Question

Use the information below to compress one-time unit per move using the least cost method. Reduce the schedule until you reach the crash point or the best cost value for this network. For each move identify what activity(s) should be crashed and the adjusted total cost. Total direct cost is $1000, total indirect cost is $800 and each time-unit reduction (cost gain) is $50. Activity Crash Cost per unit-time) Normal Normal Maximum time cost Crash Time 100 150 200 200 150 Total Direct Cost: 1,000 Total Direct Cost: Activities Changed: Total Direct Cost: Activities Changed:

Answer 1

Step 1: Identify the alternative paths and Critical path. Critical path is the path of longest duration in the network A-B-D-F 11 Critical path А-С-Е-F 13 Normal Time unit-times 13 Total Direct Cost 1,000 Total indirect cost 800 Cost gain 50 per unit-time Step 2: Project Crashing using least cost method 1. Identify and list the various alternative paths through the network and their respective duration 2. Determine Max crash time (=Normal time Crash time) and Crash cost per unit time -(Crash cost - Normal cost)/Max Crash Time for each activity. Also determine whether the crash cost rate remains constant as the activity is crashed, or it changes. Determine the variable crash costs by time, if they are variable. 3. Determine the critical path, i.e. the path of longest duration. Only activities along the critical path need to be crashed 4. Identify the eligible activity on the critical path having the least crash cost per unit time. and reduce by 1 time unit at a time. See if the critical path changes as the activities along the critical path are crashed. 5. If there are multiple critical paths at any stage during the crashing. Then determine whether there is any of the activites common to the critical paths. Then calculate whether the crash cost of common activity is less than the combined crash costs of the least cost crash cost activities along the critical paths. Cumulative Total Direct Activity Crash Path 1 Path 2 Project Activity Crash Cost Crash Cost Total ТОTAL Crashing Cost Gain Indirect Cost Duration Crashed Time A-B-D-F A-C-E-F COST Cost 0 11 13 13 1,000 800 0 1,800 1 C 1 11 12 12 50 50 1,050 800 50 1,800 2 1 11 11 11 70 120 1,120 800 100 1,820 3 F 1 10 10 10 90 210 1,210 800 150 1,860 D 1 10 10 60 270 1,270 800 150 1,920 4 1,940 1 9 9 70 340 1,340 800 200 In the above table, TOTAL COST Total direct cost + Total indirect cost - Cost Gain We see that after fourth crashing, all the activities of critical path (A-C-E-F) are fully crashed So, no further crashing is possible. Minimum-time schedule is reached. Minimum-Time Schedule Project Cost 1,940 Project Duration 9

Normal Time = 13

Total Direct Cost =1000

1)

Time = 12

Total Direct Cost =1050

Activities Changed: C

2)

Time = 11

Total Direct Cost =1120

Activities Changed: E

3)

Time = 10

Total Direct Cost =1210

Activities Changed: F

4)

Time = 9

Total Direct Cost =1340

Activities Changed: D, E