Deck 5: Project Scheduling Models

Question 1

The critical path:

A)is the shortest path through the network.
B)is necessarily unique.
C)Is defined by activities with zero slack.
D)Shows, by elimination, which activities management can safely ignore.

Answer 1

C

Question 2

Since PERT allows randomness, it is not necessary to know the precise activity precedence relations to use PERT.

Answer 2

False

Question 3

Resource leveling can apply to either costs or to the time of people working on the project.

Answer 3

True

Question 4

If a critical task is delayed, we either must add resources, miss the project deadline, or sacrifice quality.

Question 5

The "forward pass" determines the earliest start and finish times for activities in a project.The "backward pass" establishes latest start and finish times.

Question 6

The earliest start (ES) time for an activity is the latest earliest finish (EF) time of all its immediate predecessors.

Question 7

Any attempt at resource leveling always will involve lengthening the project completion time beyond its "non-leveled" minimum.

Question 8

A Gantt chart, by definition, does not show precedence relations.However, you could add precedence relations by drawing arrows on the Gantt chart.

Question 9

The critical path shows the earliest project completion date by finding the shortest path through the directed network.

Question 10

The earliest start time (ES) of an activity:

A)equals its earliest finish time (EF) minus task time.
B)equals the minimum earliest finish time (EF) of all immediate predecessors.
C)equals the latest start time (LS) for non-critical activities.
D)may not be the same for two or more activities.

Question 11

A PERT/CPM network can be represented as a linear programming model by letting the decision variables be the activity start times.

Question 12

In project scheduling, activities:

A)must be completed sequentially.
B)are the tasks of a project.
C)are work packages.
D)are not represented on Gantt charts.

Question 13

Typically, the first step in project scheduling is the construction of a:

A)Gantt chart.
B)Critical path chart.
C)PERT chart.
D)set of precedence relationships between the activities.

Question 14

In PERT, the acceptance of a Beta distribution for activity completion times and the presence of a sufficient number of activities, lead to the assumption of a normal distribution of possible completion times for the overall project.

Question 15

PERT (Program Evaluation and Review Technique) generally treats activity completion times as probabilistic and:

A)is used to construct a Gantt chart.
B)is used to determine the probability that a project will be complete within a given time frame.
C)can be used to determine the exact completion time of an activity.
D)can be used to determine the exact completion time of a project.

Question 16

GANTT stands for "Generalized Activity Normalization Time Table."

Question 17

The critical path is always unique.

Question 18

Overall project completion time will not be affected if an activity possessing slack time is started at any time between its earliest and latest start time.

Question 19

Using the Critical Path Method, the normal time to complete activity D is 10 weeks, and its normal cost is $500.Under maximum crashing, activity D can be completed is 4 weeks for $2,300.Therefore, if $1,100 is spent on activity D, its completion time will be 6 weeks.

Question 20

A disadvantage of Gantt chart methodology is that an earliest possible completion date for the project cannot be determined.

Question 21

When attempting to use PERT methodology, how do you estimate the mean completion time and standard deviation when, for a given activity, the time estimates a, b, and m (pessimistic, optimistic, and most likely) are all identical? What implications does this have if several activities have this property?

Question 22

In the critical path method (CPM), crashing does not:

A)deal with accelerating a project's overall completion time.
B)assume that every activity completion time can be crashed.
C)require two time estimates for each activity's duration time.
D)take into account the possibility of creating multiple critical paths.

Question 23

Activity T has a single immediate predecessor, activity S.However, T may actually be initiated anytime after S is 50% complete.Can this situation be accommodated using standard project scheduling techniques? Explain.

Question 24

Let T_i = normal completion time for task iR_i = crash completion time for task i C_i = normal cost for task i
H_i = crash cost for task i
X_i = start time for task i
Y_i = amount of time by which task i is to be crashed.
What is the objective function of a linear programming model for project crashing?

A) $\Sigma$ _{all i} Y_i(H_i - C_i)/(T_i - R_i)
B) $\Sigma$ _{all i on critical path} Y_i(H_i - C_i)/(T_i - R_i)
C) $\Sigma$ _{all i} X_iY_i
D) $\Sigma$ _{all i} Y_iH_i

Question 25

A "forward pass" in network analysis of a project, determines:

A)earliest times.
B)latest times.
C)slack times.
D)most likely times.

Question 26

Which of the following is true?

A)PERT gives a better solution than the expected value criterion.
B)To use the expected value criterion, we must know every possible outcome.
C)The expected value criterion determines the optimal decision by choosing the best expected payoff.
D)Adding resources will decrease the project time to completion.

Question 27

The probabilistic approach characterized by PERT does not use:

A)optimistic activity times.
B)median activity times.
C)pessimistic activity times.
D)most likely activity times.

Question 28

Discuss the assumptions required for determining the probability that a project will be completed within a certain time period by using a normal distribution of the activity time along the critical path determined by mean completion times of the critical activities.Do you think they are realistic for most projects?

Question 29

In the PERT probabilistic approach, statisticians have found which distribution most helpful in describing possible activity times?

A)Beta
B)Gamma
C)normal
D)uniform

Question 30

Activity C is an immediate predecessor of activity G.Both activities have 4 hours of slack time.If both activities are delayed 3 hours, and these are the only delays, the overall effect of these delays is to delay the minimum project completion time by:

A)0 hours.
B)2 hours.
C)6 hours.
D)The overall delay cannot be determined with only this information.

Question 31

Ajax is about to embark on a project involving the design, manufacture, and introduction of a new microwave oven.The first three activities and the immediate predecessors are: $\begin{array}{lcc}&\text { Activity } &\text { Predecessor }\\\text { A } & \text { Prototype Design } & \text { none } \\\text { B } & \text { Acquisition of Materials } & \text { A } \\\text { C } & \text { Prototype Construction } & \text { B }\end{array}$
However, it has not yet been decided whether the prototype materials will be purchased from a vendor (taking two weeks) or produced in another Ajax division (four weeks).What are the implications of this regarding usage of any standard project scheduling technique?

Question 32

A project contains activities D and K.Activity D has 5 hours of slack, and activity K has 7 hours of slack.If activity D is delayed 4 hours, activity K is delayed 6 hours, and these are the only delays, then the overall effect of these delays is to delay the minimum project completion time by:

A)0 hours.
B)2 hours.
C)11 hours.
D)The overall delay cannot be determined with only this information.

Question 33

Which of the following is not a fundamental, inherent weakness in the probabilistic approach to PERT?

A)One may have difficulty in obtaining three reliable time estimates for each activity.
B)There is the possibility of large variances for non-critical activities.
C)The assumption that activity times are independent of each other.
D)The assumption that possible overall project completion times are Beta-distributed.

Question 34

PERT/Cost is a cost-center based system, where the "centers" are:

A)locations.
B)work packages of groups of related activities.
C)activities.
D)departments.

Question 35

PERT/Cost:

A)allows for activity interruption.
B)assumes costs are evenly spread over time.
C)monitors project performance relation to cost, not time.
D)cannot help identify cost under-runs.

Question 36

Let B = budgeted total cost for a work package T = estimated completion time for a work package
P = percent complete
A = actual expenses to date
M = time used to date
What is the definition of cost overrun, C?

A)C = A - PB
B)C = A - (1 - P)TB
C)C = A - PTB
D)C = A - MB/T

Question 37

Which of the following is false?

A)Crashing an activity on the critical path can cause another path to become the critical path.
B)The maximum crash time reduction for each and every activity is limited.
C)CPM assumes that adding resources to crash an activity from its normal time to its crash time will reach a point of diminishing returns.
D)Crashing non-critical activities will not reduce the project time.

Question 38

In using PERT/CPM, why does management need to pay any attention at all to non-critical path activities?

Question 39

Which statement does not represent a set of constraints for a linear programming approach to project crashing?

A)There is a limit to the time reduction for each activity.
B)No activity can be reduced more than its slack time.
C)Activity start time must be greater than the finish time of all immediate predecessors.
D)The project must be completed by the deadline (or within budget).

Question 40

Which of the following is true?

A)Slack = (LF - LS)
B)(LF - LS) > (EF - ES)
C)Slack is never "shared."
D)(LS - ES) $\ge$ 0

Question 41

Given the following data for work packages in a PERT/Cost network at week 18:
$\begin{array}{cccccc}\text { Activity } & \begin{array}{c}\text { Immediate } \\\text { Predecessors }\end{array} & \begin{array}{c}\text { Budgeted } \\\text { Time } \\\text { (weeks) }\end{array} & \begin{array}{c}\text { Budgeted } \\\text { Value }\end{array} & \begin{array}{c}\text { Percent } \\\text { Complete }\end{array} & \begin{array}{c}\text { Expense To } \\\text { Date }\end{array} \\\text { A } & -- & 12 & \$ 50,000 & 1008 & \$ 48,000 \\\text { B } & -- & 8 & \$ 20,000 & 1008 & \$ 21,000 \\\text { C } & \text { A } & 6 & \$ 60,000 & 758 & \$ 40,000 \\\text { D } & \text { B } & 16 & \$ 40,000 & 508 & \$ 25,000 \\\text { E } & \text { C, D } & 16 & \$ 45,000 & 08 & 0 \\\text { F } & \text { B } & 28 & \$ 80,000 & 758 & \$ 55,000\end{array}$
A.Is the project currently experiencing a cost overrun?
B.Is the project on target to be completed within 40 weeks?
C.What corrective action, if any, could you recommend?

Question 42

Explain the Excel functions
NORMINV(0.98,200,10)
NORMDIST(190,200,10,TRUE).

Question 43

Why must we solve two linear programming models to model a PERT/CPM network?

Question 44

A project consists of the following seven activities and immediate predecessors: $$\begin{array} { c c } \text { Artivity } & \text { Predecegsor } \\\text { A } & \text { None } \\\text { B } & \text { A } \\\text { C } & \text { A } \\ \text { D } & \text { B } \\\text { E } & \text { B, C }\\\text { F } & \text { D, E }\\\text { G } & \text { F }\end{array}$$ Construct an AON network diagram for the project.

Question 45

Activity A is critical.Activity B has a slack time of 5 days.What is the impact of a 7 day delay in either A or B?

Question 46

For an activity, an engineer estimatesa (optimistic time) = 4
b (pessimistic time) = 11
m (most likely time) = 6
What is the mean for this activity? The variance?

Question 47

Suppose the estimated completion times for activities A through G in problem 1 were 5, 4, 3, 6, 2, 5, 2 respectively.Draw an earliest completion Gantt chart for the data.

Question 48

In a PERT network, you are given the following data with times in weeks. $\begin{array}{ccccc}\text { Activity } & \text { Immediate } & \text { Optimistic } & \text { Most Likely } & \text { Pessimistic } \\& \text { Predecessors } & \text { Time } & \text { Time } & \text { Time }\\\text { A } & -- & \text { G } & 11 & 13 \\\text { B } & -- & 4 & 9 & 20 \\\text { C } & \text { A } & 2 & 11 & 14 \\\text { D } & \text { A, B } & 5 & 6 & 13 \\\text { E } & \text { D } & 3 & 6 & 11 \\\text { F } & \text { C, D } & 9 & 10 & 11 \\\text { G } & \text { E }, \text { F } & 7 & 20 & 21\end{array}$
A.What is the critical path?
B.What is the probability the project will be completed within one year (52 weeks)?

C.Which activity has the most slack?

Question 49

Consider the following information for the activities comprising a small construction project which is scheduled to complete in 26 days.(Costs are in $1000's.)
$\begin{array}{cccccc}&&\text { Normal }&\text { Schedule}&\text { Crash}&\text { Schedule }\\\text { Activity } & \text { Slack } & \text { Time } & \text { Cost } & \text { Time } & \text { Cost } \\\text { M } & 0 & 7 & 10 & 4 & 19 \\\text { II } & 2 & 5 & 6 & 5 & 6 \\\text { O } & 0 & 4 & 7 & 2 & 12 \\\text { P } & 0 & 5 & 9 & 3 & 13 \\\text { Q } & 2 & 2 & 5 & 1 & 6 \\\text { R } & 0 & 4 & 9 & 4 & 9 \\\text { S } & 0 & 6 & 12 & 5 & 15\end{array}$ A.If the project must be completed in 25 days, which activity should be accelerated? Why?
B.Will the critical path be altered?
C.What is the total estimated cost of the project on the accelerated 25 day schedule?

Question 50

For the data in problem 6,A.Using the normal times, prepare a chart giving the earliest and latest start and finish times and slack for each activity.
B.What is the critical path and the project completion time using normal times?
C.What is the effect of a 2 week delay to activity B? What is the effect of a 2 week delay to activity B combined with a 2 week delay to activity D?

Question 51

Using PERT, we have determined the mean completion time for each activity ( $\mu$ _j) and the standard deviation for each activity completion time ( $\sigma$ _j).How do we use these data to determine the overall project completion time?

Question 52

For a CPM model, you are given the following data with time in weeks. $\begin{array}{cccccc}\text { Activity } & \begin{array}{c}\text { Immediate } \\\text { Predecessors }\end{array} & \begin{array}{c}\text { Normal } \\\text { Time }\end{array} & \text { Normal Cost } & \begin{array}{c}\text { Crash } \\\text { Time }\end{array} & \text { Crash Cost } \\\text { A } & -- & 9 & 3200 & 5 & 6000 \\\text { B } & -- & 7 & 1400 & 5 & 2400 \\\text { C } & \text { A } & 6 & 1500 & 5 & 2000 \\\text { D } & \text { B } & 5 & 2500 & 3 & 4000 \\\text { E } & \text { A, B } & 4 & 1800 & 3 & 2800 \\\text { F } & \text { D, E } & 3 & 1800 & 1 & 4800\end{array}$
A.If activity A needed to be completed in 6 weeks, what would its cost be?
B.If $3000 were allocated to activity D, how long would it take to complete?

Question 53

Consider the following activity schedule chart for a maintenance project. $\begin{array}{ccccr}\text { Activity } & \text { ES } & \text { EF } & \text { IS } & \text { LF } \\\text { A } & 0 & 6 & 1 & 7 \\\text { B } & 0 & 5 & 0 & 5 \\\text { C } & 6 & 14 & 7 & 15 \\\text { D } & 6 & 10 & 14 & 18 \\\text { E } & 14 & 16 & 15 & 17 \\\text { F } & 5 & 14 & 5 & 14 \\\text { G } & 14 & 17 & 14 & 17 \\\text { H } & 14 & 19 & 16 & 21 \\\text { I } & 10 & 13 & 18 & 21 \\\text { J } & 17 & 21 & 17 & 21\end{array}$ A.What are the slack values?
B.Identify the activities on the critical path.
C.If the time is in weeks, what is the impact of a two week delay in activity D, H, or C?

Question 54

For the data in problem 6,
A.Write a linear programming model that will give the minimum cost solution for completing the project in 14 weeks.
B.How would your model change if the objective were to complete the project in minimum time given a budget of $15,000?

Question 55

What type of distribution does PERT assume for the activity completion times?