Plan production for a four-month period

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7

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: FCFS 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?

Based on the average flow time measured from today (start of Day 4), the preferred sequence is

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.

8. (6 points)

It currently costs a total of $1,000 for an automobile engine repair following a breakdown. This is based on performing oil changes every 60,000 miles. However, for every 10,000 miles an oil change is delayed, the engine repair costs following a breakdown increases by $100 (for example if the oil change is 70,000 miles, the repair cost is $1,100). Following is breakdown information for a fleet of five automobiles. The average number of breakdowns between oil changes for this fleet is as follows:

Thousands of Miles between Oil Changes

Average Number of Breakdowns between Oil Changes

60

0.2500

70

0.7265

80

1.8131

90

3.6469

100

5.5822

A custom oil change with filter, long-wearing oil, and careful adjustments costs $200 at each oil change for each automobile assuming that the oil is changed every 60,000 miles. For every 10,000 miles the oil change is delayed, the cost of an oil change increases by $25. For example, if the oil change is every 70,000 miles, the oil change is $225.

Which interval between oil changes would you select for a fleet of five automobiles? Base this recommendation on the economics as presented.

9. (20 points)

You are to plan production for a four-month period: February through May. For February and March, you should produce to the exact demand forecast. During February and March, you will follow a matching strategy and hire and layoff the works as required. For April and May, you should use overtime and inventory with a stable workforce. Stable means that the number of workers needed for March will be held constant through May. However, government constraints put a maximum of 5,000 hours of overtime labor per month in April and May. There is no overtime allowed in February and March. If demand exceeds supply, then backorders occur. If there is excess capacity in May, the workers are paid but there is no work performed hence there are no extra units produced in May. There are 100 workers on January 31. You are given the following demand forecast

February - 80,000

March - 64,000

April - 100,000

May - 40,000

Productivity is four units per worker hour. Each worker works eight hours per day, 20 days per month. Assume zero inventory on February 1. There is to be no inventory at the end of May. Hiring costs are $50 per worker, while layoff costs are $70 per worker. The inventory holding cost is $10 per unit per month based on the number of units in inventory at the end of the month. Straight time labor is $10 per hour and overtime is 150% of the straight time labor rate. Backorder costs are $20 per unit per month.

Find the total cost of this plan.

10. (22 points)

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

image1.emf

X1X2RHSShadow

Price

Maximize4030

Constraint 10.40.5<=2033.3333

Constraint 20.00.2<=50

Constraint 30.60.3<=2144.4444

Solution2520

VariableValueReduced

Cost

Original

Value

Lower

Bound

Upper

Bound

X1250402460

X2200302050

ConstraintShadow

Price

Slack/

Surplus

Original

Value

Lower

Bound

Upper

Bound

Constraint 133.333302014.0021.50

Constraint 20154.00Infinity

Constraint 344.444402118.7530.00

Sensitivity Analysis

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.

_1224965531.xls

Sheet1

X1 X2 RHS Shadow Price

Maximize 40 30

Constraint 1 0.4 0.5 <= 20 33.3333

Constraint 2 0.0 0.2 <= 5 0

Constraint 3 0.6 0.3 <= 21 44.4444

Solution 25 20

Sensitivity Analysis

Variable Value Reduced Cost Original Value Lower Bound Upper Bound

X1 25 0 40 24 60

X2 20 0 30 20 50

Constraint Shadow Price Slack/ Surplus Original Value Lower Bound Upper Bound

Constraint 1 33.3333 0 20 14.00 21.50

Constraint 2 0 1 5 4.00 Infinity

Constraint 3 44.4444 0 21 18.75 30.00

Sheet2

Sheet3