MGT 3410 Final Examination Spring 2014

Answer all questions (take-home examination) Academic Honesty Policy:I understand that this is an open books/notes exam and I may use a computer to perform computations as necessary. I have neither given nor received help on this exam.

Due Date: May 8 by 11:59pm

Submit your solution electronically in a folder called “Final Examination” under Dropbox on D2L.

1. Thomas Industries and Washburn Corporation supply three firms (Zrox, Hewes, Rockwright) with customized shelving for its offices. They both order shelving from the same two manufacturers, Arnold Manufacturers and Supershelf, Inc.

Because of long standing contracts based on past orders, unit costs from the manufacturers to the suppliers are given below: Thomas

Washburn

Arnold

5

8

Supershelf

7

4

The chart below gives the cost to install the shelving at the various locations: Zrox

Hewes

Rockwright

Thomas

1

5

8

Washburn

3

4

4

Currently weekly demand by the user are 50 for Zorx, 60 for Hewes, and 40 for Rockwright. Both Arnold and Supershelf can supply at most 75 units to its customers.

a.

Draw a network representation for this problem. (6 points) b.

Formulate this problem as a LP model and solve it. (12 points) MGT 3410 Final Examination Spring 2014

Answer all questions (take-home examination) Academic Honesty Policy:I understand that this is an open books/notes exam and I may use a computer to perform computations as necessary. I have neither given nor received help on this exam.

Due Date: May 8 by 11:59pm

Submit your solution electronically in a folder called “Final Examination” under Dropbox on D2L.

1. Thomas Industries and Washburn Corporation supply three firms (Zrox, Hewes, Rockwright) with customized shelving for its offices. They both order shelving from the same two manufacturers, Arnold Manufacturers and Supershelf, Inc.

Because of long standing contracts based on past orders, unit costs from the manufacturers to the suppliers are given below: Thomas

Washburn

Arnold

5

8

Supershelf

7

4

The chart below gives the cost to install the shelving at the various locations: Zrox

Hewes

Rockwright

Thomas

1

5

8

Washburn

3

4

4

Currently weekly demand by the user are 50 for Zorx, 60 for Hewes, and 40 for Rockwright. Both Arnold and Supershelf can supply at most 75 units to its customers.

a.

Draw a network representation for this problem. (6 points) b.

Formulate this problem as a LP model and solve it. (12 points) 2. Bart’s Barometer Business (BBB) is a retail outlet that deals exclusively with weather equipment. Currently BBB is trying to decide on an inventory and reorder policy for home barometers. These cost BBB $50 each and demand is about 500 per year distributed fairly evenly throughout the year. Reordering costs are $80 per order and holding costs are figured at 20% of the cost of the item.

BBB is open 300 days a year (6 days a week and closed two weeks in August).

Lead time is 60 working days.

a. Develop a total cost model for this system. (7 points) b. What is the optimal reorder quantity? (7 points) c. What is the cycle time? (7 points)

d. What is the reorder policy for BBB? (7 points) e. What total annual cost does the model give? (6 points) 3. Given the following network with activities and times estimated in days, D

A

E

Start

B

F

I

K

Finish

C

G

H

J

2. Bart’s Barometer Business (BBB) is a retail outlet that deals exclusively with weather equipment. Currently BBB is trying to decide on an inventory and reorder policy for home barometers. These cost BBB $50 each and demand is about 500 per year distributed fairly evenly throughout the year. Reordering costs are $80 per order and holding costs are figured at 20% of the cost of the item.

BBB is open 300 days a year (6 days a week and closed two weeks in August).

Lead time is 60 working days.

a. Develop a total cost model for this system. (7 points) b. What is the optimal reorder quantity? (7 points) c. What is the cycle time? (7 points)

d. What is the reorder policy for BBB? (7 points) e. What total annual cost does the model give? (6 points) 3. Given the following network with activities and times estimated in days, D

A

E

Start

B

F

I

K

Finish

C

G

H

J

Most

Activity

Optimistic

Probable

Pessimistic

A

2

5

6

B

1

3

7

C

6

7

10

D

5

12

14

E

3

4

5

F

8

9

12

G

4

6

8

H

3

6

8

I

5

7

12

J

12

13

14

K

1

3

4

a. Fill in all the blanks in the following table. (15 points)

Note:

i) To reduce the computation load, please round the expected activity time ( t) up to an integer if the computed expected activity time is not an integer. For example, if tA=4.15, round it up to 5.

ii) For variance ( ?2) in activity time, keep two decimal places.

Precedence

Expected

Varianc

Critical

Activity

Activities

Time t (days)

e ?2

ES

LS

EF

LF

Slack

Path?

A

B

C

D

E

F

G

H

I

J

K

b. What is the expected time and variance to complete the project? (8 points) c. What is the probability the project will take more than 28 days to complete? (8

points)

Most

Activity

Optimistic

Probable

Pessimistic

A

2

5

6

B

1

3

7

C

6

7

10

D

5

12

14

E

3

4

5

F

8

9

12

G

4

6

8

H

3

6

8

I

5

7

12

J

12

13

14

K

1

3

4

a. Fill in all the blanks in the following table. (15 points)

Note:

i) To reduce the computation load, please round the expected activity time ( t) up to an integer if the computed expected activity time is not an integer. For example, if tA=4.15, round it up to 5.

ii) For variance ( ?2) in activity time, keep two decimal places.

Precedence

Expected

Varianc

Critical

Activity

Activities

Time t (days)

e ?2

ES

LS

EF

LF

Slack

Path?

A

B

C

D

E

F

G

H

I

J

K

b. What is the expected time and variance to complete the project? (8 points) c. What is the probability the project will take more than 28 days to complete? (8

points)

d. Suppose activity G were delayed for 7 days. By how much would the entire project be delayed? (5 points)

4. Suzie’s Sweatshirts is a home-based company that makes upscale, hand-painted sweatshirts for children. Forecasts of sales for the next year are Autumn: 125

Winter: 350

Spring: 75

Each Shirt is sold for $15. The holding cost per shirt is 6% of the selling price per quarter. The shirts are painted by part-time workers who earn $4.50 per hour during the autumn. Because of the high demand for part-time help during the winter holiday season, labor rates are higher in the winter, and Suzie must pay the workers $6.00 per hour. In the spring, labor is more difficult to keep, and Suzie finds that she must pay $5.50 per hour to get qualified help. Each shirt takes 1.5

hours to complete. Formulate the problem to a LP model to help Suzie plan production over the three quarters to minimize the combined production and inventory holding cost. Suppose there is no inventory at the beginning of the autumn. (12 points)

(Note: You do not need to solve the model.) d. Suppose activity G were delayed for 7 days. By how much would the entire project be delayed? (5 points)

4. Suzie’s Sweatshirts is a home-based company that makes upscale, hand-painted sweatshirts for children. Forecasts of sales for the next year are Autumn: 125

Winter: 350

Spring: 75

Each Shirt is sold for $15. The holding cost per shirt is 6% of the selling price per quarter. The shirts are painted by part-time workers who earn $4.50 per hour during the autumn. Because of the high demand for part-time help during the winter holiday season, labor rates are higher in the winter, and Suzie must pay the workers $6.00 per hour. In the spring, labor is more difficult to keep, and Suzie finds that she must pay $5.50 per hour to get qualified help. Each shirt takes 1.5

hours to complete. Formulate the problem to a LP model to help Suzie plan production over the three quarters to minimize the combined production and inventory holding cost. Suppose there is no inventory at the beginning of the autumn. (12 points)

(Note: You do not need to solve the model.)