Copyright © 2008 Pearson Education, Inc. Slide 13-1 Unit 13C Scheduling Problems.

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Presentation transcript:

Copyright © 2008 Pearson Education, Inc. Slide 13-1 Unit 13C Scheduling Problems

Copyright © 2008 Pearson Education, Inc. Slide 13-2 A House Building Project 13-C  Each edge is labeled with the number of months needed to complete the task.  In some phases of the project, only one task can be undertaken at a time.  During other phases, two or more tasks can be carried out concurrently.

Copyright © 2008 Pearson Education, Inc. Slide 13-3 Limiting Tasks and Critical Path When two (or more) tasks can occur at the same time between two stages of the project, the task that requires the most time is called the limiting task. The critical path through the network is the path that includes all the limiting tasks. The length of the critical path is the completion time for the project. 13-C

Copyright © 2008 Pearson Education, Inc. Slide 13-4

a) Finance b) Trim Work c) Design-> Finance -> Construction -> Trim work Copyright © 2008 Pearson Education, Inc. Slide 13-5

Copyright © 2008 Pearson Education, Inc. Slide 13-6 Finding Earliest Start and Finish Times The earliest start time (EST) of a task leaving a particular vertex is the largest of the earliest finish times of the tasks entering that vertex. The earliest finish time (EFT) of a task is the earliest start time of that task plus the time required for the task. That is, EFT = EST + time for task. 13-C

Copyright © 2008 Pearson Education, Inc. Slide 13-7

Copyright © 2008 Pearson Education, Inc. Slide 13-8

Copyright © 2008 Pearson Education, Inc. Slide 13-9 Finding Latest Start and Finish Times The latest finish time (LFT) of a task entering a particular vertex is the smallest of the latest start times of the tasks leaving that vertex. The LFT of a task is the time by which it must be completed to avoid delays. The latest start time (LST) of a task is the latest finish time of that task minus the time required for the task. That is, LST = LFT  time for task The LST of a task is the latest possible start without delaying the overall project. 13-C

Copyright © 2008 Pearson Education, Inc. Slide 13-10

Copyright © 2008 Pearson Education, Inc. Slide 13-11

Slack Time The amount of time a task can go over its allotted time without putting the entire project behind schedule. This number is nonnegative. Tasks on the critical path have no slack time. Slack time = LST – EST = LFT – EFT Copyright © 2008 Pearson Education, Inc. Slide 13-12

Slack Time Copyright © 2008 Pearson Education, Inc. Slide 13-13

The Impact of Slack Time Copyright © 2008 Pearson Education, Inc. Slide Example:

The Impact of Slack Time Copyright © 2008 Pearson Education, Inc. Slide Example:

Painting Tasks (hrs) Copyright © 2008 Pearson Education, Inc. Slide 13-16

ANSWERS 21. a, e, f, g, 22. f, g, I, k 23. a, e, f, g, I, h (longest time) Copyright © 2008 Pearson Education, Inc. Slide 13-17

Copyright © 2008 Pearson Education, Inc. Slide 13-18

ANSWERS 29. a) EST - e: 2hs i: 7.5 hrs b) LST - e: 2hrs i: 7.5 hrs 30. a) EST - h: 4.5 k: 9.5 b) LST - h: 5.5 hrs k: 9.5 Copyright © 2008 Pearson Education, Inc. Slide 13-19