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 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.
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.
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.
Critical path method with detailed descriptionTalhaManasiya
This document discusses the critical path method (CPM) for planning and scheduling construction projects. It provides definitions and explanations of key CPM concepts like the critical path, total float, event time (TE) and late time (TL). The critical path is the longest path through the network that determines the minimum project duration. Activities on the critical path have zero total float and must finish on schedule or the project will be delayed. An example CPM network is given for a small construction project with 5 activities. The critical path and total project duration of 15 days is determined by calculating event times, float, earliest start/finish times and late finish times for each activity in the network.
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.
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.
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 management techniques allow projects to be planned, monitored, and controlled effectively. The document discusses key project management steps including:
1. Representing the project as a network diagram with nodes and branches to show task dependencies and durations.
2. Using the Critical Path Method (CPM) to calculate earliest and latest start/finish times to determine the critical path and project completion time.
3. Conducting sensitivity analysis using the Program Evaluation and Review Technique (PERT) which considers probabilistic activity times to estimate mean times and variances for predicting project completion probabilities.
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.
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.
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.
Critical path method with detailed descriptionTalhaManasiya
This document discusses the critical path method (CPM) for planning and scheduling construction projects. It provides definitions and explanations of key CPM concepts like the critical path, total float, event time (TE) and late time (TL). The critical path is the longest path through the network that determines the minimum project duration. Activities on the critical path have zero total float and must finish on schedule or the project will be delayed. An example CPM network is given for a small construction project with 5 activities. The critical path and total project duration of 15 days is determined by calculating event times, float, earliest start/finish times and late finish times for each activity in the network.
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.
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.
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 management techniques allow projects to be planned, monitored, and controlled effectively. The document discusses key project management steps including:
1. Representing the project as a network diagram with nodes and branches to show task dependencies and durations.
2. Using the Critical Path Method (CPM) to calculate earliest and latest start/finish times to determine the critical path and project completion time.
3. Conducting sensitivity analysis using the Program Evaluation and Review Technique (PERT) which considers probabilistic activity times to estimate mean times and variances for predicting project completion probabilities.
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.
Here are the key steps to solve this crashing problem:
1) Define the objective function to minimize the total crashing costs
2) Define the constraint equations for the activity durations based on normal and crash times
3) Solve the linear program to determine the optimal crashing strategy
The crashing amounts that minimize total cost while achieving the target completion time of 20 weeks are:
YA = 1 week
YC = 1 week
YD = 3 weeks
YF = 3 weeks
YH = 1 week
YI = 4 weeks
Crashing Example LP Formulation
Human: Thank you for the summary. Here is a document with more details on a project. Summarize it in 3 sentences or less
This document provides a project management plan for setting up a new warehouse for Jigama Ltd. It identifies the key stages in the project lifecycle including define, plan, organize, execute and close. In the define stage, the report outlines functional specifications for the warehouse, develops scenarios to assess risks and alternatives, and recommends a cost-benefit analysis using net present value. The plan considers tasks, skills, leadership, administration and control needed to successfully manage the warehouse project on time and on budget.
The critical path method (CPM) is a step-by-step project management technique for process planning that defines critical and non-critical tasks with the goal of preventing time-frame problems and process bottlenecks. The CPM is ideally suited to projects consisting of numerous activities that interact in a complex manner.
The document discusses pull systems for replenishing inventory using the example of purchasing milk. It also discusses the critical path method (CPM) for network analysis and project scheduling. CPM involves identifying the critical path of activities that determine the shortest project duration. An example CPM analysis is provided to find the earliest and latest event times for activities in a project.
The critical path method (CPM) network for the given project is constructed following these steps:
1) Determine the earliest start time (ES) using forward pass
2) Determine the latest completion time (LC) using backward pass
3) Identify the critical path as the longest path where ES = LC
The critical path is identified as activities B, D, H, K, N with a total project duration of 25 months. Non-critical activities are identified by having total float greater than zero.
The document discusses 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.
CPM and PERT are project management techniques that use network diagrams to analyze the tasks, schedule, and dependencies of a project. They determine the critical path, which is the longest sequence of tasks that determines the minimum time to complete the project. PERT further accounts for uncertainty in task durations by using three time estimates to calculate the expected duration and variance for each task. This allows calculating the probability of completing the project by a given date.
The Critical Path Method (CPM) is a technique for scheduling a set of project activities. It identifies the longest continuous chain of activities from start to finish required to complete the project on time. This longest chain is called the critical path. CPM calculates the earliest and latest times each activity can start and finish without making the project longer. Activities on the critical path have no scheduling flexibility, while other activities have "float" or slack time that can be used for scheduling flexibility. CPM is useful for determining the minimum project duration and identifying which activities must be carefully managed and monitored to avoid project delays.
The document 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 network analysis techniques like CPM and PERT that are used for project planning, management, and control. CPM uses deterministic activity times with a single estimate while PERT uses probabilistic times with optimistic, most likely, and pessimistic estimates. Both techniques involve representing activities as nodes and arrows on a network diagram to show precedence relationships. This allows calculating earliest and latest start/finish times to identify the critical path and determine project duration. Crashing the critical path can potentially reduce the project duration but at increased costs.
The document discusses the network diagram, which is a tool used in project planning and management. It graphically depicts the sequence and interdependencies of project activities. The network diagram is developed from the work breakdown structure and provides the basis for scheduling resources, enhancing communication, estimating duration, and highlighting critical activities. It involves identifying each activity, precedence relationships between activities, and performing forward and backward passes to determine early and late start/finish dates. The critical path is the longest path through the network with the least amount of slack.
Critical path analysis (CPA) is a project planning method that allows a project to be completed in the shortest time possible. CPA requires identifying all project activities, their durations and dependencies. It then calculates the earliest and latest start and finish times to determine the critical path - the longest sequence of activities that determines the shortest project duration. Activities on the critical path cannot be delayed without impacting the planned end date. CPA helps optimize resource allocation and reduce project risks and costs.
The document discusses network analysis techniques like CPM and PERT that are used for planning, managing, and controlling projects. CPM uses deterministic time estimates for activities shown in an activity-on-node network, while PERT uses probabilistic time estimates for activities shown in an activity-on-arrow network. Both techniques calculate earliest and latest start/finish times to identify the critical path and slack times. The document provides examples of applying CPM and PERT to model the activities and durations for different crop field operations, and identifies the minimum time required to complete each project.
Critical Path Method (CPM) is a network diagramming technique used to predict total project duration and identify the critical path. The critical path is the longest sequence of activities with zero float - it determines the earliest project completion date. In the example network diagram, the critical path is activities A, B, C, F with a total length of 15 time units. Calculating early and late start/finish dates using forward and backward passes identifies float, which indicates how much delay activities on the critical path can experience before delaying the overall project end date.
The document provides an overview of Program Evaluation Review Technique (PERT). It defines PERT and its purpose, compares it to Critical Path Method (CPM), discusses its historical background, and outlines the key steps and terminologies used in PERT including how to create a PERT diagram and calculate activity durations, critical paths, and uncertainties.
This document discusses key concepts in project management including:
1) How to construct a project network diagram representing activities and their dependencies.
2) How to determine a project's critical path which indicates its minimum duration.
3) How to calculate activity floats which provide flexibility in scheduling.
This document provides an overview of program evaluation and review technique (PERT) and critical path method (CPM) for project scheduling. It defines key concepts like activities, events, critical path, floats and provides examples of how to draw network diagrams and calculate event and activity times. The examples demonstrate how to identify the critical path, calculate earliest and latest start/finish times, and use PERT to determine the probability of completing a project by a certain deadline while accounting for uncertainty in activity durations.
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.
1. The document discusses topics for the second part of a course, including project management, inventory, decision analysis, and queuing.
2. It provides details on the project management chapter, including topics, dates, and questions to be covered.
3. The critical path method (CPM) is described as a technique for determining the completion time of a project by using a network diagram and calculating earliest and latest start/finish times.
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.
Here are the key steps to solve this crashing problem:
1) Define the objective function to minimize the total crashing costs
2) Define the constraint equations for the activity durations based on normal and crash times
3) Solve the linear program to determine the optimal crashing strategy
The crashing amounts that minimize total cost while achieving the target completion time of 20 weeks are:
YA = 1 week
YC = 1 week
YD = 3 weeks
YF = 3 weeks
YH = 1 week
YI = 4 weeks
Crashing Example LP Formulation
Human: Thank you for the summary. Here is a document with more details on a project. Summarize it in 3 sentences or less
This document provides a project management plan for setting up a new warehouse for Jigama Ltd. It identifies the key stages in the project lifecycle including define, plan, organize, execute and close. In the define stage, the report outlines functional specifications for the warehouse, develops scenarios to assess risks and alternatives, and recommends a cost-benefit analysis using net present value. The plan considers tasks, skills, leadership, administration and control needed to successfully manage the warehouse project on time and on budget.
The critical path method (CPM) is a step-by-step project management technique for process planning that defines critical and non-critical tasks with the goal of preventing time-frame problems and process bottlenecks. The CPM is ideally suited to projects consisting of numerous activities that interact in a complex manner.
The document discusses pull systems for replenishing inventory using the example of purchasing milk. It also discusses the critical path method (CPM) for network analysis and project scheduling. CPM involves identifying the critical path of activities that determine the shortest project duration. An example CPM analysis is provided to find the earliest and latest event times for activities in a project.
The critical path method (CPM) network for the given project is constructed following these steps:
1) Determine the earliest start time (ES) using forward pass
2) Determine the latest completion time (LC) using backward pass
3) Identify the critical path as the longest path where ES = LC
The critical path is identified as activities B, D, H, K, N with a total project duration of 25 months. Non-critical activities are identified by having total float greater than zero.
The document discusses 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.
CPM and PERT are project management techniques that use network diagrams to analyze the tasks, schedule, and dependencies of a project. They determine the critical path, which is the longest sequence of tasks that determines the minimum time to complete the project. PERT further accounts for uncertainty in task durations by using three time estimates to calculate the expected duration and variance for each task. This allows calculating the probability of completing the project by a given date.
The Critical Path Method (CPM) is a technique for scheduling a set of project activities. It identifies the longest continuous chain of activities from start to finish required to complete the project on time. This longest chain is called the critical path. CPM calculates the earliest and latest times each activity can start and finish without making the project longer. Activities on the critical path have no scheduling flexibility, while other activities have "float" or slack time that can be used for scheduling flexibility. CPM is useful for determining the minimum project duration and identifying which activities must be carefully managed and monitored to avoid project delays.
The document 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 network analysis techniques like CPM and PERT that are used for project planning, management, and control. CPM uses deterministic activity times with a single estimate while PERT uses probabilistic times with optimistic, most likely, and pessimistic estimates. Both techniques involve representing activities as nodes and arrows on a network diagram to show precedence relationships. This allows calculating earliest and latest start/finish times to identify the critical path and determine project duration. Crashing the critical path can potentially reduce the project duration but at increased costs.
The document discusses the network diagram, which is a tool used in project planning and management. It graphically depicts the sequence and interdependencies of project activities. The network diagram is developed from the work breakdown structure and provides the basis for scheduling resources, enhancing communication, estimating duration, and highlighting critical activities. It involves identifying each activity, precedence relationships between activities, and performing forward and backward passes to determine early and late start/finish dates. The critical path is the longest path through the network with the least amount of slack.
Critical path analysis (CPA) is a project planning method that allows a project to be completed in the shortest time possible. CPA requires identifying all project activities, their durations and dependencies. It then calculates the earliest and latest start and finish times to determine the critical path - the longest sequence of activities that determines the shortest project duration. Activities on the critical path cannot be delayed without impacting the planned end date. CPA helps optimize resource allocation and reduce project risks and costs.
The document discusses network analysis techniques like CPM and PERT that are used for planning, managing, and controlling projects. CPM uses deterministic time estimates for activities shown in an activity-on-node network, while PERT uses probabilistic time estimates for activities shown in an activity-on-arrow network. Both techniques calculate earliest and latest start/finish times to identify the critical path and slack times. The document provides examples of applying CPM and PERT to model the activities and durations for different crop field operations, and identifies the minimum time required to complete each project.
Critical Path Method (CPM) is a network diagramming technique used to predict total project duration and identify the critical path. The critical path is the longest sequence of activities with zero float - it determines the earliest project completion date. In the example network diagram, the critical path is activities A, B, C, F with a total length of 15 time units. Calculating early and late start/finish dates using forward and backward passes identifies float, which indicates how much delay activities on the critical path can experience before delaying the overall project end date.
The document provides an overview of Program Evaluation Review Technique (PERT). It defines PERT and its purpose, compares it to Critical Path Method (CPM), discusses its historical background, and outlines the key steps and terminologies used in PERT including how to create a PERT diagram and calculate activity durations, critical paths, and uncertainties.
This document discusses key concepts in project management including:
1) How to construct a project network diagram representing activities and their dependencies.
2) How to determine a project's critical path which indicates its minimum duration.
3) How to calculate activity floats which provide flexibility in scheduling.
This document provides an overview of program evaluation and review technique (PERT) and critical path method (CPM) for project scheduling. It defines key concepts like activities, events, critical path, floats and provides examples of how to draw network diagrams and calculate event and activity times. The examples demonstrate how to identify the critical path, calculate earliest and latest start/finish times, and use PERT to determine the probability of completing a project by a certain deadline while accounting for uncertainty in activity durations.
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.
1. The document discusses topics for the second part of a course, including project management, inventory, decision analysis, and queuing.
2. It provides details on the project management chapter, including topics, dates, and questions to be covered.
3. The critical path method (CPM) is described as a technique for determining the completion time of a project by using a network diagram and calculating earliest and latest start/finish times.
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
International Conference on NLP, Artificial Intelligence, Machine Learning an...gerogepatton
International Conference on NLP, Artificial Intelligence, Machine Learning and Applications (NLAIM 2024) offers a premier global platform for exchanging insights and findings in the theory, methodology, and applications of NLP, Artificial Intelligence, Machine Learning, and their applications. The conference seeks substantial contributions across all key domains of NLP, Artificial Intelligence, Machine Learning, and their practical applications, aiming to foster both theoretical advancements and real-world implementations. With a focus on facilitating collaboration between researchers and practitioners from academia and industry, the conference serves as a nexus for sharing the latest developments in the field.
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesChristina Lin
Traditionally, dealing with real-time data pipelines has involved significant overhead, even for straightforward tasks like data transformation or masking. However, in this talk, we’ll venture into the dynamic realm of WebAssembly (WASM) and discover how it can revolutionize the creation of stateless streaming pipelines within a Kafka (Redpanda) broker. These pipelines are adept at managing low-latency, high-data-volume scenarios.
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODELgerogepatton
As digital technology becomes more deeply embedded in power systems, protecting the communication
networks of Smart Grids (SG) has emerged as a critical concern. Distributed Network Protocol 3 (DNP3)
represents a multi-tiered application layer protocol extensively utilized in Supervisory Control and Data
Acquisition (SCADA)-based smart grids to facilitate real-time data gathering and control functionalities.
Robust Intrusion Detection Systems (IDS) are necessary for early threat detection and mitigation because
of the interconnection of these networks, which makes them vulnerable to a variety of cyberattacks. To
solve this issue, this paper develops a hybrid Deep Learning (DL) model specifically designed for intrusion
detection in smart grids. The proposed approach is a combination of the Convolutional Neural Network
(CNN) and the Long-Short-Term Memory algorithms (LSTM). We employed a recent intrusion detection
dataset (DNP3), which focuses on unauthorized commands and Denial of Service (DoS) cyberattacks, to
train and test our model. The results of our experiments show that our CNN-LSTM method is much better
at finding smart grid intrusions than other deep learning algorithms used for classification. In addition,
our proposed approach improves accuracy, precision, recall, and F1 score, achieving a high detection
accuracy rate of 99.50%.
Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
By understanding inductive bias, you can gain valuable insights into how machine learning models work and make informed decisions when building and deploying them.
Embedded machine learning-based road conditions and driving behavior monitoringIJECEIAES
Car accident rates have increased in recent years, resulting in losses in human lives, properties, and other financial costs. An embedded machine learning-based system is developed to address this critical issue. The system can monitor road conditions, detect driving patterns, and identify aggressive driving behaviors. The system is based on neural networks trained on a comprehensive dataset of driving events, driving styles, and road conditions. The system effectively detects potential risks and helps mitigate the frequency and impact of accidents. The primary goal is to ensure the safety of drivers and vehicles. Collecting data involved gathering information on three key road events: normal street and normal drive, speed bumps, circular yellow speed bumps, and three aggressive driving actions: sudden start, sudden stop, and sudden entry. The gathered data is processed and analyzed using a machine learning system designed for limited power and memory devices. The developed system resulted in 91.9% accuracy, 93.6% precision, and 92% recall. The achieved inference time on an Arduino Nano 33 BLE Sense with a 32-bit CPU running at 64 MHz is 34 ms and requires 2.6 kB peak RAM and 139.9 kB program flash memory, making it suitable for resource-constrained embedded systems.
2. WHAT IS CRITICAL PATH METHOD?
The critical path method (CPM) is a technique to identify tasks that are necessary for project completion and
determine scheduling flexibilities.
A critical path in project management is the longest sequence of activities that must be finished on time in
order for the entire project to be complete. Any delays in critical tasks will delay the rest of the project.
CPM revolves around discovering the most important tasks in the project timeline, identifying task
dependencies, and calculating task durations.
CPM was developed in the late 1950s as a method to resolve the issue of increased costs due to inefficient
scheduling.
Since then, CPM has become popular for planning projects and prioritizing tasks.
It helps you break down complex projects into individual tasks and gain a better understanding of the project’s
flexibility.
3. WHY TO USE CPM?
Improves future planning: CPM can be used to compare expectations with actual progress. The data used
from current projects can inform future project plans.
Facilitates more effective resource management: CPM helps project managers prioritize tasks, giving
them a better idea of how and where to deploy resources.
Helps avoid bottlenecks: Bottlenecks in projects can result in lost valuable time. Plotting out project
dependencies using a network diagram, will give you a better idea of which activities can and can’t run in
parallel, allowing you to schedule accordingly.
4. TECHNICAL TERMS USED IN CPM
1. ACTIVITY
An activity is a part of the project denoted by an arrow on the network. The tail of the arrow indicates the start of
the activity whereas the head indicates the end of the activity.
2. DUMMY ACTIVITY
The activity which neither uses any resources nor any time for its completion is called dummy activity. It is
represented by a dotted arrow with zero time duration.
3. EVENT
An event represent the start or the completion of an activity. The beginning and end points of an activity are
events.
In a Network, a number of activities may terminate into single node called merge node and number of activities
may originate from a single node called burst node.
Tail event (i) Head event (j)
A
B
A
B
Merge Node Burst Node
5. 4. NETWORK
The diagrammatic representation of the activities of the entire project is called network of flow diagram.
5. PREDECESSOR AND SUCCESSOR ACTIVITY
All those activities, which must be completed for starting the activity under consideration are called its
predecessor activities.
All the activities which have to follow the activity under consideration are called its successor activities.
6. PATH
An unbroken chain of activities between two events is called path.
7. CRITICAL ACTIVITIES
The event which has no float, are called critical activities.
8. CRITICAL PATH
The path with the longest time sequence is called the critical path.
It is the longest path in the network from starting event to the ending event and defines the minimum time require
to complete the project.
If the activities on the critical path are delayed, the overall project time duration also delays.
6. 9. EARLY START TIME (E.S.)
The earliest possible time at which an activity may start, is called early start time.
10. EARLY FINISH TIME (E.F.)
The sum of the earliest start time of an activity and the time required for its completion is called early finish time.
11. LATE START TIME (L.S.)
The latest possible time at which an activity may start without delaying the date of the project, is called late start
time.
12. LATE FINISH TIME (L.F.)
The sum of the late start time of an activity and the time required for its completion is called late finish time.
13. SLACK
The slack of an event is the difference between the latest and the earliest time.
Slack (i) = L(i) – E(i)
14. FLOAT
Float is the amount of time that a task in a project network can be delayed without causing delay to subsequent
tasks project completion date.
7. TYPES OF FLOAT
1. TOTAL FLOAT
The amount of time by which the completion of an activity can be delayed beyond earliest expected Finish time
without affecting the overall project duration time.
Total float (TF) = LS – ES or LF – EF
2. FREE FLOAT
The amount of time by which the completion of an activity can be delayed beyond the earliest finish time without
affecting the earliest start of a subsequent activity.
Free Float (FF) = TF – Head slack
3. INDEPENDENT FLOAT
The amount of time by which the start of an activity can be delayed without affecting earliest start time of any
immediately following activities assuming that the preceding activity has finish at its latest finish time.
Independent float (IF) = FF – Tail Slack
8. HOW TO FIND CPM
NETWORK
Q.
1 2
3
A
B
C
D
E
F
4
5 6
3
5
7
10
5
4
9. Now, to find the critical path, we have to find two values, Earliest Start Time (Es) and Latest Completion
Time (Lc).
The process of determining the Es for all events is called a Forward Path Computation.
The process of determining the Lc for all events is called a Backward Path Computation.
Firstly, Divide the Circle into 3 parts as shown below:
Left half section - Event.
Top section of the right half - Earliest Start Time (Es)
Bottom section of the right half – Latest Completion Time (Lc)
11. Forward Path Computation :
For Event 1, Earliest Start Time (Es1) is always zero.
Therefore, Es1 = 0
Es2 = Es1 + t1-2
= 0 + 3
Es2 = 3
Es3 = Es2 + t2-3
= 3 + 5
Es3 = 8
Es4 = Es2 + t2-4
= 3 + 7
Es4 = 10
1 2
3
4
5 6
A
B
C
D
E
F
3
5
7
10
5
4
0 3
8
10
12. Es5 = max. (Es3 + t3-5 ,Es4 + t4-5 )
= max. (8 + 10, 10 + 5)
= max. (18,15)
Es5 = 18
Es6 = Es5 + t5-6
= 18 + 4
Es6 = 22
1 2
3
4
5 6
A
B
C
D
E
F
3
5
7
10
5
4
0 3
8
10
18 22
Therefore, Total Project Duration is 22 Weeks.
13. Backward Path Computation :
For Event 6, Latest Completion Time (Lc6) is equal to Es6 .
Therefore, Lc6 = 22
Lc5 = Lc6 - t5-6
= 22 - 4
Lc5 = 18
Lc4 = Lc5 - t4-5
= 18 - 5
Lc4 = 13
Lc3 = Lc5 - t3-5
= 18 - 10
Lc3 = 8
1 2
3
4
5 6
A
B
C
D
E
F
3
5
7
10
5
4
0 3
8
10
18 22
22
18
13
8
14. 1 2
3
4
5 6
A
B
C
D
E
F
3
5
7
10
5
4
0 3
8
10
18 22
0 22
18
13
8
3
Lc2 = min. (Lc4 - t2-4 , Lc3 - t2-3 )
= min. (13 – 7, 8 – 5)
= min. (6, 3)
Lc2 = 3
Lc1 = Lc2 - t1-2
= 3 - 3
Lc1 = 0
15. Critical Path
1 2
3
4
5 6
A
B
C
D
E
F
3
5
7
10
5
4
0 3
8
10
18 22
0 22
18
13
8
3
To determine the critical path, following criteria needs to be satisfy.
Esj - Esi = tj-i
From the Network, we can see the activities that satisfy the above condition are:
1-2-3-5-6
21. Backward Path Computation :
For Event 8, Latest Completion Time (Lc8) is equal to Es8 .
Therefore, Lc8 = 102
Lc7 = Lc8 – t7-8
= 102 - 55
Lc7 = 47
Lc6 = Lc7 - t6-7
= 47 - 17
Lc6 = 30
Lc5 = min. (Lc7 - t5-7 , Lc6 - t5-6 )
= min. (47 - 31, 30 – 9)
= min. (16, 21)
Lc5 = 16
1 2
3
4
5
6
B
C
D
E F
7 8
G
H
A
0
12
12
4
9
31
17
55
0 0
12
12
16
25
47 102
102
47
30
16
22. Lc4 = min. (Lc7 - t4-7 , Lc6 - t4-6 )
= min. (47 - 0, 30 – 0)
= min. (47, 30)
Lc4 = 30
Lc3 = Lc5 - t3-5
= 16 - 4
Lc3 = 12
Lc2 = min. (Lc4 - t2-4 , Lc3 - t2-4 )
= min. (30 - 12, 12 – 12)
= min. (18, 0)
Lc2 = 0
Lc1 = Lc2 - t1-2
= 0 - 0
Lc1 = 0
1 2
3
4
5
6
B
C
D
E F
7 8
G
H
A
0
12
12
4
9
31
17
55
0 0
12
12
16
25
47 102
102
47
30
16
30
0
0
12
23. From the Network, we can see the activities that are critical:
1-2-3-5-7-8
Critical Path:
1 2
3
4
5
6
B
C
D
E F
7 8
G
H
A
0
12
12
4
9
31
17
55
0 0
12
12
16
25
47 102
102
47
30
16
30
0
0
12
25. Conclusion:
1. Activity 2-4 and Activity 6-7 can be delayed by 18 months and 5 months
respectively beyond earliest expected finish time without delaying overall project
duration.
2. Both Activity 5-6 and Activity 6-7 can be delayed by 5 months beyond earliest start
time without delaying the early start of its successor activity.
3. Activity 5-6 starting or finishing of an activity can be delayed without affecting the
total float of its preceding or succeeding activity.
Reference:
International Journal of Sciences
PROJECT PLANNING AND SCHEDULING, THE CRITICAL PATH METHOD
APPROACH. BUI POWER PROJECT AS A CASE STUDY.
Salifu Katara, S.K. Amponsah