# OPS MGMT Assignment

Assignment 2

1. (15 marks)

A spice store orders 4800 pounds of black pepper per year. The store purchases each pound at a cost of \$10. Management of the store has estimated the annual holding cost at \$2 per pound. The cost of placing an order is \$20.
a. If management orders once per month, what is the current total (ordering + holding + purchase) cost per year?
b. Determine EOQ for this problem.
c. How much would the firm save annually if the EOQ were used?

2. (20 marks)

An airline company uses a fixed order size with safety stock system to control inventory of a fast-moving item. The inventory position of the item is tracked continually. The following is relevant information about the item.

Expected annual demand 1920 units per year
Average monthly demand 1920/12 = 160 units per month
Ordering cost \$25 per order
Annual holding cost as a fraction of unit value
36 percent
Unit purchase price \$20 per unit
Standard deviation of monthly demand 30 units

The manager specifies the probability of no stockout in an inventory cycle to be 96 percent. Demand per month is normally distributed.
a. Suppose Q = EOQ. Determine EOQ and R, the reorder point. Assume that demand in any given month is normally distributed and is independent of demand in other months.

b. What is the safety stock for this item?

3. (20 marks)

Product A is made of one unit of C, two units of D, and one unit of E. Product B is made of one unit of E and one unit of F. Item F is made of one unit of D and two units of G. The shipping (i.e., gross) requirements for A and B are given below:
Item 1 2 3 4 5 6 7 8
Product A        40 50     30 10     30
Product B     40 25 35 20 20

a. Draw product structure trees for A and B.

b. Develop the MRP schedule for all items given the following information:
Item Present on hand Lead time Lot-size rule
A    50 1 week L4L
B    75 1 week L4L
C    80 2 weeks L4L
D    100 1 week L4L
E    20 1 week L4L
F    0 2 weeks *FOQ of 60 units
G    5 1 week *FOQ of 50 units

*Note: FOQ stands for fixed order quantity. For example, FOQ = 30 indicates that any order quantity must be 30 units or some integer multiple of 30 units. FOQ is usually because our supplier is only willing to sell the item by the box (and in this example, each box contains 30 units).

In your tables, show on hand at the beginning of a given period, before receiving the planned order receipt for the period. Also, assume that all receipts and releases are at the beginning of each period.

Week 1 2 3 4 5 6 7 8
Gross Req’ts
On Hand
A (LT =) Net Req’ts
P.O. Receipts
P.O. Releases
Gross Req’ts
On Hand
B (LT =) Net Req’ts
P.O. Receipts
P.O. Releases
Gross Req’ts
On Hand
C (LT =) Net Req’ts
P.O. Receipts
P.O. Releases

Gross Req’ts
On Hand
D (LT =) Net Req’ts
P.O. Receipts
P.O. Releases
Gross Req’ts
On Hand
E (LT =) Net Req’ts
P.O. Receipts
P.O. Releases
Gross Req’ts
On Hand
F (LT =) Net Req’ts
P.O. Receipts
P.O. Releases

Gross Req’ts
On Hand
G (LT =) Net Req’ts
P.O. Receipts
P.O. Releases

4. (20 marks)

The following are the operation times and due dates for six jobs (each job undergoes a single operation):
Job Processing Time (days) Due Date (days hence)
A 4 6
B 3 8
C 10 20
D 5 16
E 10 12
F 5 15

The firm operates seven days per week. Assign the jobs according to each of the following priority rules:
a. shortest operation time (SOT)
b. earliest due date (EDD)
c. slack time remaining (STR)
d. critical ratio (CR)
If a priority rule results in a tie between two or more jobs, break the tie by scheduling the tied jobs in alphabetical order.
Evaluate each of the above priority rules with the objective of minimizing the mean tardiness. The term tardiness is used here, rather than lateness, to indicate that there is no credit for a job completed early. A job completed early simply has a tardiness value of 0. In other words, lateness and tardiness are the same if the job is completed after the due date, but different if the job is completed before the due date. For minimizing mean tardiness, no rule is best under all circumstances.

Which one of the priority rules did you determine to be best in this particular case?

5. (15 marks)

While the process was operating in control, 20 samples of size n = 4 were taken from a process that fills large tubes of shampoo. The average of the sample means was 450 ml, and the average of the sample ranges was 8.45 ml.
a. Calculate 3 control limits for mean and range charts to monitor this process.

b. Five additional samples of size 4 have been taken from the toothpaste filling line; the individual measurements are recorded in the following table:
Sample No. Ml    Sample Mean Sample Range
1 448.6 455.4 447.5 452.1 ? ?
2 443 453.6 456.8 451 ? ?
3 452.3 445.9 447.9 446.3 ? ?
4 454.9 453.3 448.7 458.7 ? ?
5 448.6 447.9 448.8 456.3 ? ?

Calculate the mean and range for each sample.

c. Draw the mean and range charts for this process. Plot the results of the five samples on the chart.

d. Does the process appear to be in control?

6. (10 marks)

A sheet of steel is periodically taken from the output of a rolling mill and carefully inspected for minor defects. When the process is operating in control, the average number of minor defects found on a sheet is 13.8.
Calculate 3 control limits for a c-chart to monitor this process.

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