MTH309: Project Management Construct Mathematical Models - Management Assignment Help

Assignment Task:

Task:

You are required to submit a handwritten or typed solution to the following 4 questions which are worth 5 marks each for questions 1 and 4, 10 marks each for question 2 and 3. This assignment covers content from Modules 5, 6, 7 and 8, and looks at how to formulate and solve problems in project management, inventory models, waiting line models and decision analysis.

Rationale

This task is designed to demonstrate your mastery of the subject material in the associated topics and give you feedback on how you are doing. It is designed to assess the following learning outcomes:

•  Be able to identify applications in project management, inventory models, waiting line models and decision analysis, and use appropriate techniques in the decision making process;
•  Be able to construct mathematical models for the various management applications in the topics;
•  Be able to interpret/analyse results from the mathematical models studied, (manually or automatically where appropriate) and use them in making better management decisions;
•  Be familiar with the automated tools that are available in the process of decision making.

Presentation

The assignment must be typed or neatly handwritten (handwritten is preferred) and uploaded to EASTS as a single Word or PDF file. Assignments submitted in non- printable formats such as a ZIP file or as a collection of images will not be marked. If your scanner produces separate graphics files please paste them into a Word document before submitting to EASTS. Pages must be numbered, and your name and student number must be included on every page.

Question 1 (5 marks)

A computer manufacture wants to develop a new computer. The design of the computer must first be conducted – this takes 20 weeks. Then the tasks of building a prototype and evaluating equipment can be done independently, in which building a prototype takes 5 weeks and evaluating equipment takes 7 weeks. The task of testing the prototype must follow building the prototype and takes 2 weeks. After completing both tasks of evaluating equipment and testing the prototype, the equipment report and the methods report must be prepared. The equipment report takes 5 weeks and the methods report takes 8 weeks. The final report can be prepared once both the equipment and methods reports are compelte and takes 2 weeks.

a. Construct a network for this project, including finding the slack for each activity.

b. Identify the critical path and determine the completion time for the project.

c. By how many days can the task of writing the equipment report be delayed without changing the completion time of the project?

Question 2 (10 marks)
A project involves 10 tasks that must be completed. The table below summarises the tasks, their precedence, and estimates of the number of days need to complete them under different circumstances.

Activity Optimistic Estimate (a)

Most Likely Estimate (m)

Pessimistic Estimate (b)

Immediate predecessor

a 10 22 22 -
b 20 20 20 -
c 4 10 16 -
d 2 14 32 a
e 8 8 20 b, c
f 8 14 20 b, c
g 4 4 4 b, c
h 2 12 16 c
i 6 16 38 g, h
j 2 8 14 d, e

a. Draw up a table including expected time and variance for each activity, and then construct the project network.

b. Find the critical path.

c. Determine the expected completion time for the project.

d. Calculate the probability that the project will be completed within 50 days.

Question 3 (10 marks)
A company has an annual demand of 12 000 units of a certain product. The cost of placing an order is $5, and the holding cost ratio is 20% of the cost of a unit per year. The cost per unit is $0.05 but it is discounted based on the size of the order according to the table below:

Order quantity Discount
0-4,999 0%
5,000-9,999 5%
10,000-19,999 10%
20,000+ 15%

The goal in this question is to determine the optimal order quantity and corresponding total annual inventory cost.

a. Find the economic order quantity Q* for each group ie. the order quantity that minimises the total annual cost TC for each order quantity band.

b. Find the total annual inventory cost TC for each group from the values of Q* found in (a).

c. From (a) and (b) state the order quantity that gives the minimum total annual cost.
 

Question 4 (5 marks)
The computer lab at a university has a help desk to assist students working on computer spreadsheet assignments. The students patiently form a single line in front of the desk to wait for help. Students are served based on a first-come, first-served priority rule. On average, 15 students per hour arrive at the help desk. Student arrivals are best described using a Poisson distribution. The help desk server can help an average of 20 students per hour, with the service rate being described by an exponential distribution.

Calculate the following operating characteristics of the service system.

a. The probability there are no students in the queue.
b. The average number of students in the queue.
c. The average number of students in the system.
d. The average time a student spends waiting in line.
e. The average time a student spends in the system.

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