The document discusses concepts related to project scheduling including floats, critical paths, time crashing, and developing a time-cost tradeoff model. It provides information on normal and crash estimates for activities, calculating cost slopes, and sequentially crashing critical activities to determine the minimum total project cost and duration.

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7. Total float: Can change the successor activity times & bring new critical path Free Float: Can delay without any problem. No change in successor activities. Independent Float: Can delay even if the previous activities are late

8. FLOATS : Flexibility in delaying an activity 0

9. Critical Path In project management , a critical path is the sequence of project network activities with the longest overall duration , determining the shortest time possible to complete the project. Any delay of an activity on the critical path directly impacts the planned project completion date (i.e. there is no float on the critical path)..

10. Critical Path A project can have several, parallel critical paths. An additional parallel path through the network with the total durations shorter than the critical path is called a sub-critical or non-critical path and the activities are non-critical activities. If the float of activity is negaive: supercritcial activites; need more resources, Special attention. Originally, the critical path method considered only logical dependencies among terminal elements. Since then, it has been expanded to allow for the inclusion of resources related to each activity

11. Update CPM Diagram As the project progresses, the actual task completion times will be known and the network diagram can be updated to include this information. A new critical path may emerge, and structural changes may be made in the network if project requirements change.

12. Time Crashing Normally project is planned for the completion period of the network. Increasing the duration of the project increase project costs. But, under some circumstances, may compel to reduce the completion time: To avoid delay which attract heavy penalty or loss of goodwill. To venture on another project To earn bonus for early completion, if found feasible. To transfer the resources needed elsewhere.

13. Project Cost Components

14. Direct & Indirect Costs Direct cost : For Accomplishing the work Indirect Cost : Related to control & direction of work, financial overheads, lost production, insurance claims

15. Direct project Cost

16. Variation of Cost with Time

17. Indirect Cost Only considering overheads and supervision

18. Indirect Cost If there is loss in profits Penalty due to delay OUTAGE LOSS

19. Indirect Cost (Overhead + Outage Loss)

20. Total Project Cost

21. CPM Cost Model In CPM- Time is related to cost ---- Therefore objective is to develop optimum time-cost relationship. The project duration can be reduced by reducing the duration of critical activities. By deploying more resources By relaxing the technical specifications

22. Cost Variation with Time

23. Normal & Crash Estimates Normal Estimate: Emphasis is on cost with time being associated with minimum cost. Crash Estimate: Absolute minimum time required for the job and the cost necessary to achieve it.

24. Cost –Time Curve Normal Time (t n ): Normal time is the standard time that an estimator would usually allow for an activity. Crash Time (t c ): Minimum possible time in which an activity can be completed by deploying extra resources. Normal Cost (C n ): This is the direct cost required to complete the activity in normal time duration Crash Cost (C c ) : This is the direct cost corresponding to the completion of the activity within crash time.

25. Generalized direct cost-time curve

26. Direct Cost Curve

27. Total Project Cost & Optimum Duration Total Cost Curve Linear Approximation

28. Cost Slope The slope of each cost versus time trade-off for each activity as follows:

29. Time-Cost Model Assumptions The time-cost model described above relies on the following assumptions: The normal cost for an activity is lower than the crash cost. There is a linear relationship between activity time and cost. The resources are available to shorten the activity.

30. Project Crashing The activities having the lowest cost per unit of time reduction should be shortened first. In this way, one can step through the critical path activities and create a graph of the total project cost versus the project time.

31. Project Crashing Attention should be given to the critical path to make sure that it remains the critical path after the activity time is reduced. If a new critical path emerges, it must considered in subsequent time reductions. To minimize the cost, those activities that are not on the critical path can be extended to minimize their costs without increasing the project completion time.

32. Project Overhead costs are @ Rs 300/day Determine: Direct Cost-duration relationship Total cost –duration relationship and corresponding least cost plan Activity Normal Duration (Days) Normal Cost (Rs. ) Crash Duration (Days) Crash Cost (Rs.) 1-2 9 8000 6 9500 2-3 5 5000 3 5500 1 2 3 9 (6) 5 (3)

33. 1. Find out the cost slope for each activity ? 2. Find out Normal Duration Direct Cost ?

34. 3. Crash the activity with least cost slope ? 4. Find out the extra cost of crashing ? 5. Add to the normal direct cost of the project

35. 6. Crash another activity ? 7. Find out the extra cost of crashing ? 8. Add to the normal direct cost of the project ?

39. Critical Path

40. Normal Duration & Direct Cost

41. Cost Slope

42. First Stage crashing: Critical Activity with minimum cost -slope Not 3 weeks: (The path should remain critical)

43. Second-Stage crashing 2-3, 2-4 or 2-4, 3-4. minimum cost slope Simultaneously

44. Third Stage of Crashing: Activity 2-4 & 3-4

45. Fourth Stage of Crashing

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