
TL2 = TL4 – t2, 4 = 10 – 1 = 9
TL1 = Min (TL2 – t1, 2 and TL3 – t1, 3)
= Min (9 – 4 and 1 – 1) = 0
03/13/18 107Dr. Varaprasada Rao GGSESTC
109. (iii) From the Table 8.6, we observe that the
activities 1 – 3, 3 – 5, 5 – 7,7 – 8 and 8 – 10 are
critical activities as their floats are zero.
03/13/18 109Dr. Varaprasada Rao GGSESTC
110. PROJECT EVALUATION REVIEW TECHNIQUE, (PERT)
In the critical path method, the time estimates are assumed to be
known with certainty. In certain projects like research and
development, new product introductions, it is difficult to estimate
the time of various activities.
Hence PERT is used in such projects with a probabilistic method using three time
estimates for an activity, rather than a single estimate, as shown in Figure 8.22.
Optimistic time tO:
It is the shortest time taken to complete the
activity. It means that if everything goes well
then there is more chance of completing the
activity within this time.
Most likely time tm:
It is the normal time taken to complete an
activity, if the activity were frequently repeated
under the same conditions.
Pessimistic time tp:
It is the longest time that an activity would take to
complete. It is the worst time estimate that an
activity would take if unexpected problems are
faced.03/13/18 110
Dr. Varaprasada Rao GGSESTC
111. Taking all these time estimates into consideration, the expected time
of an activity is arrived at.
The average or mean (ta) value of
the activity duration is given by,
The variance of the activity
time is calculated using the
formula,
The probability of completing the project
within the scheduled time (Ts) or contracted
time may be obtained by using the standard
normal deviate where Te is the expected time
of project completion.
Probability for Project Duration
Probability of completing the project
within the scheduled time is,
03/13/18 111Dr. Varaprasada Rao GGSESTC
112. An R & D project has a list of tasks to be performed whose time estimates
are given in the Table 8.11, as follows.
Example
a. Draw the project network.
b. Find the critical path.
c. Find the probability that the project is completed in 19 days. If the
probability is less than 20%, find the probability of completing it in 24
days.
03/13/18 112Dr. Varaprasada Rao GGSESTC
113. Time expected for each activity is
calculated using the formula (5):
Similarly, the expected time is
calculated for all the activities.
The variance of activity time is
calculated using the formula (6).
Similarly, variances of all the activities
are calculated.
03/13/18 113Dr. Varaprasada Rao GGSESTC
114. calculate the time earliest
(TE) and time Latest (TL)
for all the activities.
Construct a network diagram:
From the network diagram Figure 8.24, the critical path
is identified as
1-4, 4-6, 6-7, with a project duration of 22 days.
03/13/18 114Dr. Varaprasada Rao GGSESTC
115. The probability of completing the project within 19 days is given by, P (Z< Z0)
To find Z0 ,
we know, P (Z <Z Network Model 0) = 0.5 – z (1.3416) (from normal tables, z (1.3416) = 0.4099)
= 0.5 – 0.4099
= 0.0901
= 9.01% Thus, the probability of completing the R & D project in 19 days is
9.01%.
Since the probability of completing the project in 19 days is less than 20% As in question, we
find the probability of completing it in 24 days.
03/13/18 115Dr. Varaprasada Rao GGSESTC
116. COST ANALYSIS
The two important components of any activity are the cost and time.
Cost is directly proportional to time and vice versa.
For example, in constructing a shopping complex, the expected time of completion can be
calculated using the time estimates of various activities. But if the construction has to be
finished earlier, it requires additional cost to complete the project. We need to arrive at a
time/cost trade-off between total cost of project and total time required to complete it.
Normal time:
Normal time is the time required to complete
the activity at normal conditions and cost.
Crash time:
Crash time is the shortest possible activity
time; crashing more than the normal time
will increase the direct cost.
Cost Slope
Cost slope is the increase in cost per unit of
time saved by crashing. A linear cost curve
is shown in Figure 8.27.
03/13/18 116Dr. Varaprasada Rao GGSESTC
117. An activity takes 4 days to complete at a normal cost of Rs. 500.00. If it is
possible to complete the activity in 2 days with an additional cost of Rs.
700.00, what is the incremental cost of the activity?
Example
Incremental Cost or Cost Slope
It means, if one day is reduced we have to spend Rs. 100/- extra
per day.
Project Crashing
Procedure for crashing
Step1: Draw the network diagram and mark the Normal time and Crash time.
Step2: Calculate TE and TL for all the activities.
Step3: Find the critical path and other paths.
Step 4: Find the slope for all activities and rank them in ascending order.
03/13/18 117Dr. Varaprasada Rao GGSESTC
118. Step 5: Establish a tabular column with required field.
Step 6: Select the lowest ranked activity; check whether it is a critical activity. If
so,crash the activity, else go to the next highest ranked activity.
Note: The critical path must remain critical while crashing.
Step 7: Calculate the total cost of project for each crashing
Step 8: Repeat Step 6 until all the activities in the critical path are fully
crashed.
Example
The following Table
8.13 gives the activities
of a construction
project and other
data.
If the indirect cost is Rs. 20 per day, crash the activities to find the minimum
duration of the project and the project cost associated.
03/13/18
118
Dr. Varaprasada Rao GGSESTC
119. From the data provided in the table, draw the network diagram (Figure 8.28)
and find the critical path.
Solution
From the diagram, we observe that the
critical path is 1-2-5 with project duration of
14 days
The cost slope for all activities and their
rank is calculated as shown in Table 8.14
03/13/18 119Dr. Varaprasada Rao GGSESTC
120. The available paths of the network are listed down in Table 8.15
indicating the sequence of crashing (see Figure 8.29).
The sequence of crashing
and the total cost involved
is given in Table 8.16 Initial
direct cost = sum of all
normal costs given
= Rs. 490.00
03/13/18 120Dr. Varaprasada Rao GGSESTC
121. It is not possible to crash more than 10 days, as all
the activities in the critical path are fully crashed.
Hence the minimum project duration is 10 days
with the total cost of Rs. 970.00.
Activity
Crashed
Project
Duration
Critical
Path
Direct Cost in (Rs.) Indirect
Cost in
(Rs.)
Total
Cost in
(Rs.)
- 14 1-2-5 490 14 x 20 =
280
770
1 – 2(2)
2 – 5(2)
2 – 4(1)
3 – 4(2)
10 1 – 2 – 5
1 – 3 – 4 – 5
1 – 2 – 4 – 5
490 + (2 x 15) + (2 x
100) + (1 x 10) + (2 x
20) = 770
10 x 20 =
200
970
03/13/18 121Dr. Varaprasada Rao GGSESTC
125. a. Draw the project network diagram.
b. Calculate the length and variance of the critical path.
c. What is the probability that the jobs on the critical path can be
completed in 41 days?
03/13/18 125Dr. Varaprasada Rao GGSESTC
126. Dr. Varaprasada Rao GGSESTC 126
Dr. M Varaprasada Rao
Director.ggsestc@gmail.com
03/13/18