Homework Assignment $5($Project Management$)$

POM $333$ Introduction to Business Analytics

Note: Attempt all questions as per rubric. Problems including case study has a weightage of $10$ marks each. The maximum you can score is $50.$ Use QM for Windows wherever possible.

Problem$-1$:

Sid Davidson is the personnel director of Babson and Willcount, a company that specializes in consulting and research. One of the training programs that Sid is considering for the middle$-$ level managers of Babson and Willcount is leadership training. Sid has listed several activities that must be completed before a training program of this nature could be conducted. The activities and immediate predecessors appear in the following table:

Activity Immediate Predecessors A$$ B$$ C$$ DB

E A$,$ D FC G E$,$ F

Develop a network for this problem.

Problem$-2$:

Sid Davidson was able to determine the activity times for the leadership training program. He would like to determine the total project completion time and the critical path. The activity times appear in the following table $($see the previous problem$).$

Activity Time $($days$)$ A$2$ B$5$ C$1$

D $10$ E$3$ F$6$ G$8$

Total $35$ Develop a PERT$/$CPM network for this problem.

Problem$-3$:

The estimated times $($in weeks$)$ and immediate predecessors for the activities in a project are given in the following table. Assume that the activity times are

Activity A

B

C

Immediate Predecessors $$

$$

A

a m b $9101141016910115811$

D B

a$)$ Calculate the expected time and variance for each activity.

b$)$ What is the expected completion time of the critical path? What is the expected completion time of the other path in the network?

c$)$ What is the variance of the critical path? What is the variance of the other path in the network?

d$)$ If the time to complete path A$$C is normally distributed, what is the probability that this path will be finished in $21$ weeks or less?

e$)$ If the time to complete path B$$D is normally distributed, what is the probability that this path will be finished in $21$ weeks or less?

f$)$ Explain why the probability that the critical path will be finished in $21$ weeks or less is not necessarily the probability that the project will be finished in $21$ weeks or less.

Problem$-4$:

The following costs have been estimated for the activities in a project:

Activity A

B

C

D

E

F

G

Immediate Predecessors

$88,000$

Time Cost $($$$)$

$4$ A $3$ B $5$

C$,$ D $6$ C$,$ D $5$ E$,$ F $3$

$12,0006,00015,0009,00010,0006,000$

a$)$ Develop a cost schedule based on the earliest start times.

b$)$ Develop a cost schedule based on the latest start times.

c$)$ Supposethatithasbeendeterminedthatthe$$6,000$foractivityGisnotevenlyspread over the three weeks. Instead, the cost for the first week is $$4,000,$ and the cost is $$1,000$ per week for each of the last two weeks. Modify the cost schedule based on the earliest start times to reflect this situation.

$($Copy the data of cost schedule based on the earliest start times from QM for Windows and paste in Excel for modification$).$

Case Study: Southwestern University Stadium Construction

After six months of study, much political arm wrestling, and some serious financial analysis, Dr$.$ Martin Starr, president of Southwestern University, had reached a decision. To the delight of its students, and to the disappointment of its athletic boosters, SWU would not be relocating to a new football site but would expand the capacity at its on$-$ campus stadium.

Adding $21,000$ seats, including dozens of luxury skyboxes, would not please everyone. The influential football coach, Billy Bob Taylor, had long argued the need for a first$-$class stadium, one with built$-$in dormitory rooms for his players and a palatial office appropriate for the coach of a future NCAA champion team. But the decision was made, and everyone, including the coach, would learn to live with it$.$

Activity

Description

Predecessor

Optimistic time

Most Likely time

Pessimistic time

Crash Cost$/$Day $($$$)$

A

B

C

D

E F G H

J K

L

Bonding, insurance, tax structuring

Foundation, concrete footings for boxes

Upgrading skyboxes, stadium seating

Upgrading walkways, stairwells, elevators

Interior wiring, lathes Inspection approvals Plumbing Painting

$-$

A

A

C

B

E D$,$ E G

$203040$

$206580$

$5060100$

$3050100$

$253035111253035$

$102030$

$1,500$

$3,500$

$4,000$

$1,900$

$9,50002,5002,000$

I

Hardware$/$air conditioning$/$metal workings

H

$20$

$25$

$60$

$2,000$

Tile$/$carpeting$/$windows

Inspection J $1110$

Final detail I, K $2025604,500$ work$/$cleanup

H

$81012$

$6,000$

The job now was to get construction going immediately after the current season ended. This would allow exactly $270$ days until the upcoming season opening game. The contractor, Hill Construction $($Bob Hill being an alumnus, of course$),$ signed the contract. Bob Hill looked at the tasks his engineers had outlined and looked President Starr in the eye. $$I guarantee the te