Time Cost Trade-off Aspects in Network Technique

- By manipulating resources in a project, we can get a range of possible solutions and obtain a number of project durations and corresponding minimum cost.

- In any project, costs can be broadly divided as.i) Direct project costs, andii) Indirect project costs.

Direct Project Costs- Direct project costs are that expenditure, which are directly

chargeable to each and every activity of the project. - These are manpower loading, equipment utilized, material

consumed directly, etc., in respect of such activity. - Behaviour of project direct costs with time is presented below.

DirectCosts

Time

Indirect Project Costs

- Indirect project costs are those expenditures, which can not be apportioned or allocated to individual activities of the project.

- These expenditures include administrative and establishment charges, other common expenditures such as salaries and wages of engineering staff and clerical staff, etc.

- Behaviour of the indirect project costs with time is presented below:

IndirectCosts

Time

Total Project Cost- Total project cost is the sum of project direct cost and project

indirect costs. - Behaviour of total project cost with project duration is

presented below:

Total ProjectCost

XProject Duration

- At point X total project cost is minimum. - Project duration X represents minimum duration with least cost. - Point may therefore be called as the optimum Time-Cost point

of the curve which the project manager can choose for the implementation of the project.

Cost Estimates for Crashing of Activities involved in the Transmission Line Project are presented below

Activity Activity Description Normal Estimate Crash EstimateTime (weeks)

Direct Cost (Rs. lakhs)

Time (weeks)

Direct Cost(Rs. lakhs)

(1, 2) Survey 12 1.0 9 2.5(2, 3) Estimate and Sanction 4 - 3 0.4(2, 4) Tree Cutting Schedule 20 - 20 -(3, 5) Procure Stubs and

Tower Parts20 5.0 14 6.5

(3, 6) Award of Contract for Stub Setting

8 - 4 0.2

(3, 7) Award of Contract for Tower Erection

8 - 4 0.2

(6, 7) Stub Setting 8 0.5 5 1.0(4, 7) Tree Cutting 8 0.4 5 1.0(7, 8) Tower Erection and

Stringing12 3.0 9 4.0

(8, 9) Energizing 4 0.1 1 0.5Indirect Costs – Rs.35,000 per week

- Determine the project duration corresponding to minimum total cost

Solution:

Rules for Crashing of Activities in a Network- To expedite the project, the activities on the critical path shall

be crashed. - There is no use to crash activities lying on the non-critical path- Critical Path alone may be crashed until its duration reaches

the duration of near critical path- Once the duration of Critical Path reaches duration of near

Critical Path, near Critical Path also becomes Critical Path- Any further crashing will require crashing of activities lying in

Critical Path and near Critical Path (which has now become critical)

- Critical activity having least cost slope shall be crashed first. This will ensure reduction in duration of project with least increase in direct cost and this will ensure reduction in Indirect cost of the project.

- This process will be repeated until the duration of the project with least total cost of the project is achieved

Cost Slope for Direct Cost of the activities involved in the project is presented below

Activity Normal Estimates Crash Estimates Cost Slope(Rs. lakh/

week)Time

(weeks)Direct Cost

(Rs.lakh)

Time (weeks)

Direct Cost

(Rs. lakh)(1, 2) 12 1.0 9 2.5 0.5(2, 3) 4 - 3 0.4 0.4(2, 4) 20 - 20 - Non –

Crash able(3, 5) 20 5.0 14 6.5 0.25(3, 6) 8 - 4 0.2 0.05(3, 7) 8 - 4 0.2 0.05(6, 7) 8 0.5 5 1.0 0.166(4, 7) 8 0.4 5 1.0 0.20(7, 8) 12 3.0 9 4.0 0.333(8, 9) 4 0.1 1 0.5 0.133

10.0Indirect Cost = 0.35 lakh/week

- Critical Path of the Project is 1 – 2 – 3 – 5 – 6 – 7 – 8 – 9- Duration : 60 weeks- Direct cost in normal duration of 60 weeks is Rs.10,00,000/-- Indirect Cost in normal duration is Rs.0.35 X 60 = 21,00,000/-- Total Cost in Normal Duration of 60 days is Rs.31,00,000/-

Step I:- Cost slope of activity (8, 9) is one of the minimum, i.e. 0.133 lakh/week, and this

activity is common to all paths. Hence any reduction in duration of (8, 9) will reduce the duration of the project

- Activity (8,9) has been crashed by 3 weeks - Duration of the project will reduced to 57 weeks- Direct Cost for 57 weeks duration is Rs.10,00,000 + 40,000 = 10,40,000- Indirect Cost for 57 weeks duration is Rs.0.35X 57 = 19,95, 000/-- Total Cost for 57 weeks duration is Rs.30,35,000/-

Step II: - Minimum cost slope for the remaining critical activity is (6, 7) with a cost slope of

0.166 lakh/week

- Crash (6, 7) by three weeks

- Project time duration will reduced to 54 weeks- Direct Cost for 54 weeks duration is Rs.10,00,000 +40,000 + 50,000 = 10,90,000- Indirect Cost for 54 weeks duration is Rs.0.35X 54 = 18,90, 000/-- Total Cost for 54 weeks duration is Rs.29,80,000/-

Step III- We have not yet reached the near critical path’s duration.- One more week is left to reach the near critical path’s duration.- Next least cost option for critical activity is (3, 5) with a cost slope is 0.25 lakh/week

- Crash (3, 5) by 1 week

- Project time duration will be 53 weeks- Direct Cost for 53 weeks duration is Rs.10,90,000 + 25,000 = 11,15,000- Indirect Cost for 53 weeks duration is Rs.0.35X 53 = 18,55, 000/-

- Total Cost for 53 weeks duration is Rs.29,70,000/-

Step IV- Now the following paths have become critical- Path 1- 2 – 3 – 5 – 6 – 7 - 8 – 9 and path 1 – 2 – 4 – 7 – 8 – 9- Choice of crashing of activities in this stage are as follows:- Crash Activity (3, 5) and (4, 7) at total additional cost of 0.25 + 0.125 = 0.375- Crash Activity (7, 8) common to both paths and at total additional cost of = 0.333- Crash Activity (1, 2) common to both paths and at total additional cost of = 0.5- Crash Activity (2, 3) and (4, 7) at total additional cost of 0.4 + 0.125 = 0.525- Crash Activity (7, 8) by 3 weeks - Project duration will be 50 weeks

- Direct Cost for 50 weeks duration is Rs.11,15,000 + 1,00,000 = 12,15,000- Indirect Cost for 50 weeks duration is Rs.0.35X 50 = 17,50, 000/-- Total Cost for 50 weeks duration is Rs.29,65,000/-

Step V:- Choice of crashing of activities in this stage are as follows:- Crash Activity (3, 5) and (4, 7) at total additional cost of 0.25 + 0.125 = 0.375- Crash Activity (1, 2) common to both paths and at total additional cost of = 0.5- Crash Activity (2, 3) and (4, 7) at total additional cost of 0.4 + 0.125 = 0.525

- Crash Activities (3, 5) and (4, 7) each by 4 weeks

- Project duration will be 46 weeks - Direct Cost for 46 weeks duration is Rs.12,15,000+ 1,50,000 =13,65,000/-- Indirect Cost for 46 weeks duration is Rs.0.35X 46 = 16,10, 000/-- Total Cost for 46 weeks duration is Rs.29,75,000/-

- It can be observed that the Total Cost has started increasing with the reduction in duration. Thus the optimum duration of the project is 50 weeks at a total cost of Rs.29,65,000/-