The document describes the steps to develop a project network using critical path method (CPM). It involves identifying activities, developing a network diagram, estimating time for each activity, calculating earliest and latest times, determining critical path, and analyzing floats. An example network is provided to illustrate determining earliest occurrence time, latest occurrence time, and floats like total float and free float. The document also discusses scheduling when resources are limited and bounding schedules. Finally, it provides an illustration of CPM analysis to minimize total project cost by crashing critical activities.
This document provides an overview of network techniques for project management, including PERT and CPM models. Key points covered include: developing a project network diagram; determining critical paths and calculating floats; time and cost estimation; scheduling activities based on available resources; and using the network to project costs and monitor project progress. PERT uses probabilistic analysis while CPM is deterministic, focusing on time-cost tradeoffs when crashing activities. The network allows visualization of activity relationships and quantitative analysis of schedule options and resource constraints.
Network Techniques for Project ManagementIshan Gandhi
Undertaking a Project and Looking to manage the Time and Resources? This presentation provides a complete guide on how to manage the time and resources of a project.
Objectives of Network Analysis for Project Management:
1. To minimize idle resources.
2. To minimize the total project cost.
3. To trade-off between time and cost of the project.
4. To minimize production delays, interruptions and conflicts.
5. To minimize the total project duration.
This document provides information about project management applications including definitions of a project, project life cycle, and examples of projects. It also discusses network planning techniques such as Program Evaluation and Review Technique (PERT) and Critical Path Method (CPM). The key steps in CPM including forward and backward passes to determine earliest and latest start/finish times are explained. Formulas for calculating total float, free float, and independent float are provided. An example problem demonstrates drawing a network diagram and identifying the critical path and project duration.
Project management techniques like PERT and CPM are used to plan, schedule, and control projects. PERT was developed for the Polaris missile program to minimize time, while CPM was developed by DuPont to optimize cost and time tradeoffs. Both methods use network diagrams to visually display tasks and their relationships. They are used to estimate duration, identify critical paths, and determine slack. PERT additionally accounts for uncertainty in durations using three time estimates.
The document discusses project management and critical path method (CPM) for project scheduling. It defines key concepts like activities, events, earliest start time, latest finish time, total float, free float and critical path. Examples are provided to illustrate how to draw a network diagram and use CPM to find the critical path and project duration. The critical path is the longest path of activities from start to finish with no float, and determines the earliest project completion date.
This document provides instructions for calculating key Project Management metrics like the Program Evaluation and Review Technique (PERT) using both manual calculations and Microsoft Excel. It outlines 5 steps to perform PERT calculations manually: 1) define tasks, 2) organize tasks in logical order, 3) generate estimates, 4) determine earliest and latest dates, 5) determine probability of meeting dates. It then demonstrates how to set up a spreadsheet to automate the calculations and determine completion probabilities for different dates. Key lessons include that all plans are estimates and scope changes require updated estimates.
Network problem cpm and pert BY MITESH KUMARMitesh Kumar
The document discusses project scheduling techniques like PERT and CPM. It begins by defining key concepts like activities, events, critical path analysis and float/slack times. It then provides examples to demonstrate how to construct a network diagram by numbering events and determining earliest and latest times for activities. The document aims to explain the basic concepts and procedures for using PERT/CPM techniques to schedule projects.
CPM involves drawing a network diagram of activities and their relationships, analyzing paths and determining earliest and latest start/finish times to identify the critical path and calculate slack. Project crashing involves shortening activity durations by incurring costs to potentially reduce the project duration below that of the critical path. An example outlines crashing the critical
This document provides an overview of network techniques for project management, including PERT and CPM models. Key points covered include: developing a project network diagram; determining critical paths and calculating floats; time and cost estimation; scheduling activities based on available resources; and using the network to project costs and monitor project progress. PERT uses probabilistic analysis while CPM is deterministic, focusing on time-cost tradeoffs when crashing activities. The network allows visualization of activity relationships and quantitative analysis of schedule options and resource constraints.
Network Techniques for Project ManagementIshan Gandhi
Undertaking a Project and Looking to manage the Time and Resources? This presentation provides a complete guide on how to manage the time and resources of a project.
Objectives of Network Analysis for Project Management:
1. To minimize idle resources.
2. To minimize the total project cost.
3. To trade-off between time and cost of the project.
4. To minimize production delays, interruptions and conflicts.
5. To minimize the total project duration.
This document provides information about project management applications including definitions of a project, project life cycle, and examples of projects. It also discusses network planning techniques such as Program Evaluation and Review Technique (PERT) and Critical Path Method (CPM). The key steps in CPM including forward and backward passes to determine earliest and latest start/finish times are explained. Formulas for calculating total float, free float, and independent float are provided. An example problem demonstrates drawing a network diagram and identifying the critical path and project duration.
Project management techniques like PERT and CPM are used to plan, schedule, and control projects. PERT was developed for the Polaris missile program to minimize time, while CPM was developed by DuPont to optimize cost and time tradeoffs. Both methods use network diagrams to visually display tasks and their relationships. They are used to estimate duration, identify critical paths, and determine slack. PERT additionally accounts for uncertainty in durations using three time estimates.
The document discusses project management and critical path method (CPM) for project scheduling. It defines key concepts like activities, events, earliest start time, latest finish time, total float, free float and critical path. Examples are provided to illustrate how to draw a network diagram and use CPM to find the critical path and project duration. The critical path is the longest path of activities from start to finish with no float, and determines the earliest project completion date.
This document provides instructions for calculating key Project Management metrics like the Program Evaluation and Review Technique (PERT) using both manual calculations and Microsoft Excel. It outlines 5 steps to perform PERT calculations manually: 1) define tasks, 2) organize tasks in logical order, 3) generate estimates, 4) determine earliest and latest dates, 5) determine probability of meeting dates. It then demonstrates how to set up a spreadsheet to automate the calculations and determine completion probabilities for different dates. Key lessons include that all plans are estimates and scope changes require updated estimates.
Network problem cpm and pert BY MITESH KUMARMitesh Kumar
The document discusses project scheduling techniques like PERT and CPM. It begins by defining key concepts like activities, events, critical path analysis and float/slack times. It then provides examples to demonstrate how to construct a network diagram by numbering events and determining earliest and latest times for activities. The document aims to explain the basic concepts and procedures for using PERT/CPM techniques to schedule projects.
CPM involves drawing a network diagram of activities and their relationships, analyzing paths and determining earliest and latest start/finish times to identify the critical path and calculate slack. Project crashing involves shortening activity durations by incurring costs to potentially reduce the project duration below that of the critical path. An example outlines crashing the critical
The document discusses network analysis techniques used for project planning and management. It covers key concepts like work breakdown structure, network diagrams, critical path method (CPM), program evaluation and review technique (PERT), activity times, event relationships, slack, floats, crashing, and normal vs crash schedules. The document contains examples of network diagrams and questions related to calculating activity times, identifying critical paths, and crashing project schedules.
Critical Path Method/ Program Evaluation and Review TechniqueJomari Gingo Selibio
The document discusses the Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) for project planning and scheduling. CPM assumes deterministic activity durations while PERT uses three time estimates for probabilistic durations. The key steps are defining activities, creating a network diagram showing dependencies, and calculating earliest and latest start/finish times to identify the critical path and slack. Two examples demonstrate applying these concepts to sample projects by specifying activities, drawing the network, and constructing the time schedule table.
Network analysis techniques like CPM and PERT are useful for planning, scheduling, and controlling projects. They define activities, durations, and dependencies using a network diagram. The critical path is identified as the longest sequence of activities to complete the project. Monitoring progress against the network allows managers to focus on critical tasks and adjust resources if needed to minimize delays. While useful for large projects, activity definitions and time estimates require care to apply these techniques accurately.
The document discusses time-cost optimization in project management using the critical path method. It provides information on normal and crash time estimates, direct and indirect costs, and outlines the steps to determine the optimum duration that results in the lowest total project cost. These include establishing direct cost-time relationships, determining activity cost slopes, computing costs at normal durations, and crashing critical activities from lowest to highest slope while tracking total costs.
The document discusses the Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) for project scheduling. CPM determines the minimum project duration when activity times are known with certainty, while PERT estimates the probability of completing on time when activity times are uncertain. Both methods represent projects as networks and identify critical paths that must be followed to complete on schedule.
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.
The document discusses key aspects of project management including defining projects, organizing project teams, planning projects, developing schedules, and analyzing costs and time tradeoffs. Some key points are:
- Projects have a definite start and end, involve resources, and aim to be completed on time, within budget and to specifications.
- Project management involves systematically defining, organizing, planning, monitoring and controlling projects.
- Planning projects involves work breakdown structures, network diagrams, schedules, and risk assessment. The critical path is the longest sequence of activities.
- Tradeoffs between time and costs must be analyzed, as crashing activities may reduce time but increase costs.
The critical path method (CPM) is an algorithm developed in the late 1950s to schedule project activities. It involves identifying all the paths in a project, determining the earliest and latest start and finish dates for each activity, and identifying the critical activities that cannot be delayed without delaying project completion. The critical path is the longest path of critical activities that determines the minimum time required to complete the project. NASA used CPM to help schedule the tasks leading up to the first moon landing in 1969.
Crashing is the procedure by which project duration can be shorten up by expediting selective
activities with in the project. But it requires allocating more resources than usual to compress an activity’s
duration, which in turns increases the budget of that activity. So, crashing is basically a time-cost trade-off by
which specific deadline can be achieved. The traditional method of crashing only considers average activity
times for the calculation of the critical path, ignoring the stochastic nature of activity time. This report is written
to develop an algorithm for optimum crashing method to minimize the required cost while attaining a specified
completion time.
This document provides an overview of Programme Evaluation and Review Technique (PERT) and Critical Path Method (CPM), which are network analysis techniques used for project scheduling. PERT is used for projects with uncertainty, uses probabilistic time estimates, and focuses on scheduling and monitoring. CPM is used for projects with deterministic time estimates, focuses on time/cost tradeoffs, and allows expediting activities for extra cost. Both techniques identify the critical path and activities with slack. The document then discusses network terminology, provides an example project, and demonstrates how to construct a PERT network and perform calculations for expected activity times, earliest/latest event times, and slack.
This document provides steps for crashing a project schedule to reduce its duration. It begins by explaining the two types of activity durations: normal and crash. It then outlines 9 steps to determine the maximum possible time reduction for a project: 1) draw the network diagram, 2) find the critical path using normal durations, 3) find the critical path using crash durations, 4) calculate the difference in critical paths, 5) calculate the slope for each activity, 6) select the activity with the lowest slope for crashing, 7) calculate the possible crash amount, 8) redraw the network and recalculate duration and cost, 9) compare to crashed critical path and repeat steps if different. It provides two notes: the critical path may change between
The document discusses PERT (Program/Project Evaluation Review Technique), a method used to analyze and represent the tasks involved in complex projects. PERT uses three time estimates (optimistic, most likely, pessimistic) to calculate the expected duration of tasks and projects in a probabilistic manner. It also describes calculating variance, critical paths, and the probability of completing a project within a scheduled time. An example problem demonstrates drawing a PERT network, finding the critical path and calculating the probability of completing an R&D project in a given number of days. Cost analysis and crashing activities to reduce project duration at additional cost are also summarized.
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.
This document compares and contrasts PERT and CPM network techniques. PERT is used for new projects with uncertainty, uses time as a model, and is event-oriented. CPM is used for repetitive projects with certainty, uses time versus cost trade-offs, and is activity-oriented. It then provides examples of network diagrams for different projects.
The document discusses Programme Evaluation and Review Technique (PERT), a method used to analyze and represent the tasks involved in complex projects. PERT uses three time estimates - optimistic, pessimistic, and most likely - to calculate the expected time for each task. It then builds a network diagram to identify the critical path with the longest expected duration. This determines the minimum time needed to complete the project. The document provides examples to demonstrate calculating task times, constructing the network, identifying the critical path, and using PERT to determine the probability of completing a project within a deadline. It also discusses how crashing the critical path by adding resources can potentially reduce the project duration but at an increased cost.
Unit7 & 8 Performance and optimization leenachandra
This document discusses performance analysis and optimization of systems. It covers various performance measures like time, space, power and development time. It analyzes different aspects that affect performance like hardware, software, algorithms and data structures. It also discusses limitations, complexity analysis, asymptotic complexity, comparing algorithms using Big-O notation, analyzing code, data structures and different optimization techniques. The document provides examples to illustrate concepts like Amdahl's law, complexity functions, analyzing search and sort algorithms.
1. The document discusses reasons and methods to reduce project durations, including to earn incentive pay, avoid penalties, and fit contractual timelines. It then describes four common methods: using overtime, adding workers, better equipment, and subcontracting labor.
2. The optimal project duration balances minimizing total project costs, including direct costs from activities as well as indirect overhead costs. The network compression algorithm is used to iteratively shorten the critical path by accelerating individual activities until no further reduction is possible without increasing total costs.
3. An example construction project is provided to demonstrate calculating the least cost project duration using crash costs, indirect costs, and shortening cycles to optimize the project schedule.
Critical Path Method (CPM) was developed in late 1950s and is used to identify task that are necessary for completion of project on time without delay.
The document discusses critical path methods (CPM) and program evaluation and review technique (PERT) for project planning and scheduling. CPM involves identifying all activities, durations, and dependencies to create a network diagram and determine the critical path with the longest duration of activities. PERT is a probabilistic extension of CPM that accounts for uncertainty using three time estimates per activity. It calculates the expected duration and variance for each activity and the overall project to determine the probability of completing within a given timeframe. An example applies these concepts to a project with activities, time estimates, and calculations to find the critical path, project duration distribution, and probability of completing in 40 days.
The critical path method (CPM) network for the given project is constructed following these steps:
1) Determine the earliest start time (ES) using forward pass
2) Determine the latest completion time (LC) using backward pass
3) Identify the critical path as the longest path where ES = LC
The critical path is identified as activities B, D, H, K, N with a total project duration of 25 months. Non-critical activities are identified by having total float greater than zero.
This document provides a project management plan for setting up a new warehouse for Jigama Ltd. It identifies the key stages in the project lifecycle including define, plan, organize, execute and close. In the define stage, the report outlines functional specifications for the warehouse, develops scenarios to assess risks and alternatives, and recommends a cost-benefit analysis using net present value. The plan considers tasks, skills, leadership, administration and control needed to successfully manage the warehouse project on time and on budget.
The document discusses network analysis techniques used for project planning and management. It covers key concepts like work breakdown structure, network diagrams, critical path method (CPM), program evaluation and review technique (PERT), activity times, event relationships, slack, floats, crashing, and normal vs crash schedules. The document contains examples of network diagrams and questions related to calculating activity times, identifying critical paths, and crashing project schedules.
Critical Path Method/ Program Evaluation and Review TechniqueJomari Gingo Selibio
The document discusses the Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) for project planning and scheduling. CPM assumes deterministic activity durations while PERT uses three time estimates for probabilistic durations. The key steps are defining activities, creating a network diagram showing dependencies, and calculating earliest and latest start/finish times to identify the critical path and slack. Two examples demonstrate applying these concepts to sample projects by specifying activities, drawing the network, and constructing the time schedule table.
Network analysis techniques like CPM and PERT are useful for planning, scheduling, and controlling projects. They define activities, durations, and dependencies using a network diagram. The critical path is identified as the longest sequence of activities to complete the project. Monitoring progress against the network allows managers to focus on critical tasks and adjust resources if needed to minimize delays. While useful for large projects, activity definitions and time estimates require care to apply these techniques accurately.
The document discusses time-cost optimization in project management using the critical path method. It provides information on normal and crash time estimates, direct and indirect costs, and outlines the steps to determine the optimum duration that results in the lowest total project cost. These include establishing direct cost-time relationships, determining activity cost slopes, computing costs at normal durations, and crashing critical activities from lowest to highest slope while tracking total costs.
The document discusses the Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) for project scheduling. CPM determines the minimum project duration when activity times are known with certainty, while PERT estimates the probability of completing on time when activity times are uncertain. Both methods represent projects as networks and identify critical paths that must be followed to complete on schedule.
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.
The document discusses key aspects of project management including defining projects, organizing project teams, planning projects, developing schedules, and analyzing costs and time tradeoffs. Some key points are:
- Projects have a definite start and end, involve resources, and aim to be completed on time, within budget and to specifications.
- Project management involves systematically defining, organizing, planning, monitoring and controlling projects.
- Planning projects involves work breakdown structures, network diagrams, schedules, and risk assessment. The critical path is the longest sequence of activities.
- Tradeoffs between time and costs must be analyzed, as crashing activities may reduce time but increase costs.
The critical path method (CPM) is an algorithm developed in the late 1950s to schedule project activities. It involves identifying all the paths in a project, determining the earliest and latest start and finish dates for each activity, and identifying the critical activities that cannot be delayed without delaying project completion. The critical path is the longest path of critical activities that determines the minimum time required to complete the project. NASA used CPM to help schedule the tasks leading up to the first moon landing in 1969.
Crashing is the procedure by which project duration can be shorten up by expediting selective
activities with in the project. But it requires allocating more resources than usual to compress an activity’s
duration, which in turns increases the budget of that activity. So, crashing is basically a time-cost trade-off by
which specific deadline can be achieved. The traditional method of crashing only considers average activity
times for the calculation of the critical path, ignoring the stochastic nature of activity time. This report is written
to develop an algorithm for optimum crashing method to minimize the required cost while attaining a specified
completion time.
This document provides an overview of Programme Evaluation and Review Technique (PERT) and Critical Path Method (CPM), which are network analysis techniques used for project scheduling. PERT is used for projects with uncertainty, uses probabilistic time estimates, and focuses on scheduling and monitoring. CPM is used for projects with deterministic time estimates, focuses on time/cost tradeoffs, and allows expediting activities for extra cost. Both techniques identify the critical path and activities with slack. The document then discusses network terminology, provides an example project, and demonstrates how to construct a PERT network and perform calculations for expected activity times, earliest/latest event times, and slack.
This document provides steps for crashing a project schedule to reduce its duration. It begins by explaining the two types of activity durations: normal and crash. It then outlines 9 steps to determine the maximum possible time reduction for a project: 1) draw the network diagram, 2) find the critical path using normal durations, 3) find the critical path using crash durations, 4) calculate the difference in critical paths, 5) calculate the slope for each activity, 6) select the activity with the lowest slope for crashing, 7) calculate the possible crash amount, 8) redraw the network and recalculate duration and cost, 9) compare to crashed critical path and repeat steps if different. It provides two notes: the critical path may change between
The document discusses PERT (Program/Project Evaluation Review Technique), a method used to analyze and represent the tasks involved in complex projects. PERT uses three time estimates (optimistic, most likely, pessimistic) to calculate the expected duration of tasks and projects in a probabilistic manner. It also describes calculating variance, critical paths, and the probability of completing a project within a scheduled time. An example problem demonstrates drawing a PERT network, finding the critical path and calculating the probability of completing an R&D project in a given number of days. Cost analysis and crashing activities to reduce project duration at additional cost are also summarized.
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.
This document compares and contrasts PERT and CPM network techniques. PERT is used for new projects with uncertainty, uses time as a model, and is event-oriented. CPM is used for repetitive projects with certainty, uses time versus cost trade-offs, and is activity-oriented. It then provides examples of network diagrams for different projects.
The document discusses Programme Evaluation and Review Technique (PERT), a method used to analyze and represent the tasks involved in complex projects. PERT uses three time estimates - optimistic, pessimistic, and most likely - to calculate the expected time for each task. It then builds a network diagram to identify the critical path with the longest expected duration. This determines the minimum time needed to complete the project. The document provides examples to demonstrate calculating task times, constructing the network, identifying the critical path, and using PERT to determine the probability of completing a project within a deadline. It also discusses how crashing the critical path by adding resources can potentially reduce the project duration but at an increased cost.
Unit7 & 8 Performance and optimization leenachandra
This document discusses performance analysis and optimization of systems. It covers various performance measures like time, space, power and development time. It analyzes different aspects that affect performance like hardware, software, algorithms and data structures. It also discusses limitations, complexity analysis, asymptotic complexity, comparing algorithms using Big-O notation, analyzing code, data structures and different optimization techniques. The document provides examples to illustrate concepts like Amdahl's law, complexity functions, analyzing search and sort algorithms.
1. The document discusses reasons and methods to reduce project durations, including to earn incentive pay, avoid penalties, and fit contractual timelines. It then describes four common methods: using overtime, adding workers, better equipment, and subcontracting labor.
2. The optimal project duration balances minimizing total project costs, including direct costs from activities as well as indirect overhead costs. The network compression algorithm is used to iteratively shorten the critical path by accelerating individual activities until no further reduction is possible without increasing total costs.
3. An example construction project is provided to demonstrate calculating the least cost project duration using crash costs, indirect costs, and shortening cycles to optimize the project schedule.
Critical Path Method (CPM) was developed in late 1950s and is used to identify task that are necessary for completion of project on time without delay.
The document discusses critical path methods (CPM) and program evaluation and review technique (PERT) for project planning and scheduling. CPM involves identifying all activities, durations, and dependencies to create a network diagram and determine the critical path with the longest duration of activities. PERT is a probabilistic extension of CPM that accounts for uncertainty using three time estimates per activity. It calculates the expected duration and variance for each activity and the overall project to determine the probability of completing within a given timeframe. An example applies these concepts to a project with activities, time estimates, and calculations to find the critical path, project duration distribution, and probability of completing in 40 days.
The critical path method (CPM) network for the given project is constructed following these steps:
1) Determine the earliest start time (ES) using forward pass
2) Determine the latest completion time (LC) using backward pass
3) Identify the critical path as the longest path where ES = LC
The critical path is identified as activities B, D, H, K, N with a total project duration of 25 months. Non-critical activities are identified by having total float greater than zero.
This document provides a project management plan for setting up a new warehouse for Jigama Ltd. It identifies the key stages in the project lifecycle including define, plan, organize, execute and close. In the define stage, the report outlines functional specifications for the warehouse, develops scenarios to assess risks and alternatives, and recommends a cost-benefit analysis using net present value. The plan considers tasks, skills, leadership, administration and control needed to successfully manage the warehouse project on time and on budget.
The document describes determining the critical path of a project using network analysis. It lists the steps as: 1) drawing the network diagram with activities and relationships, 2) calculating earliest and latest start/finish times, 3) determining total float for each activity, 4) identifying critical activities with zero total float, and 5) calculating the project duration. An example project is provided to demonstrate the process of identifying the critical path and activities with zero total float to determine the project completion time.
This document provides a step-by-step solution to a project management problem involving determining the critical path of a project. It begins by constructing a network diagram of the project activities and their durations. It then calculates the earliest and latest start and finish times of each activity using forward and backward pass computations. This allows it to identify the critical path - the longest chain of activities where each activity finishes as late as possible. It also calculates the total float of each activity, which is the amount of time it can be delayed without delaying project completion. The critical path identified has a total project duration of 14 weeks.
The document discusses the Critical Path Method (CPM) for project scheduling, including how to develop a work breakdown structure, identify different types of activities, perform forward and backward pass calculations to determine early and late start/finish dates, and identify the critical path and float for activities. It also covers how to incorporate lags, determine event times in arrow networks, and the effects of an imposed finish date on the schedule.
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.
Lecture - Project, Planning and Control.pdflucky141651
Geometric method impossible in higher dimensions
• Algebraical methods:
• Simplex method (George B. Dantzig 1949):
skim through the feasible solution polytope.
Similar to a "Gaussian elimination".
Very good in practice, but can take an
exponential time
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.
This document discusses project management concepts including defining a project, objectives of project management, and scheduling methods. A project involves related jobs directed towards an output over a significant period of time. Project management aims to plan, direct, and control resources to meet technical, cost and time constraints. Key scheduling methods include Gantt charts, critical path method (CPM), and program evaluation and review technique (PERT).
This document provides an overview of the Project Evaluation and Review Technique (PERT) and Critical Path Method (CPM) for project management. It defines key terms like activities, events, and network diagrams. It explains how to construct a network diagram and calculate the critical path, expected activity times, total float, and free float. An example project is used to demonstrate how to perform the calculations to determine the critical activities, expected completion time, and probability of finishing within given timeframes when activity times are estimated as PERT distributions rather than fixed durations.
The document introduces Critical Path Method (CPM) for project scheduling. It defines CPM as a technique that uses mathematical calculations to schedule project activities based on their duration and dependencies. CPM was developed in 1950 to assist in building and maintaining chemical plants. The document outlines the key steps in CPM including constructing a network diagram of activities with durations and dependencies, performing forward and backward passes to calculate early/late start/finish times, and identifying the critical path with zero float. An example applies these steps to determine the critical path of a project with seven activities is the A-C-D-E-F-G path of 25 weeks.
Introduction 1
Network is a technique used for planning and scheduling of large projects in the fields of construction, maintenance, fabrication, purchasing, computer system instantiation, research and development planning etc. There is multitude of operations research situations that can be modeled and solved as network. Some recent surveys reports that as much as 70% of the real-world mathematical programming problems can be represented by network related models. Network analysis is known by many names _PERT (Programme Evaluation and Review Technique), CPM (Critical Path Method), PEP (Programme Evaluation Procedure), LCES (Least Cost Estimating and Scheduling), SCANS (Scheduling and Control by Automated Network System), etc
This chapter will present three of algorithms.
1. PERT & CPM
2. Shortest- route algorithms
3. Maximum-flow algorithms
This document discusses scheduling techniques for projects including network diagrams, PERT charts, and critical path analysis. It provides examples of how to construct network diagrams showing the logical dependencies and precedence relationships between tasks. It also demonstrates how to determine the critical path of a project by calculating the earliest and latest start/finish times for each task and identifying which tasks have zero slack and must be completed on schedule for the project to finish on time. Key terms discussed include activities, events, slack, critical path, and the importance of focusing resources on critical path tasks.
This document discusses scheduling techniques for projects including PERT (Program Evaluation and Review Technique) and CPM (Critical Path Method). It provides examples of how to create network diagrams for projects showing the logical dependencies and precedence relationships between tasks. The network diagrams are then used to calculate the earliest and latest start and finish times for each task, identify the critical path, and determine the float or slack time for non-critical tasks. The critical path identifies the minimum time needed to complete the project and any delays to critical path tasks will delay the overall project completion.
EXAMPLES OF THE USE OF DUMMYACTIVITY.pdfssuserc9c6261
This document discusses scheduling techniques for projects including network diagrams, PERT charts, and critical path analysis. It provides examples of how to construct network diagrams showing the logical dependencies and precedence relationships between tasks. It also demonstrates how to determine the critical path of a project by calculating the earliest and latest start/finish times for each task and identifying which tasks have zero slack and must be completed on schedule for the project to finish on time. Key terms discussed include activities, events, slack, critical path, and the importance of focusing resources on critical path tasks.
This document discusses network techniques like PERT (Program Evaluation and Review Technique) and CPM (Critical Path Method) which are used for scheduling projects. It provides examples of networking activities with earliest and latest start/finish times to identify the critical path. The critical path is the longest path through the network that determines the minimum project duration. Non-critical activities have float or slack time and can be delayed without extending the project completion time. The document also discusses using three time estimates (optimistic, most likely, pessimistic) for activities when there is uncertainty to calculate the expected duration and variance for each activity in a PERT network analysis.
This document discusses network techniques like PERT (Program Evaluation and Review Technique) and CPM (Critical Path Method) which are used for scheduling projects. It provides examples of networking activities with earliest and latest start/finish times to identify the critical path. The critical path is the longest path through the network that determines the minimum project duration. Non-critical activities have float or slack time and can be delayed without extending the project completion time. The document also discusses using three time estimates (optimistic, most likely, pessimistic) for activities when there is uncertainty to calculate the expected duration and variance for each activity in a PERT network.
This document discusses network techniques for scheduling projects, including PERT (Program Evaluation and Review Technique) and CPM (Critical Path Method). It provides examples of networking activities with dependencies and calculating earliest and latest start/finish times. The critical path is identified as the longest path through the network with no slack. Slack time shows how long an activity can be delayed without impacting the project completion date. The document also discusses using three time estimates (optimistic, most likely, pessimistic) for activities when there is uncertainty to calculate the expected duration and variance.
Generative AI Use cases applications solutions and implementation.pdfmahaffeycheryld
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Networktechniques
1. Development of Project Network
Step 1:
Network Diagram or Project Graph.
1
2
3 4
Take
Dinner
A Network Diagram shows the activities and
events of the project and their logical
relationships.
Receive
Guests
The Network Diagram can be developed by
using Forward Method or Backward
Method.
2. Development of Project Network
Rules for Network Construction
Each activity must have a preceding and succeeding event.
Each event should have a distinct number.
In previous example, the activity
of "Send Invitations" is
designated as (1-2)
There should be no Loops in the project network.
1
2
3
Not more than one activity can have the same preceding
and succeeding events.
2
1
3. Time Estimation
Step 2:
Time Estimates for each Activity
Three Time values are obtained from each activity:
1. Optimistic time t o
2. Most likely time t m
3. Pessimistic time tp
it should be obtained by
skipping around the network
rather than by following a
specific path.
they should be defined
independent of one another.
time available for completing
the project should not
influence the estimates.
estimates should considered
allowances which are random
variables and not others.
5. Time Estimation
Activity Optimistic Most Likely Pessimistic
t t t t
o m p e=
Average
to + 4tm
+ tp
6
1-2 9 12 21 13
1-3 6 12 18 12
2-4 1 1.5 5 2
3-4 4 8.5 10 8
2-5 10 14 24 15
4-5 1 2 3 2
te is the expected value of
activity duration;
weighted arithmetic
average time.
1
2
3 4
5
13
12
8
2
2
15
6. Determination of the Critical Path
Step 3
Determining Critical Path/s, event slacks and activity floats.
3(1). Earliest Occurrence Time (EOT)
The EOT of an event is the duration of the longest path (from beginning event
whose EOT is set at 0) leading to that event.
Hence, EOT of the end event represents the minimum time required for completing
the project.
General formula for EOT is:
EOT (i) = Max [ EOT (k) + d(k, i) ] Where,
EOT (i)= EOT of ith
event;
EOT (k)= EOT of kth
event (k precedes i);
d (k, i)= duration of activity (k, i)
8. Determination of EOT
5
2
4
3 8
2
15
2
1
13
12
0
13
12 20
28
To obtain EOT we start from
beginning event and move
forward towards the end,
hence it is called forward
pass.
The upper half of the circle : Event Number;
The left quarter in lower half: EOT;
The right corner in lower half: LOT.
9. Determination of EOT
5
2
4
3 8
2
15
2
1
13
12
0
13
12 20
28
Earliest Starting Time (EST)
EST for any activity is EOT
of an event, which is
preceding the activity.
EST (i, j) = EOT (i)
For Example,
EST of activity (2-5) will be
EST (2, 5) = EOT (2)
EST (2, 5) = 13
10. Determination of EOT
5
2
4
3 8
2
15
2
1
13
12
0
13
12 20
28
Earliest Finishing Time (EFT)
EFT for any activity
is addition of EOT of an
event, which is preceding the
activity and duration of the
activity.
EFT (i, j) = EOT (i) + d(i, j)
For Example,
EFT of activity (2-5) will be
EFT (2, 5) = EOT (2) + d(2, 5)
= 13 + 15
= 28
11. Determination of the Critical Path
3(2). Latest Occurrence Time (LOT)
The EOT of an event is the latest allowable time by which the event can occur, given
the time that is allowed for completion of the project (occurence of end event).
Hence, LOT of the an event represents the latest time by which the event should
occur to enable the project to be completed in given time.
General formula for LOT is:
LOT (i) = Min [ LOT (j) - d(i, j) ] Where,
LOT (i)= LOT of ith
event;
LOT (j)= LOT of j event (j follows i);
d (i, j)= duration of activity (i, j)
th
12. Determination of LOT
5
2
4
3 8
2
15
2
1
13
12
28
LOT (i) = Min [ LOT (j) - d(i, j)]
LOT (2)
[ LOT (4) - d(2, 4)]
= [26 - 2]
= [24]
[ LOT (5) - d(2, 5)]
= [28 - 15]
= [13]
= MIN [ ]
LOT (2) = 13
26
13. Determination of LOT
5
2
4
3 8
2
15
2
1
13
12
0
13
26
To obtain LOT we start
from end event and
move backward towards
the beginning, hence it is
called backward pass.
LOT for end event is the given time for the
project to be completed. Normally, EOT is
considered for project deadline.
28 28
18
0
14. Determination of LOT
5
2
4
3 8
2
15
2
1
13
12
0
13
26
28 28
18
0
LFT (i, j) = LOT (j)
Latest Finishing Time (LFT)
LFT for any activity is LOT of
an event, which is followed by
that activity.
For Example,
LFT of activity (2-5) will be
LFT (2, 5) = LOT (5)
= 28
15. Determination of LOT
5
2
4
3 8
2
15
2
1
13
12
0
13
26
28 28
18
0
Latest Starting Time (LST)
LST for any activity
is difference between LFT
of that activity and duration for
that activity.
LST (i, j) = LFT (i, j) - d(i, j)
For Example,
LST of activity (2-5) will be
LST (2, 5) = LFT (2,5) + d(2,5)
= 28 - 15
= 13
16. Determination of the Critical Path
3(3). Event Slack
The slack for an event is the difference between its LOT and EOT.
Event Slack
Event LOT EOT Slack = LOT - EOT
5 28 28 0
4 26 20 6
3 18 12 6
2 13 13 0
1 0 0 0
17. Determination of the Critical Path
5
2
4
3 8
2
1
12
2
0 0
13 13
28 28
20 26
12 18
13
15
5
4
3
2
1
0
6
6
0
0
3(4). Critical and Slack Paths
The critical path starts with the beginning event, terminates with the end event, and is
marked by events which have a zero slack.
Activity Slack
Hence,
Critical Path for this
project is (1-2-5)
18. Determination of the Critical Path
3(5). Activity Floats
Given the estimates of activity time and event slacks, three measures of floats are
defined:
(i) Total Float;
(ii) Free Float;
(iii) Independent Float.
Given the following, determine the Floats
2 2 4
13 13 20 26
19. 2
13 13
4
20 26
2
Determination of the Critical Path
(i) Total Float:
The total float of an activity is the extra time available to complete the activity if it is
started as early as possible, without delaying the completion of the project.
Total
Float
=
Latest occurrence
time for event 4 - time for event 2
Earliest occurrence
-
Duration of activity
(2-4)
= 26 - 13 - 2
= 11 weeks
Activities which have a
Zero Total Float lie
on critical path.
20. 2
13 13
4
20 26
2
Determination of the Critical Path
(ii) Free Float:
The free float of an activity is the extra time available to complete the activity when the
activity is started at EOT of its preceding event and completed by the EOT of its
succeeding events.
Free
Float
=
Earliest occurrence
- Earliest occurrence
-
time for event 4 time for event 2
Duration of activity
(2-4)
= 20 - 13 - 2
= 5 weeks
21. 2
13 13
4
20 26
2
Determination of the Critical Path
(iii) Independent Float:
The independent float of an activity is the extra time available to complete the
activity when the activity is started at LOT of its preceding event and completed by the
EOT of its succeeding events.
-
Latest occurrence
time for event 2
- Duration of activity
(2-4)
Independent Earliest occurrence
Float
= time for event 4
= 20 - 13 - 2
= 5 weeks
It may be noted that
Independent float of an activity
may be negative.
23. Scheduling when Resources are Limited
The Bounding Schedules
(i) Early Start Schedule:
It refers to the schedule in which all activities start as early as possible-
(a) all activities occur at
their earliest i.e. EST and
EFT.
(b) there may be time lag
between completion of
certain activities and
occurrence of events.
(c) all activities emanating
from an event begins at
same time.
1
3
2
4
5
0 5 15 25 30
20
10
24. Scheduling when Resources are Limited
The Bounding Schedules
(i) Late Start Schedule:
It refers to the schedule in which all activities start as late as possible-
(a) all activities occur at
their Latest i.e. LST
and LFT.
(b) some activities may start
after time lag subsequent to
occurrence of preceding
events.
(c) all activities leading to an
event are completed at
same time.
1
3
2
4
5
0 5 15 25 30
20
10
25. Scheduling when Resources are Limited
1
Illustration: Scheduling to Match Availability of Manpower
Activity Duration and Manpower Requirements
2
3 5
2 Days
2
1 Day
6
4
2 Days
8
Only 12 men are available
for the project.
26. Scheduling when Resources are Limited
Scheduling to Match Availability of Manpower
Early Start Schedule
Doesn't match the
manpower resource
constraint of 12
Persons.
27. Scheduling when Resources are Limited
Scheduling to Match Availability of Manpower
A Feasible Schedule
28. PERT MODEL
Introduction
Program Evaluation Review Technique (PERT) was originally developed to facilitate
the planning and scheduling of the Polaris Fleet Ballistic Missile project of the US
government.
PERT Model is designed to handle risk and uncertainty.
PERT Model is suitable for-
- Research and Development programmes
- Aerospace Projects
- Other projects involving new technology
As in such projects time required for completing various jobs or activities can be highly
variable.
Hence, the orientation of PERT is 'Probabilistic'
29. PERT MODEL
=
Measures of Variability
Variability in PERT analysis is measured by variance or standard deviation.
Steps involved in calculating standard deviation of duration of critical path:
(i) Determine Standard Deviation of duration of each activity on the critical path.
(ii) Determine S.D. of total duration of critical path on basis of step (i).
t p
- to
6
Where,
is Standard Deviation,
t p is pessimistic time,
to is optimistic time.
30. PERT MODEL
Standard Deviation and Variance of Activity Duration
on Critical Path
Activity tp to = t p- to/6 Variance = 2
(1-2)
(2-5)
21
24
9
10
2
2.33
4.00
5.43
Variance
(critical path duration)
Sum of Variances of activity
durations on the critical path
=
Standard Deviation
(critical path duration) (Sum of Variances of activity
durations on the critical path )
1/2
=
=
=
(4 + 5.43)1/2
3.07
31. PERT MODEL
Probability of Completion by a Specific Date
With information of mean (T) and standard deviation ( ) for critical path duration, we can
compute the probability of completion by a specified date (D) as follows:
Z =
D - T
Where,
Z is number of S.D by which D, exceeds T
D is the specified date
T mean critical path duration
32. PERT MODEL
Probability of Completion by a Specific Date
Illustration
Specified Date (D) Z Probability of Completion by D
20
25
30
20 - 28
3.07
= -2.6
25 - 28
= -1.0
3.07
3.07
30 - 28
= 0.6
0.005
0.159
0.726
33. CPM MODEL
Introduction
Critical Path Method (CPM) was developed independently by Du Pont Company to
solve scheduling problems in industrial settings.
CPM Model is primarily concerned with the trade-off between cost and time.
CPM Model is applied to projects that employ a fairly stable technology and are
relatively risk free.
The main thrust of CPM analysis is on time-cost relationships
and it seeks to determine the project schedule which
minimizes total cost.
34. CPM MODEL
Assumptions under CPM Model
1. Two types of costs are associated with the project: Direct Costs
and Indirect Costs.
2. Activities of projects can be expedited (sooner) by crashing which involves
employing more resources.
3. Crashing reduces time but enhances direct costs because of factors like
overtime payments, extra payments and wastage.
4. Indirect costs associated with project increase linearly with project duration.
35. CPM MODEL
Procedure of CPM Analysis
1. Obtain the critical path in the network model. Determine project duration
and direct cost.
2. Examine cost-time slope of activities on the critical path obtained and
crash the activity which has the least slope.
3. Construct the new critical path after crashing as per step 2. Determine
project duration and cost.
4. Repeat step 2 and 3 till activities on the critical path are crashed.
49. CPM MODEL
Activities Crashed
Project
Duration
In weeks
Total
Direct
Cost
Total
Indirect
Cost
Total Cost
None 30 45200 60000 105,200
(2-4) 29 46700 58000 104,700
(2-4) and (5-6) 27 49500 54000 103,500
(1-2), (2-4) and (5-6) 24 52500 48000 100,500
(1-2), (2-4), (5-6) and (6-7) 211/2 55200 42000 97,200
(1-2), (2-4), (3-5), (5-6) and (6-7) 20 57100 40000 97,100
(1-2), (2-4), (3-5), (5-6), (4-6) and (6-7) 19 58300 39000 97,300
Project Duration and Total Cost
Indirect Cost is Rs 2000 per week
50. Network Cost System
Introduction
Network Cost System was developed to provide vehicle for cost
planning and control of projects.
Basic principle is: Costs are planned, measured, analysed and
controlled in terms of project activities.
For cost projections it is assumed that the expenditure for any activity
is incurred evenly over the duration of activity.
51. Network Cost System
Analysis and Control of Costs
1. Cost incurred to date
In NCS, Cost are recorded activity wise. Costs incurred to date can be obtained by
summing up costs for various activities.
2. Budgeted cost to date
is the cost projections made at the beginning.
3. Value of work done to date
is equal to budgeted costs * percentage of work accomplished.
4. Cost over-run (under-run) to date
Actual Cost - Value of work completed
Vaue of work completed
* 100
52. Network Cost System
Analysis and Control of Costs
5. Time over-run (under-run) to date
Time over-run is usually defined in terms of months behind or months ahead.