1. Time-Cost Trade-off Models
Develops the relationship between direct costs, indirect costs, and time to complete the project by minimizing the sum of direct and indirect costs.
Crash – shortening activity duration
Crash Costs
Additional costs of an activity when time to complete it is shortened.
Crashing costs increase as project duration decreases
Indirect costs increase as project duration increases

2. Time-Cost Tradeoff Minimum cost = optimal project time Total cost
Indirect cost
Direct cost
Crashing
Time
Project Duration

3. Minimum-Cost Scheduling
Step 1: Prepare the network diagram.
a. Normal cost (NC)
b. Normal time (NT)
c. Crash time (CT)
d. Crash Cost (CC)
Step 2: Determine cost per unit of time to crash each activity.
Step 3: Compute the critical path.
Step 4: Shorten the critical path at the least cost.

4. Time-cost Trade-offs: Crashing
Procedure for crashing
Crash the project one period at a time
Only an activity on the critical path
Crash the least expensive activity
Multiple critical paths: find the sum of crashing the least expensive activity on each critical path

5. Activity Graph

6. Project Crashing
Crashing is reducing project time by expending additional resources
Crash time is an amount of time an activity is reduced
Crash cost is the cost of reducing the activity time
Goal is to reduce project duration at minimum cost

7. Project Crashing
Crashing a project involves paying more money to complete a project more quickly.
Since the critical path determines the length of a project, it makes sense to reduce the length of activities on the critical path.
CP activities should be reduced until the project is reduced to the desired length or you are paying more per day than you save..

8. Cost-Time Trade-Off Example

9. Cost-Time Trade-Off Example (continued)

11. Project Cost-Time Graph

13. Calculation of Cost/Day to Accelerate Each Activity

14. Reducing Project Completion Time One Day at a Time

15. Plot of Costs and Minimum Cost Schedule

16. House-building Network
Activity times in weeks 3 8 12 4 1 2 4 6 7 12 4 4 4 5

17. Normal Activity And Crash Data
Total
Normal Crash Allowable Crash
Time Time Normal Crash Crash Time Cost per
Activity (wks) (wks) Cost Cost (wks) Week
$3,000 $5,000 5 $400
,000 3,
,000 7, ,000 ,
,000 71, ,000 ,
,000 22, ,000
$75,000 $110,700

18. Network With Crashing Costs
Activity 1-2 can be crashed a total of 5 weeks for $2000
Crash cost per week = Total crash cost/Total crash time
= $2,000/5 = $400 per week 3
$500 8
$7,000 12 4
$7,000 1 2 4 6 7
$400
$3,000 12 4 4 4
$200
$200 5

19. Crashing Solution Normal Crash Crash Crash Crashing
Time Time Time Cost per Cost
Activity (wks) (wks) Used Week Incurred
$400 $2,000
,500
,000 0
,000 21,000
,000 7,000
12 $31,500

20. Crashed Project 1 2 4 6 7 3 5
Original time Crashed times

21. Project Crashing: Example1 12 2 8 4 3 5 6 7

22. Normal Activity and Crash Data
TOTAL
NORMAL CRASH ALLOWABLE CRASH
TIME TIME NORMAL CRASH CRASH TIME COST PER
ACTIVITY (WEEKS) (WEEKS) COST COST (WEEKS) WEEK
$3,000 $5,000 5 $400
,000 3,
,000 7, ,000
,000 71, ,000 , ,
,000 22, ,000
$75, $110,700

23. FROM … TO… Project Duration: 36 weeks Project Duration: 31 weeks
$7000
$500
Project Duration:
36 weeks 12 4 2 8
$700 7 4 1 12
FROM … 6 4
$400 3 4 5 4
$200
$3000
$200 1 7 2 8 3 4 5 6
$400
$500
$3000
$7000
$200
$700 12
TO…
Project Duration:
31 weeks
Additional Cost:
$2000