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[solution] » 6. (18 points) Today is the start of Day 4 and John Smith is ready to start schedu

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6. (18 points)

Today is the start of Day 4 and John Smith is ready to start scheduling the following jobs. Jobs are assigned a letter of the alphabet, starting with the letter A, based on their arrival.

Job | Processing Time (in days) | Due Date (End of Day) |

A | 3 | 10 |

B | 10 | 12 |

C | 2 | 25 |

D | 4 | 8 |

E | 5 | 15 |

F | 8 | 18 |

G | 7 | 20 |

a) Sequence these jobs based on the following scheduling rules: Slack and Critical Ratio (CR) (time to due date/processing time).

b) Based on average flow time measured from today (start of Day 4), which of the sequencing rules is preferred?

c) Based on the average lateness with no credit given for jobs completed early, which of the sequencing rules is preferred?

d) Based on the average early time with zero days early if the job is completed late, which of the sequencing rules is preferred?

7. (23 points)

The information technology department of Bellevue University buys paper for its copier machine frequently. The office manager would like to determine the best quantity to order each time an order is placed. She has estimated that the ordering cost is $12 each time an order is placed. The monthly demand for paper is 135 reams (500 sheets to a ream). The cost of paper is $6.50 per ream, and the carrying cost is 25 percent of the paper cost per month. Base your answers to the following questions on the economics that are provided and using the traditional inventory models we have studied.

a) How many reams should be ordered at a time?

b) Suppose the information technology department of the university only has space to hold 35 reams of paper at any time. How many reams should be ordered at a time? Why?

c) There are 350 working days per year and the lead time is 3 days. What are the reorder point and the inventory position immediately after placing the order?

d) If the university were to order at least 60 reams of paper every time it places an order, the paper company will lower the price of the paper by $0.33 for all reams of paper. The university can now acquire all of the storage space that it needs. However, it will cost the university an additional $1.00 per ream per month for storage. What is the difference in the annual inventory cost between this policy and the policy found in a)? Consider all relevant costs.

10. (20 points)

Attached is the computer solution to a linear programming problem linear programming:

Note: The Reduced Cost is often referred to as the Coefficient Sensitivity.

For the above information, answer the following questions. Provide your answers based on the above information and explain your answers in terms of this information.

a) Write the objective function in equation form and write the constraints as equalities or inequalities.

b) What are the values of the variables at optimality and what is the value of the objective function at optimality?

c) If there was an opportunity to purchase additional units of each resource (as expressed by the constraints), based on the sensitivity analysis which resource(s) would you consider for purchase? Why? Identify all of the resources that you would consider. If you did not consider a resource for purchase, why did you exclude it? Remember that Constraint 1 is equivalent to Resource 1, Constraint 2 is Resource 2, and Constraint 3 is Resource 3.

d) Suppose the contribution of variable X2 in the objective function increases by 10. What are the values of the variables at optimality now and what is the value of the objective function at optimality with this change? Use the above sensitivity analysis in answering this question and provide the sensitivity analysis information you used.

6. (18 points)

Today is the start of Day 4 and John Smith is ready to start scheduling the following jobs. Jobs

are assigned a letter of the alphabet, starting with the letter A, based on their arrival.

Job

A

B

C

D

E

F

G Processing Time (in days)

3

10

2

4

5

8

7 Due Date (End of Day)

10

12

25

8

15

18

20 a) Sequence these jobs based on the following scheduling rules: Slack and Critical Ratio (CR)

(time to due date/processing time).

Critical ratio = Due Date ? Today?s Date

Total Time Remaining

Slack = (Due Date ? Today?s Date) ? Total Shop Time Remaining

Number of Operations Remaining b) Based on average flow time measured from today (start of Day 4), which of the sequencing

rules is preferred? c) Based on the average lateness with no credit given for jobs completed early, which of the

sequencing rules is preferred? d) Based on the average early time with zero days early if the job is completed late, which of the

sequencing rules is preferred? 7. (23 points)

The information technology department of Bellevue University buys paper for its copier machine

frequently. The office manager would like to determine the best quantity to order each time an

order is placed. She has estimated that the ordering cost is $12 each time an order is placed. The

monthly demand for paper is 135 reams (500 sheets to a ream). The cost of paper is $6.50 per

ream, and the carrying cost is 25 percent of the paper cost per month. Base your answers to the

following questions on the economics that are provided and using the traditional inventory

models we have studied.

a) How many reams should be ordered at a time? b) Suppose the information technology department of the university only has space to hold 35

reams of paper at any time. How many reams should be ordered at a time? Why? c) There are 350 working days per year and the lead time is 3 days. What are the reorder point

and the inventory position immediately after placing the order?

350 days/12 months = 29.17 or average of 29 working days/month

EOQ = ? 2 DS/ H

? 2?135?12

=

0.25?6.50

= ? 3240/1.625

= ? 1993.85

= 44.65

ROP

IP = (135 reams/29.17 days)*3 = 13.88 reams

= EOQ + (lead time) * (daily demand)

= 44.65 + 3 * 29.17

= 47.65 * 29.17

= 1389.95 d) If the university were to order at least 60 reams of paper every time it places an order, the

paper company will lower the price of the paper by $0.33 for all reams of paper. The university

can now acquire all of the storage space that it needs. However, it will cost the university an

additional $1.00 per ream per month for storage. What is the difference in the annual inventory

cost between this policy and the policy found in a)? Consider all relevant costs. ( Q2 ) H +( QD ) S C=

= 10. (20 points)

Below is the computer solution to a linear programming problem linear programming: Note: The Reduced Cost is often referred to as the Coefficient Sensitivity.

For the above information, answer the following questions. Provide your answers based on the

above information and explain your answers in terms of this information.

a) Write the objective function in equation form and write the constraints as equalities or

inequalities.

b) What are the values of the variables at optimality and what is the value of the objective

function at optimality?

c) If there was an opportunity to purchase additional units of each resource (as expressed by the

constraints), based on the sensitivity analysis which resource(s) would you consider for

purchase? Why? Identify all of the resources that you would consider. If you did not consider a resource for purchase, why did you exclude it? Remember that Constraint 1 is equivalent to

Resource 1, Constraint 2 is Resource 2, and Constraint 3 is Resource 3.

d) Suppose the contribution of variable X2 in the objective function increases by 10. What are

the values of the variables at optimality now and what is the value of the objective function at

optimality with this change? Use the above sensitivity analysis in answering this question and

provide the sensitivity analysis information you used.

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DATE ANSWEREDOct 14, 2020

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