Use the information contained below to compress one time unit per move using the
ID: 376817 • Letter: U
Question
Use the information contained below to compress one time unit per move using the least cost method. Assume the total indirect cost for the project is $2000 and there is a savings of $100 per time unit reduced. Calculate the total direct, indirect, and project costs for each duration. What is the optimum cost-time schedule for the project? Note: The correct normal project duration and total direct cost are provided Activity Crash cost Maximum Slope) ID Crash Time Normal time Normal cost 2 4 $50 200 200 100 40 40 $200 1,000 800 1,000 800 1,000 1,000 200 4 Total direct normal costs $6,000Explanation / Answer
ACTIVITY ID
CRASH COST
MAX CRASH TIME
NORMAL TIME
NORMAL COST
CRASH COST/TIME UNIT
A
$ -
0
2
$ 200
$ -
B
$ 50.0
1
4
$ 1,000
$ 50.00
C
$ 200.0
2
5
$ 800
$ 100.00
D
$ 200.0
2
5
$ 1,000
$ 100.00
E
$ 100.0
1
3
$ 800
$ 100.00
F
$ 40.0
1
5
$ 1,000
$ 40.00
G
$ 40.0
1
4
$ 1,000
$ 40.00
H
$ -
0
1
$ 200
$ -
TOTAL DIRECT NORMAL COSTS
$ 6,000
TOTAL INDIRECT COST
$ 2,000
TOTAL PROJECT COST (W/O CRASHING)
$ 8,000
SAVING/TIME UNIT REDUCED
$ 100
POSSIBLE PATHS
DURATION
ABCEFH
20
<- CRITICAL PATH
ABCEGH
19
ABDEFH
20
<- CRITICAL PATH
ABDEGH
19
ACTIVITIES ARE CRASHED ONLY ON CRITICAL PATH
(CRITICAL ACTIVITY WITH MINIMUM CRASH COST/TIME UNIT IS CRASHED FIRST FOR THE MAX CRASH TIME )
ACTIVITY CRASHED:
F
CRASH COST/TIME UNIT
$ 40
CRASH DURATION
1
TIME UNIT
SAVING
$ 100
PROJECT COST
$ 7,940
COMPRESSING FROM TIME PERIOD 20 TO 19, ACTIVITY 'F' IS CRASHED
ADJUSTED TOTAL COST AT TIME PERIOD 19
$ 7,940
POSSIBLE PATHS
DURATION
ABCEFH
19
<- CRITICAL PATH
ABCEGH
19
<- CRITICAL PATH
ABDEFH
19
<- CRITICAL PATH
ABDEGH
19
<- CRITICAL PATH
(NOW ONLY ACTVITIES A,B,E & H CAN BE CRASHED AS ONLY THEY ARE COMMON IN ALL THE CRITICAL PATHS)
ACTIVITY CRASHED:
B
CRASH COST/TIME UNIT
$ 50
CRASH DURATION
1
SAVING
$ 100
PROJECT COST
$ 7,890
COMPRESSING FROM TIME PERIOD 19 TO 18, ACTIVITY 'B' IS CRASHED
ADJUSTED TOTAL COST AT TIME PERIOD 18
$ 7,890
POSSIBLE PATHS
DURATION
ABCEFH
18
<- CRITICAL PATH
ABCEGH
18
<- CRITICAL PATH
ABDEFH
18
<- CRITICAL PATH
ABDEGH
18
<- CRITICAL PATH
ACTIVITY CRASHED:
E
CRASH COST/TIME UNIT
$ 100
CRASH DURATION
1
SAVING
$ 100
PROJECT COST
$ 7,890
COMPRESSING FROM TIME PERIOD 18 TO 17, ACTIVITY 'B' IS CRASHED
ADJUSTED TOTAL COST AT TIME PERIOD 17
$ 7,890
POSSIBLE PATHS
DURATION
ABCEFH
17
<- CRITICAL PATH
ABCEGH
17
<- CRITICAL PATH
ABDEFH
17
<- CRITICAL PATH
ABDEGH
17
<- CRITICAL PATH
NO ACTIVITY CAN BE CRASHED FURTHER, AS ALL THE ACTIVITIES COMMON TO ALL PATHS HAVE BEEN CRASHED TO THEIR MAX ALLOWED LIMIT.
OPTIMUM COST-TIME SCHEDULE
TIME PERIOD
17
TOTAL COST
$ 7,890
ACTIVITY ID
CRASH COST
MAX CRASH TIME
NORMAL TIME
NORMAL COST
CRASH COST/TIME UNIT
A
$ -
0
2
$ 200
$ -
B
$ 50.0
1
4
$ 1,000
$ 50.00
C
$ 200.0
2
5
$ 800
$ 100.00
D
$ 200.0
2
5
$ 1,000
$ 100.00
E
$ 100.0
1
3
$ 800
$ 100.00
F
$ 40.0
1
5
$ 1,000
$ 40.00
G
$ 40.0
1
4
$ 1,000
$ 40.00
H
$ -
0
1
$ 200
$ -
TOTAL DIRECT NORMAL COSTS
$ 6,000
TOTAL INDIRECT COST
$ 2,000
TOTAL PROJECT COST (W/O CRASHING)
$ 8,000
SAVING/TIME UNIT REDUCED
$ 100
POSSIBLE PATHS
DURATION
ABCEFH
20
<- CRITICAL PATH
ABCEGH
19
ABDEFH
20
<- CRITICAL PATH
ABDEGH
19
ACTIVITIES ARE CRASHED ONLY ON CRITICAL PATH
(CRITICAL ACTIVITY WITH MINIMUM CRASH COST/TIME UNIT IS CRASHED FIRST FOR THE MAX CRASH TIME )
ACTIVITY CRASHED:
F
CRASH COST/TIME UNIT
$ 40
CRASH DURATION
1
TIME UNIT
SAVING
$ 100
PROJECT COST
$ 7,940
COMPRESSING FROM TIME PERIOD 20 TO 19, ACTIVITY 'F' IS CRASHED
ADJUSTED TOTAL COST AT TIME PERIOD 19
$ 7,940
POSSIBLE PATHS
DURATION
ABCEFH
19
<- CRITICAL PATH
ABCEGH
19
<- CRITICAL PATH
ABDEFH
19
<- CRITICAL PATH
ABDEGH
19
<- CRITICAL PATH
(NOW ONLY ACTVITIES A,B,E & H CAN BE CRASHED AS ONLY THEY ARE COMMON IN ALL THE CRITICAL PATHS)
ACTIVITY CRASHED:
B
CRASH COST/TIME UNIT
$ 50
CRASH DURATION
1
SAVING
$ 100
PROJECT COST
$ 7,890
COMPRESSING FROM TIME PERIOD 19 TO 18, ACTIVITY 'B' IS CRASHED
ADJUSTED TOTAL COST AT TIME PERIOD 18
$ 7,890
POSSIBLE PATHS
DURATION
ABCEFH
18
<- CRITICAL PATH
ABCEGH
18
<- CRITICAL PATH
ABDEFH
18
<- CRITICAL PATH
ABDEGH
18
<- CRITICAL PATH
ACTIVITY CRASHED:
E
CRASH COST/TIME UNIT
$ 100
CRASH DURATION
1
SAVING
$ 100
PROJECT COST
$ 7,890
COMPRESSING FROM TIME PERIOD 18 TO 17, ACTIVITY 'B' IS CRASHED
ADJUSTED TOTAL COST AT TIME PERIOD 17
$ 7,890
POSSIBLE PATHS
DURATION
ABCEFH
17
<- CRITICAL PATH
ABCEGH
17
<- CRITICAL PATH
ABDEFH
17
<- CRITICAL PATH
ABDEGH
17
<- CRITICAL PATH
NO ACTIVITY CAN BE CRASHED FURTHER, AS ALL THE ACTIVITIES COMMON TO ALL PATHS HAVE BEEN CRASHED TO THEIR MAX ALLOWED LIMIT.
OPTIMUM COST-TIME SCHEDULE
TIME PERIOD
17
TOTAL COST
$ 7,890
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