ME 443

1. ME 443 NETWORK PLANNING Prof. Dr. Mustafa Gökler

2. GANTTCHART In GANTT CHART, the time intervals are given along the horizontal axis, while the activities comprising the project are given along the vertical axis. The starting time, finishing time and duration of each activity can be seen on the chart. From this diagram, the overall time for the project can be seen, but inter-relationship of the activities comprising the total project cannot be seen.

3. GANTT CHART (Example : Design of a Bike) ACTIVITIES 1. CONCEPTUAL DESIGN 2. DESIGN OF FRAME 3. DESIGN OF TRANSMISSION 4. DESIGN OF WHEELS 5. DESIGN OF BRAKE 6. DESIGN OF ACCESSORIES 7. SYSTEM INTEGRATION 8. MANUF. OF PROTOTYPE 9. ROAD TEST 10. FINALISING THE DESIGN 11. TECH. PACK. FOR MASS PRODUCTION 0 1 2 3 4 5 6 7 8 9 10 11 12 MONTHS

4. NETWORK DIAGRAMS A network diagram is drawn to show the inter-relationship of the activities comprising the total project. From this diagram the overall time for the project can be found as well as the times at which particular resources will be required.

5. NETWORK DIAGRAMS A basis is thus provided for resources to be reallocated depending on the relative importance of cost and time. When the network diagram has been drawn in its final form, it serves as a master plan which can be updated and amended as work proceeds.

6. NETWORK PLANNING METHODS For especially large scale projects, the network planning methods are: 1. C.P.M (Critical Path Method) 2. P.E.R.T (Programme Evaluated Review Technique) However, drawing the Gannt Chart is still most commonly used method for the projects comprising relatively smaller number of activities.

7. NETWORK CONVENTIONS Tasks, usually mental or physical work, are called ACTIVITIES and incated by arrows: The termination of activities are referred as NODES and are shown by circles:

8. NETWORK CONVENTIONS Event at the start of activity is called TAIL EVENT. Event at the finish of activity is called HEAD EVENT. Activity Tail Event Head Event If an activity cannot be started until both of two earlier activities have been completed, it is shown as follow,

9. NETWORK CONVENTIONS If a number of activities cannot start until a previous single activity has finished, it is represented as follow;

10. NETWORK CONVENTIONS Dummy activities are activities of zero time duration, which are used to define the sequence of activities. Dummy activities are shown by broken lines. If activity N depends on the completion of activity L, and activity M cannot start until activities K and L have finished; these are shown as follows; K M L N

11. NETWORK PLANNING In Network Planning, the first step is to determine the logical sequence and interdependence of activities. The size of the network will depend on the complexity of the project and on the amount of detailed included. One of the difficulties in producing a network is to decide how many elements of work should be bracketed together to form a single activity. If too much sub-division occurs, the significance of main activities may become lost in a fog of details.

12. CPM After the definition of activities, the time likely to be taken by each activity (i.e. duration) is estimated. By considering logical sequence and interdependence of activities, CPM chart are drawn due to the the network conventions. Each activity is named with a letter or with the tail and head event (node) numbers. For example, Activity B or Activity 2-4 is shown as follow; B 2 4

13. CPM (EXAMPLE) 1 1.5 2.5 5 8 0.5 3 6 8 7 2 4 6 3 1 5 7

14. CPM (EXAMPLE)

15. CPM (EXAMPLE) The total project time = 17 days The earliest completion time must be the longer time path, if more than one paths exist to reach the particular event(node)

16. CPM (EXAMPLE) EARLIEST OCCURANCE 1 1.5 0.5 2.5 5 8 3 6 8 7 2 0.5 4 5.5 6 9 3 3 7 17 1 0 5 9

17. CPM (EXAMPLE)

18. CPM (EXAMPLE) LATEST OCCURANCE 1 1.5 0.5 2.5 5 8 3 6 8 7 2 0.5 6.5 4 5.5 7.5 6 9 9 3 3 3 7 17 17 1 0 0 5 9 9

19. CPM (EXAMPLE) CRITICAL PATH CRITICAL PATH : 1-3-5-6-7 1 1.5 0.5 2.5 5 8 3 6 8 7 2 0.5 6.5 4 5.5 7.5 6 9 9 3 3 3 7 17 17 1 0 0 5 9 9

20. ACTIVITY TIMES Activities of the critical path are not trapped between their head and tail events but have some freedom of movement. For instance, activity 2-4, which occupies only 1 day, can start as early as half-way through the first day, yet as late as half-way through the sixth day.The earliest finishing time for this activity is therfore the day 1.5 and the last is the day 7.5. 0 1 2 3 4 5 6 7 8

21. CPM (EXAMPLE)

22. SLACKS AND FLOATS Slack is the difference between earliest and latest event times. HEAD SLACK = LATEST OCCURANCE of HEAD EVENT – EARLIEST OCCURANCE of HEAD EVENT HS = LOH - EOH TAIL SLACK = LATEST OCCURANCE of TAIL EVENT – EARLIEST OCCURANCE of TAIL EVENT TS = LOT – EOT

23. SLACKS AND FLOATS TOTAL AVAILABLE TIME= LATEST OCCURANCE OF HEAD EVENT - EARLIEST OCCURANCE OF TAIL EVENT TAT=LOH-EOT TOTAL FLOAT = TOTAL AVAILABLE TIME - DURATION OF THE ACTIVITY TF = TAT – D

24. SLACKS AND FLOATS TAT=LOH-EOT TF = TAT – D TF = (LOH – EOT) – D ES = EOT LS = LF –D EF = EOT + D TF = LOH – EOT – D = LOH-(EOT+D) L F = LOH TF = LF – EF TOTAL FLOAT = LATEST FINISH – EARLIEST FINISH

25. SLACKS AND FLOATS FREE FLOAT = TOTAL FLOAT- HEAD SLACK FF = TF - HS INDEPENDENT FLOAT = FREE FLOAT – TAIL SLACK IF= FF - TS

26. SLACKS AND FLOATS 1 2 0.5 6.5 4 5.57.5 HS = LOH – EOH HS = 7.5 - 5.5 =2 TS = LOT – EOT TS = 6.5 - 0.5 = 6 TAT=LOH-EOT TAT = 7.5 - 0.5 = 7 TF = TAT - D = 7 - 1 = 6 TF = LF - EF= 7.5 - 1.5 =6 FF = TF - HS = 6 - 2 = 4 IF = FF - TS= 4 - 6 = -2

27. FLOATS StartFinishFloats ActivityDurationEarliestLatestEarliestLatestTotalFree Independent 1-2 0.5 day 0 6 0.5 6.5 6 0 0 1-3 3 days 0 0 3 3 0 0 0 1-5 8 days 0 1 8 9 1 1 1 2-4 1 day 0.5 6.5 1.5 7.5 6 4 -2 3-4 2.5 days 3 5 5.5 7.5 2 0 0 3-5 6 days 3 3 9 9 0 0 0 3-6 5 days 3 4 8 9 1 1 1 4-6 1.5 days 5.5 7.5 7 9 2 2 0 5-6 0 day 9 9 9 9 0 0 0 5-7 7 days 9 10 16 17 1 1 1 6-7 8 days 9 9 17 17 0 0 0

28. PERT One of the original features of PERT was a probabilistic approach to the estimation of activity times. This approach complicates the technique of networking, but is sometimes of advantage if the time estimates are subject to considerable variation. Three estimates are required for each activity: to = optimistic time tp = pessimistic time tm= the most likely estimate time

29. PERT o

30. PERT to - tm -tp

31. PERT (EXAMPLE-1) Calculate the probability of completion in 100 days by both alternative routes 36 - 45 - 60 2 41-50-59 5 1 33-39-51 20 -29 - 44 3 4 15-21-45

32. PERT (EXAMPLE-1) Activity to tm tp te var (σ2) σ 1-2 41 50 59 50 9 2-5 36 45 60 46 16_____________ (Route A) µ = ∑ te = 96 25 5 1-3 20 29 44 30 16 3-4 15 21 45 24 25 4-5 33 39 51 40 9____________ (RouteB) µ = ∑ te = 94 50 7.09

33. CUMULATIVE PROBABILITY CHART

34. PERT (EXAMPLE-1) Probability of completion in 100 days using route A Probability of completion in 100 days using route B

35. PERT (EXAMPLE -1) Using the expected values only, it will be seen that the route B should be selected, but owing to the greater activity time variance of the route B, the probability of earlier achivement by this route is not significantly greater than by the route A.

36. PERT (EXAMPLE-2) 4- 8-13 2-4-6 8-9-12 5-11-20 7-12-15 1-2-3 6-10-15 2-7-9 2 5 3 1 6 4 What is the total expected time for the completion of the project ?

37. PERT (EXAMPLE-2) Activity to tm tp te 1-4 6 10 15 10.17 4-6 2 7 9 6.5 µ = ∑ te = 16.67 1-4 6 10 15 10.17 4-3 1 2 3 2 3-5 2 4 6 4 5 -6 8 9 12 9.33 µ = ∑ te = 25.5

38. PERT (EXAMPLE-2) Activity to tm tp te 1-3 7 12 15 11.67 3-5 2 4 6 4 5-6 8 9 12 9.33 µ = ∑ te = 25 1-2 5 11 20 11.5 2-5 4 8 1 3 8.16 5-6 8 9 12 9.33 µ = ∑ te = 28.99 TOTAL EXPECTED TIME = 28.99