1. OPSM 301 Operations Management Class 27: Project Management: project crashing Koç University Zeynep Aksin zaksin@ku.edu.tr

2. Trade-Offs And Project Crashing  The project is behind schedule  The completion time has been moved forward It is not uncommon to face the following situations: Shortening the duration of the project is called project crashing

3. Factors to Consider When Crashing A Project  The amount by which an activity is crashed is, in fact, permissible  Taken together, the shortened activity durations will enable us to finish the project by the due date  The total cost of crashing is as small as possible

4. Steps in Project Crashing 1.Compute the crash cost per time period. For crash costs assumed linear over time: 2.Using current activity times, find the critical path 3.If there is only one critical path, then select the activity on this critical path that (a) can still be crashed, and (b) has the smallest crash cost per period. If there is more than one critical path, then select one activity from each critical path such that (a) each selected activity can still be crashed, and (b) the total crash cost of all selected activities is the smallest. Note that the same activity may be common to more than one critical path. 4.Update all activity times. If the desired due date has been reached, stop. If not, return to Step 2

5. Crashing The Project Time (Wks)Cost ($)Crash CostCritical ActivityNormalCrashNormalCrashPer Wk ($)Path? A2122,00022,750750Yes B3130,00034,0002,000No C2126,00027,0001,000Yes D4348,00049,0001,000No E4256,00058,0001,000Yes F3230,00030,500500No G5280,00084,5001,500Yes H2116,00019,0003,000Yes Table 3.5

6. Crash and Normal Times and Costs for Activity B (for Yozgat Paper)

7. Critical Path And Slack Times For Yozgat Paper Figure 3.17 E4E4 F3F3 G5G5 H2H2 481315 4 813 7 15 1013 8 48 D4D4 37 C2C2 24 B3B3 03 Start 0 0 0 A2A2 20 42 84 20 41 00 Slack = 1 Slack = 0 Slack = 6 Slack = 0

8. AON Network for Yozgat Paper Manufacturing with Incremental Crashing Costs Start A B C D F F G H H 13 2 15 H G 8 8 5 13 H F 4 10 3 7 13 H C 2 2 2 4 4 H E 4 4 4 8 8 H D 3 4 4 7 8 H B 0 1 3 3 4 H A 0 0 2 2 2 H 0 0 0 0 0 Start I=750 I=2000 I=1000 I=500 I=1500 I=3000

9. Look at all paths-as you crash other paths may become critical!  A-C-E-G-H critical 15 days  A-D-G-H 13 days  A-C-F-H 9 days  B-D-G-H 14 days

10. A has lowest crash cost on critical path-it can be crashed by 1 week  A-C-E-G-H critical 15 days -  14 days  A-D-G-H 13 days  12 days  A-C-F-H 9 days  8 days  B-D-G-H 14 days

11. A can no longer be crashed Need to consider both critical paths  A-C-E-G-H critical 15 days -  14 days  A-D-G-H 13 days  12 days  A-C-F-H 9 days  8 days  B-D-G-H 14 days  C is the next cheap activvity to crash  BUT Crashing C will require crashing another activity on th B-D-G-H path  G is common to both paths-just crashing one activity will take care of both paths!

12. Crashing Yozgat Paper Manufacturing Project  Minimum crashing plan: Activity A by 1 week and Activity G by 1 week Total Cost=$750 + $1500 = $2250 Why didn’t we crash Activity C??