ABC Construction has developed the following set of activities for its budgeting

Question

ABC Construction has developed the following set of activities for its budgeting process.

Activity

Predecessor

Normal Activity Time (Days)

Resulting Activity Time if Activity is Crashed (Days)

Total Cost to complete activity in Normal Time

Total Cost to complete activity in Crash Time

A

--

4

2

$200

$600

B

A

6

3

$300

$1200

C

A

4

1

$300

$900

D

B, C

3

2

$500

$550

E

D

4

1

$500

$1700

a) Using the Normal Times, what is the critical path and project completion time for the budgeting process? Also, what is the cost to complete the project based on the Normal Times?

b) If we want to reduce the project completion time to the minimum possible time by crashing activities, what is the new project completion time and what is the new total project cost?

c) Modify the problem as follows. There is now an indirect cost of $75 per day, which is in addition to the cost identified above. There is also a penalty cost of $200 per day for any project completion time over 11 days. What is the minimum cost schedule for the project and what is the total cost for this schedule? Identify what are the time and the path of this minimum cost schedule.

d) Suppose that the company wants to crash the project 4 days. Based on the information provided in the table and in part c) and the results from part c), what would the minimum penalty cost have to be for this to be supported by the economics in the problem? Assume that the indirect cost remains at $75 per day.  

Activity

Predecessor

Normal Activity Time (Days)

Resulting Activity Time if Activity is Crashed (Days)

Total Cost to complete activity in Normal Time

Total Cost to complete activity in Crash Time

A

--

4

2

$200

$600

B

A

6

3

$300

$1200

C

A

4

1

$300

$900

D

B, C

3

2

$500

$550

E

D

4

1

$500

$1700

Explanation / Answer

(a) After drawing the network diagram, the Critical path is

A - B- D - E = 17 days

Means the project completion time is 17 days

Project cost will = 200 + 300 + 500 + 500 = $ 1500

(b) for crashing one has to find out the slope = Crash cost - Normal cost / Normal time - Crash time

Activity Slope

A 600 - 200 / 4-2 = $ 200 per day

B 1200 - 300 / 3 = $ 300

C 900 -300 / 3 = $ 200

D 550 -500 / 1 = $ 50

E 1700 - 500 / 3 = $400

After that we will select one by one each activity lying on the critical path.

Then the resultant reduced project time is = 11 days and

Cost is Normal cost + Crashing cost

Cost = $ 1500 + $ 5 + $ 400 + $ 900 = $ 2850

(c) Indirect cost given = $ 75per day

Total cost = direct + indirect = $ 2850 + 11 x 75 = $ 3675

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