1. 3/18/2016 12:47 AM 1 Time-Cost Trade-Off (Time Reduction = Time Compression = Time Shortening)

2. 3/18/2016 12:47 AM 2  The results of the planning and scheduling stages of the critical path method provide a network plan for the activities making up the project and a set of earliest and latest start and finish times for each activity. normal  In particular, the earliest occurrence time for the network terminal event is the estimated “normal” project duration time, based on “normal” activity time estimates.  The results of the planning and scheduling stages of the critical path method provide a network plan for the activities making up the project and a set of earliest and latest start and finish times for each activity. normal  In particular, the earliest occurrence time for the network terminal event is the estimated “normal” project duration time, based on “normal” activity time estimates.  Time-Cost Trade-off

3. 3/18/2016 12:47 AM 3  To meet the customer contractually required time.  To recover time of delays, that occur in the early stages of the project, to avoid paying liquated damages, or avoid damaging the company relationship with the customer.  To complete a project early, free key resources and move on to another project.  To avoid adverse weather.  To receive an early-completion bonus.  To meet a client’s desire for expediting the project.  To meet the customer contractually required time.  To recover time of delays, that occur in the early stages of the project, to avoid paying liquated damages, or avoid damaging the company relationship with the customer.  To complete a project early, free key resources and move on to another project.  To avoid adverse weather.  To receive an early-completion bonus.  To meet a client’s desire for expediting the project.  Why Project Time Reduction

4. 3/18/2016 12:47 AM 4 1.Free Time  Reviewing the job logic (critical activities in parallel).  Reviewing duration of critical activities.  Use overlap.  Use subcontractor. 1.Free Time  Reviewing the job logic (critical activities in parallel).  Reviewing duration of critical activities.  Use overlap.  Use subcontractor.  How to Shorten Project Time

5. 3/18/2016 12:47 AM 5 2.Buy Time overtime  Have the existing crew work overtime. additional workers (resources)  Bring in additional workers (resources) up to practical limit. shifts  Work on multiple shifts. incentive payments  Achieve more output by offering incentive payments. advanced equipment  Use better/more advanced equipment.  Use more quickly installed materials. subcontractors  Use subcontractors.  Change construction method. 2.Buy Time overtime  Have the existing crew work overtime. additional workers (resources)  Bring in additional workers (resources) up to practical limit. shifts  Work on multiple shifts. incentive payments  Achieve more output by offering incentive payments. advanced equipment  Use better/more advanced equipment.  Use more quickly installed materials. subcontractors  Use subcontractors.  Change construction method.  How to Shorten Project Time

6. 3/18/2016 12:47 AM 6 a minimum increase in the project direct costsbuying timecritical path least cost The main purpose of this topic is to demonstrate a procedure to determine activity schedules to reduce the project duration time with a minimum increase in the project direct costs, by buying time along the critical path (s) where it can be obtained at least cost.  Purpose of Time Reduction Technique Assumption Assumption: It is assumed in all of the procedures that are presented in this topic that unlimited resources are available.

7. 3/18/2016 12:47 AM 7  Definitions Activity time-cost trade-off input for the CPM procedure

8. 3/18/2016 12:47 AM 8 1.Activity Direct Costs 1.Activity Direct Costs : include the cost of the material, equipment, and direct labor required to perform the activity in question. If the activity is being performed in its entirety by a subcontractor, then the activity direct cost is equal to the price of the subcontract, plus any fee that may be added. 2.Project indirect costs 2.Project indirect costs : may include, supervision and other customary overhead costs, the interest charges on the cumulative project investment, penalty costs for completing the project after a specified date, and bonuses for early project completion. 1.Activity Direct Costs 1.Activity Direct Costs : include the cost of the material, equipment, and direct labor required to perform the activity in question. If the activity is being performed in its entirety by a subcontractor, then the activity direct cost is equal to the price of the subcontract, plus any fee that may be added. 2.Project indirect costs 2.Project indirect costs : may include, supervision and other customary overhead costs, the interest charges on the cumulative project investment, penalty costs for completing the project after a specified date, and bonuses for early project completion.  Definitions

9. 3/18/2016 12:47 AM 9 Normal Activity Time-cost Point 3.Normal Activity Time: normal 3.Normal Activity Time: It is the normal time that is used in the basic critical path planning and scheduling based on the normal level of resource. 4.Normal Activity Cost: direct costs 4.Normal Activity Cost: The normal activity cost is equal to the minimum of direct costs required to perform the activity, and the corresponding activity duration is called the normal time.  The normal time is actually the shortest time required to perform the activity under the minimum direct cost constraint. Normal Activity Time-cost Point 3.Normal Activity Time: normal 3.Normal Activity Time: It is the normal time that is used in the basic critical path planning and scheduling based on the normal level of resource. 4.Normal Activity Cost: direct costs 4.Normal Activity Cost: The normal activity cost is equal to the minimum of direct costs required to perform the activity, and the corresponding activity duration is called the normal time.  The normal time is actually the shortest time required to perform the activity under the minimum direct cost constraint.  Definitions

10. 3/18/2016 12:47 AM 10 Crash Activity Time-cost Point 5.Crash Activity Time: 5.Crash Activity Time: is fully expedited or minimum activity duration time that is technically possible. 6.Crash Cost: direct cost 6.Crash Cost: is assumed to be the minimum direct cost required to achieve the crash performance time. Crash Activity Time-cost Point 5.Crash Activity Time: 5.Crash Activity Time: is fully expedited or minimum activity duration time that is technically possible. 6.Crash Cost: direct cost 6.Crash Cost: is assumed to be the minimum direct cost required to achieve the crash performance time.  Definitions

11. 3/18/2016 12:47 AM 11  The relationship between the activity direct cost and activity time may be straight line, continuous curve, discrete values, or point.  The direct cost tends to increase if less time is available for activity. simple linear  Time reduction approach (learned here) will be based on simple linear time-cost trade-off curves for each activity  The relationship between the activity direct cost and activity time may be straight line, continuous curve, discrete values, or point.  The direct cost tends to increase if less time is available for activity. simple linear  Time reduction approach (learned here) will be based on simple linear time-cost trade-off curves for each activity  Activity Direct Cost / Time Relationship Activity time-cost trade-off input for the CPM procedure

12. 3/18/2016 12:47 AM 12  The indirect cost tends to increase if more time is consumed for the project. linearly  The indirect cost is generally vary approximately linearly with the time.  The indirect cost tends to increase if more time is consumed for the project. linearly  The indirect cost is generally vary approximately linearly with the time.  Indirect Cost / Time Relationship

13. 3/18/2016 12:47 AM 13  Optimum Contract Duration Optimum contract duration = project schedule for minimum total cost Determining project schedule for minimum total cost

14. 3/18/2016 12:47 AM 14 The 8 step hand procedure presented below is a slight modification of the method developed by Siemens. The key element of this procedure is the cost slope and time available. The cost slope will be denoted by C ij for an arbitrary activity (i – j). 1.Cost Slope (C ij ) for an arbitrary activity (i – j) = [Crash cost (C d ) - Normal cost (C D )] ij / [Normal duration (D) - Crash duration(d)] ij 2.Time Available (TA ij ) = [Normal duration (D ) - Crash duration(d)] ij An “effective” cost slope, EC ij, is defined as the cost slope divided by the number of inadequately shortened paths, N ij, which contain activity (i –j) 3.Effective Cost Slope (EC ij ) = Cost slope (C ij ) / Number of inadequately shortened paths (N ij )  The procedure described below chooses from among all available activities to be shortened, the one with the lowest effective cost slope.  Modified Siemens Algorithm

15. 3/18/2016 12:47 AM 15 1.Prepare the project network and time estimates, and list in columns all paths through the network whose expected lengths are greater than the desired (scheduled) project duration, T s. The length of a path is merely the sum of the durations of all activities on the path in question. Also note at the bottom of each path column (row marked iteration 0), the time reduction that is required, i.e., expected path length minus T s. 2.List (in rows) all activities present in at least one of the listed paths noting for each activity its cost slope, C ij, and time reduction available, TA ij. 3.Compute the effective cost slopes, EC ij, and record them in the column headed iteration 1.  Modified Siemens Algorithm

16. 3/18/2016 12:47 AM 16 4.For the path(s) with the most remaining time reduction required, select the activity with the lowest effective cost slope. Break ties by considering the following ordered list: 1.Give preference to the activity which lies on the greatest number of inadequately shortened paths. 2.Give preference to the activity which permits the greatest amount of shortening. 3.Choose an activity at random. 5.Shorten the selected activity (i-j) as much as possible, which will be equal to the minimum of the following: 1.The unallocated time remaining for the selected activity (i-j), or 2.The smallest demand of those inadequately shortened paths containing the activity (i-j).  Modified Siemens Algorithm

17. 3/18/2016 12:47 AM 17 6.Sell back, or deshorten, as much time possible on paths that have been overcut, as long as this action does not cause any new paths to become inadequately shortened. 7.Stop of all paths have been adequately shortened. If not, recalculate those effective cost-slopes where any of the following have occurred: 1.A path which was inadequately shortened prior to this iteration, has been adequately shortened, or 2.All unallocated time for the activity just shortened has been consumed and there are one or more additional cost- slope/supply pairs for this activity. 8.Return to Step 4.  Modified Siemens Algorithm

18. 3/18/2016 12:47 AM 18  Example 1 The below network shows the activities of a small engineering project. Data of the project is given in the below table. The indirect cost is estimated to be SR100/day. It required to reduce the project duration to 17 days. Also draw the contract total cost/time curve and determine the optimum contract duration. Activity Code Time (day)Cost (SR) NormalCrashNormalCrash A 43210280 B 86400560 C 64500600 D 97540600 E 415001,100 F 54150240 G 33150 H 76600750

19. 3/18/2016 12:47 AM 19 Project Network  Example 1

20. 3/18/2016 12:47 AM 20  Example 1

21. 3/18/2016 12:47 AM 21  Reduction Project Time from 22 to ActivityPath s Requiring Reduction Cost Slope Time Reduction Available Effective Cost Slope Iteration No. 123456

22. 3/18/2016 12:47 AM 22 1.Reduction Project Time from 22 to 17 day ActivityPath s Requiring Reduction Cost Slope Effective Cost Slope Time Reduction Available A-C-F-HA-D-HB-F-H A (0,1)1170351 0 B (0,2)180 2 1 C (1,2)250 2 0 D (1,4)130 2 1 F (2,4)1190451 0 H (4,5)111150501 0  The cross-hatching in the above Figure is used to denote the activities that are not present in the path indicated at the head of the column.

23. 3/18/2016 12:47 AM 23  Reduction Project Time from 22 to 21 ActivityPath s Requiring Reduction Cost Slope Effective Cost Slope Time Reduction Available A-C-F-H A (0,1)70 1 C (1,2)150 2 1 F (2,4)90 1 H (4,5)150 1

24. 3/18/2016 12:47 AM 24  Reduction Project Time from 22 to 20 ActivityPath s Requiring Reduction Cost Slope Effective Cost Slope Time Reduction Available A-C-F-H A (0,1)70 1 C (1,2)250 2 0 F (2,4)90 1 H (4,5)150 1

25. 3/18/2016 12:47 AM 25  Reduction Project Time from 22 to 19 ActivityPath s Requiring Reduction Cost Slope Effective Cost Slope Time Reduction Available A-C-F-HA-D-HB-F-H A (0,1)1170351 0 B (0,2)80 2 C (1,2)150 2 D (1,4)30 2 F (2,4)1190451 0 H (4,5)150501

26. 3/18/2016 12:47 AM 26  Reduction Project Time from 22 to 18 ActivityPath s Requiring Reduction Cost Slope Effective Cost Slope Time Reduction Available A-C-F-HA-D-HB-F-H A (0,1)1170351 B (0,2)80 2 C (1,2)150 2 D (1,4)30 2 F (2,4)1190451 H (4,5)111150501

27. 3/18/2016 12:47 AM 27 Project Duration (Days) 171819202122 Total Direct Costs (SR)357034103260315031003050 Indirect Costs (SR)170018001900200021002200 Total Costs (SR) 527052105160515052005250  Direct Cost / Time Relationship

28. 3/18/2016 12:47 AM 28 Project Duration (Days) 171819202122 Total Direct Costs (SR)357034103260315031003050 Indirect Costs (SR)170018001900200021002200 Total Costs (SR) 527052105160515052005250  Indirect Cost / Time Relationship

29. 3/18/2016 12:47 AM 29 Project Duration (Days) 171819202122 Total Direct Costs (SR)357034103260315031003050 Indirect Costs (SR)170018001900200021002200 Total Costs (SR) 527052105160515052005250  Optimum Contract Duration

30. 3/18/2016 12:47 AM 30  Optimum Contract Duration Optimal Project Duration = 20

31. 3/18/2016 12:47 AM 31 The durations and direct costs for each activity in the network of a small engineering project under both normal and crash conditions are given in below Table. Determine the optimum duration of the contract assuming the indirect cost amounts to SR 125/ week. ActivityPreceded by NormalCrash Duration (weeks) Cost (SR) Duration (weeks) Cost (SR) A—127000107200 BA8500065300 CA154000124600 DB235000235000 EB5100041050 FC5300043300 GE,C206000156300 HF132500112580 ID, G, H123000103150  36,500  Example 2

32. 3/18/2016 12:47 AM 32 2@100 0012 0 A 1@300 27232 29534 F 3@200 12027 121527 C 2@150 12220 14822 B 0 20443 242347 D 1@50 20225 22527 E 5@60 27047 272047 G 2@75 47059 471259 I 2@40 32245 341347 H ESTFEF LSDLF Activity Time Available @ Cost Slope  Example 2

33. 3/18/2016 12:47 AM 33  Reduction Project Time from 59 to ActivityPath s Requiring Reduction Cost Slope Time Reduction Available Effective Cost Slope Iteration No. 123456

34. 3/18/2016 12:47 AM 34  Reduction Project Time from 59 to 57 ActivityPath s Requiring Reduction Cost Slope Effective Cost Slope Time Reduction Available A-C-G-I A100 2 C200 3 G260 5353 I75 2

35. 3/18/2016 12:47 AM 35  Reduction Project Time from 59 to 55 ActivityPath s Requiring Reduction Cost Slope EC (1) EC (2) EC (3) EC (4) EC (5) Time Reduction Available A-C-G-IA-B-E-G-IA-C-F-H-I A10033.31002 C2001002003 G26030605353 I2227525X2020 B150 X2 E50 X1 F300 X1 H40 X2

36. 3/18/2016 12:47 AM 36  Reduction Project Time from 59 to 53 ActivityPath s Requiring Reduction Cost Slope Effective Cost Slope (1) Effective Cost Slope (2) Effective Cost Slope (3) Time Reductio n Available A-C-G-IA-B-E-G-IA-C-F-H-IA-B-D-I A221002533.3502020 C200100 3 G226030 605353 I22227518.75XX2020 B15075150X2 E50 X1 F300 1 H40 2 DXXXX0

37. 3/18/2016 12:47 AM 37  Reduction Project Time from 59 to 51 ActivityPath s Requiring Reduction Cost Slope EC (1) EC (2) EC (3) EC (4) EC (5) Time Reduction Available A-C-G-IA-B-E-G-IA-C-F-H-IA-B-D-I A222210025 XXX2020 C200100 3 G2 426030 60 5353 I22227518.XXXX2020 B15075 150XX2020 E50 XX1 F300 1 H240 X2020 DXXXXXX0

38. 3/18/2016 12:47 AM 38  Reduction Project Time from 59 to 49 ActivityPath s Requiring Reduction Cost Slope EC (1) EC (2) EC (3) EC (4) EC (5) EC (6) Time Reduction Available A-C-G-IA-B-E-G-IA-C-F-H-IA-B-D-I A222210025 XXXX2020 C22200100 3 G446030 60 5151 I22227518.XXXXX2020 B215075 150 X2020 E50 XXX1 F300 1 H240 XX2020 DXXXXXXX0

39. 3/18/2016 12:47 AM 39 Cycle #Project DurationDirect CostIndirect CostTotal Cost 05936500737543875 15736620712543745 25536770687543645 35336970662543595 45137170637543545 54937870612543995  Optimum Contract Duration

40. 3/18/2016 12:47 AM 40  Class work