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For the activity on arrow network information given below (activity durations are givenin the table under part b): a. Compute the earliest event occurrence time (TEj), the latest allowable event occurrence time (TLj), and the event slack (ESj) for all nodes/events.

For the activity on arrow network information given below (activity durations are givenin the table under part b): a. Compute the earliest event occurrence time (TEj), the latest allowable event occurrence time (TLj), and the event slack (ESj) for all nodes/events.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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For the activity on arrow network information given below (activity durations are givenin the table under part b):

a. Compute the earliest event occurrence time (TEj), the latest allowable event
occurrence time (TLj), and the event slack (ESj) for all nodes/events.

b. Compute the four schedule dates (ESDij, EFDij, LSDij, LFDij) and the floats
(TFij, FFij) for all activities.

**Title: Critical Path Analysis for Project Management** The diagram provided is a network chart used for critical path analysis in project management. It consists of nodes and directed edges indicating the sequence and dependency of project activities. **Description of Diagram Components:** 1. **Nodes (Events/Tasks):** - Each circle represents a project milestone or event. - The numbers inside the circles represent the earliest event occurrence time (TE) at the top left and latest allowable event occurrence time (TL) at the bottom right. 2. **Edges (Activities):** - Solid lines connecting nodes represent activities that must be completed to move from one milestone to another. - Dotted lines indicate dependencies between tasks that do not consume time but affect scheduling. 3. **Numbers on Node Connections:** - These are the duration estimates for each activity connecting two nodes. **Objective:** - **Compute the following for all nodes/events:** - **Earliest Event Occurrence Time (TE\(_i\))**: The earliest time at which an event can occur given the durations of preceding activities. - **Latest Allowable Event Occurrence Time (TL\(_i\))**: The latest time an event can occur without delaying the project. - **Event Slack (ES\(_i\))**: The difference between TL and TE for an event, representing the flexibility in scheduling an event without affecting the project timeline. This analysis helps in identifying the critical path, which is the longest duration path through the network. The critical path determines the minimum project time frame and highlights tasks that cannot be delayed without extending the project. **Conclusion:** Critical path analysis is essential in project planning to optimize the schedule, allocate resources effectively, and foresee potential delays. Understanding TE, TL, and ES helps in making informed decisions and ensuring timely project delivery.
Transcribed Image Text:**Title: Critical Path Analysis for Project Management** The diagram provided is a network chart used for critical path analysis in project management. It consists of nodes and directed edges indicating the sequence and dependency of project activities. **Description of Diagram Components:** 1. **Nodes (Events/Tasks):** - Each circle represents a project milestone or event. - The numbers inside the circles represent the earliest event occurrence time (TE) at the top left and latest allowable event occurrence time (TL) at the bottom right. 2. **Edges (Activities):** - Solid lines connecting nodes represent activities that must be completed to move from one milestone to another. - Dotted lines indicate dependencies between tasks that do not consume time but affect scheduling. 3. **Numbers on Node Connections:** - These are the duration estimates for each activity connecting two nodes. **Objective:** - **Compute the following for all nodes/events:** - **Earliest Event Occurrence Time (TE\(_i\))**: The earliest time at which an event can occur given the durations of preceding activities. - **Latest Allowable Event Occurrence Time (TL\(_i\))**: The latest time an event can occur without delaying the project. - **Event Slack (ES\(_i\))**: The difference between TL and TE for an event, representing the flexibility in scheduling an event without affecting the project timeline. This analysis helps in identifying the critical path, which is the longest duration path through the network. The critical path determines the minimum project time frame and highlights tasks that cannot be delayed without extending the project. **Conclusion:** Critical path analysis is essential in project planning to optimize the schedule, allocate resources effectively, and foresee potential delays. Understanding TE, TL, and ES helps in making informed decisions and ensuring timely project delivery.
### Project Scheduling Table The table below is an essential component for project scheduling and management, commonly utilized in techniques such as the Critical Path Method (CPM). It provides detailed activity data necessary for calculating schedule dates and identifying critical activities. | Node i | Node j | Activity | Duration | ESD | EFD | LSD | LFD | TF | FF | |--------|--------|----------|----------|-----|-----|-----|-----|----|----| | 5 | 10 | S | 6 | | | | | | | | 5 | 15 | R | 4 | | | | | | | | 10 | 20 | A | 1 | | | | | | | | 10 | 25 | E | 4 | | | | | | | | 10 | 30 | d1 | 0 | | | | | | | | 15 | 30 | G | 1 | | | | | | | | 15 | 35 | B | 5 | | | | | | | | 20 | 40 | d2 | 0 | | | | | | | | 20 | 60 | L | 2 | | | | | | | | 25 | 40 | K | 1 | | | | | | | | 25 | 45 | d3 | 0 | | | | | | | | 30 | 45 | C | 5 | | | | | | | | 30 | 50 | H | 5 | | | | | | | | 35 | 45 | d4 | 0 | | | | | | | | 35 | 55 | J
Transcribed Image Text:### Project Scheduling Table The table below is an essential component for project scheduling and management, commonly utilized in techniques such as the Critical Path Method (CPM). It provides detailed activity data necessary for calculating schedule dates and identifying critical activities. | Node i | Node j | Activity | Duration | ESD | EFD | LSD | LFD | TF | FF | |--------|--------|----------|----------|-----|-----|-----|-----|----|----| | 5 | 10 | S | 6 | | | | | | | | 5 | 15 | R | 4 | | | | | | | | 10 | 20 | A | 1 | | | | | | | | 10 | 25 | E | 4 | | | | | | | | 10 | 30 | d1 | 0 | | | | | | | | 15 | 30 | G | 1 | | | | | | | | 15 | 35 | B | 5 | | | | | | | | 20 | 40 | d2 | 0 | | | | | | | | 20 | 60 | L | 2 | | | | | | | | 25 | 40 | K | 1 | | | | | | | | 25 | 45 | d3 | 0 | | | | | | | | 30 | 45 | C | 5 | | | | | | | | 30 | 50 | H | 5 | | | | | | | | 35 | 45 | d4 | 0 | | | | | | | | 35 | 55 | J
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