Project Test Bank is composed of activities we will refer to as A,B,C,and D for convenience (and lack of creativity).Durations and precedence requirements are shown in the table.Each of these activities can be conveniently laddered into two sub-activities of equal duration.The first half of each activity serves as the predecessor to its second half and the first half of the original following activity.What is the expected completion time of the laddered project? $$\begin{array} { | l | l | l | }
\hline \text { Activity } & \text { Length } & \text { Predecessor } \
\hline \text { A } & 10 & -- \
\hline B & 18 & \text { A } \
\hline C & 14 & \text { A } \
\hline D & 20 & \text { B, C } \
\hline
\end{array}$$
A)34
B)38
C)42
D)48

Question

Project Test Bank is composed of activities we will refer to as A,B,C,and D for convenience (and lack of creativity).Durations and precedence requirements are shown in the table.Each of these activities can be conveniently laddered into two sub-activities of equal duration.The first half of each activity serves as the predecessor to its second half and the first half of the original following activity.What is the expected completion time of the laddered project? $$\begin{array} { | l | l | l | } 
\hline \text { Activity } & \text { Length } & \text { Predecessor } \
\hline \text { A } & 10 & -- \
\hline B & 18 & \text { A } \
\hline C & 14 & \text { A } \
\hline D & 20 & \text { B, C } \
\hline
\end{array}$$
A)34
B)38
C)42
D)48

Quizplus · Accepted Answer

Laddering the project means breaking down each activity into two parts, each with half the original duration. The original project has activities A, B, C, and D with durations of 10, 18, 14, and 20 days, respectively. By laddering, we get:- A1 and A2 (5 days each),- B1 and B2 (9 days each),- C1 and C2 (7 days each),- D1 and D2 (10 days each).The critical path considering laddering and the precedence requirements (A before B and C; B and C before D) would be A1-A2-B1-B2-D1-D2. The total duration is 5 (A1) + 5 (A2) + 9 (B1) + 9 (B2) + 10 (D1) + 10 (D2) = 48 days. However, because B and C can start simultaneously after A, and their second halves (B2 and C2) can overlap with the first half of D (D1), the actual critical path duration is reduced. The longest path is through B (A1-A2-B1-B2-D1-D2), which totals 5 (A1) + 5 (A2) + 9 (B1) + 9 (B2) + 10 (D1) + 10 (D2) = 48, but with laddering and overlapping, the completion time is actually the sum of the longest sequence without unnecessary waiting, which is A (10) + B (18) + D (20) = 48. However, considering the correct calculation for the laddered and overlapped activities, the actual completion time is shorter. The correct calculation should consider the overlapping of activities and the correct sequence, leading to a different total duration. The mistake in the explanation is not accounting for the effective overlap in the laddered approach, which actually shortens the project duration from the original calculation. The correct approach would calculate the effective project duration based on the laddered activities and their overlaps, leading to a shorter duration than the longest individual path calculated without considering the laddering benefits. The correct answer, considering the laddering and the overlaps, should reflect the shortest project duration achievable with this method.

Project Test Bank Is Composed of Activities We Will Refer