MBA576 Homework 8 Week 8

Unit 8: Homework

Analyzing Waiting Lines and Project Management

Many large organizations have the operations and project management staff located in two different departments, and this is done on purpose.  Operational processes are on-going, whereas projects are: 1) short term; 2) have a definite end state; 3) usually contain many parallel tasks; and 4) the objectives are specific to the project.  There is also more uncertainty with projects because we don’t do them that often, hence there is more risk management required. 

Projects are managed by deadlines and utilize a work breakdown structure to divide the total work required to complete the project into manageable tasks that can be scheduled and monitored.  The project manager usually has several tasks going on at the same time on a project, while simultaneously planning the sequencing of upcoming tasks.  These factors require project managers to have a different skill set than operations managers, and quite often project management positions require the person staffing the position to hold a professional certification in project management.

To manage the “work”, i.e. tasks, required to complete a project, the project manager will use tools specifically designed for project management.  Examples are Gantt charts, network diagrams, and computer software such as Microsoft’s Project.  In unit 8, you will utilize these tools as you roleplay a project manager to answer end of chapter problems.

In addition to problems involving project management, you will also apply quantitative analysis to waiting line problems.  Specifically, you will use Markovian models to determine statistics such as the average time waiting in a queue, the average length of a queue, and the probability of n units waiting in a queue.  Understanding waiting lines is important to both operations and project managers, but for different reasons.  Waiting in line for the operations manager usually indicates we have inefficiencies in a machine or service somewhere in the process before the waiting line.  On the other hand, a project manager who detects a long waiting line on a project is concerned about delays to tasks that follow the task causing the wait.  In summary, operations managers want to know how waiting lines affect current operations, whereas project managers are concerned about impacts the waiting lines have on pending tasks.

Unit Learning Outcomes

1. Demonstrate an understanding of project management techniques to include: work breakdown structure, Gantt Charts, PERT charts, and Critical Path Method (CPM). (CLO 1, 4, 5, 6, and 7)

2. Determine the project life cycle for a project an organization is considering.  (CLO 5 and 6)

3. Construct network diagrams and identify the critical path for a project. (CLO 1, 6, and 7)

4. Identify potential risk in a project and create a risk management plan.   (CLO 1, 2, 3, 4, 5, 6, and 7)

5. Calculate waiting line metrics such as average wait time and average queue length. (CLO 2, 4, and 5)

Directions

End of Chapter Problems (60 points):  Answer the following end of chapter problems from the textbook:

Chapter 17 – problems 1, 8, and 12 (pages 774-777, 10 points each).

View the following example videos before working the problems:

https://canvas.park.edu/courses/62827/files/8248178/download?download_frd=1

https://canvas.park.edu/courses/62827/files/8248179/download?download_frd=1

1. For each of the following network diagrams, determine both the critical path and the expected project duration. The numbers on the arrows represent expected activity times.

a. AOA diagram

b. Page 775AON diagram

c. AOA diagram

d. AON diagram

8. The new director of special events at a large university has decided to completely revamp graduation ceremonies. Toward that end, a PERT chart of the major activities has been developed. The chart has five paths with expected completion times and variances, as shown in the table. Graduation day is 16 weeks from now. Assuming the project begins now, what is the probability that the project will be completed before

a. Graduation time?

a. The end of week 15?

a. The end of week 13?

Path	Expected Duration (weeks)	Variance
A	10	1.21
B	8	2.00
C	12	1.00
D	15	2.89
E	14	1.44
12. A project manager has compiled a list of major activities that will be required to install a computer information system in her firm. The list includes estimated completion times for activities and precedence relationships. Activity Immediate Predecessor Estimated Times (weeks) A — 2-4-6 D A 6-8-10 E D 7-9-12 H E 2-3-5 F A 3-4-8 G F 5-7-9 Activity Immediate Predecessor Estimated Times (weeks) B — 2-2-3 I B 2-3-6 J I 3-4-5 K J 4-5-8 C — 5-8-12 M C 1-1-1 N M 6-7-11 O N 8-9-13 End H, G, K, O Construct a network diagram. You can use either AOA or AON (see  Example 5 ). If the project is finished within 26 weeks of its start, the project manager will receive a bonus of $1,000; and if the project is finished within 27 weeks of its start, the bonus will be $500. Find the probability of each bonus.

Chapter 18 – problems 1, 3, and 18 (pages 818-821, 10 points each).

View the following example videos before working the problems:

https://canvas.park.edu/courses/62827/files/8248180/download?download_frd=1

https://canvas.park.edu/courses/62827/files/8248182/download?download_frd=1

https://canvas.park.edu/courses/62827/files/8248181/download?download_frd=1

a. λ=3 customers/hourμ=5 customers/hourM=1

(1) What is the system utilization?

(2) What is the average number of customers waiting for service?

(3) What is the average time customers wait in line for service?

b. Page 819Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed, with a mean of two hours per call. Requests for copier repairs come in at a mean rate of three per eight-hour day (assume Poisson). Determine the following:

(1) The average number of customers awaiting repairs

(2) System utilization

(3) The amount of time during an eight-hour day that the repairman is not out on a call

(4) The probability of two or more customers in the system

c. An average of 18 customers arrive at a service center each hour. There are two servers on duty, and each server can process 12 customers per hour.

(1) What is the system utilization?

(2) What is the average number of customers in the system (waiting plus being served)?

(3) What is the average time customers wait in line for service?

(4) What is the average waiting time for customers who actually have to wait?

3.Many of a bank’s customers use its automatic teller machine to transact business after normal banking hours. During the early evening hours in the summer months, customers arrive at a certain location at the rate of one every other minute. This can be modeled using a Poisson distribution. Each customer spends an average of 90 seconds completing his or her transactions. Transaction time is exponentially distributed. Determine the following:

a. The average time customers spend at the machine, including waiting in line and completing transactions

a. The probability that a customer will not have to wait upon arriving at the automatic teller machine

a. The average number waiting to use the machine

18.During the morning hours at a catalog sales department, telephone calls come in at the rate (Poisson) of 40 per hour. Calls that cannot be answered immediately are put on hold. The system can handle eight callers on hold. If additional calls come in, they receive a busy signal. The three customer service representatives who answer the calls spend an average of three minutes with a customer.

d. What is the probability that a caller will get a busy signal? (Hint: Solve for log K or ln K using trial and error.)

What is the probability that a customer will be put on hold?