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DMS2030
Individual Assignment
1. Resistors for electronic circuits are manufactured on a high-speed automated machine. The machine
is set up to produce a large run of resistors of 1,000 ohms each. To set up the machine and to create a
control chart to be used throughout the run, 15 samples were taken with four resistors in each sample.
The complete list of samples and their measured values are as follows.
Sample Number Readings (in ohms)
a. Suppose the first 10 samples are in control, develop an 𝑋𝑋
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-chart and an 𝑅𝑅-chart and plot the values.
(Please use three-standard deviation limits)
b. From the charts, what comments can you make about the process?
2. Completed forms from a particular department of an insurance company were sampled daily to
check the performance quality of that department. To establish a tentative norm for the department, one
sample of 100 units was collected each day for 15 days, with these results:
Sample Sample Size
Number of Forms with Errors
a. Suppose the first 10 samples are in control, develop a 𝑝𝑝-chart using a 95 percent confidence interval
(𝑧𝑧 = 1.96).
b. What comments can you make about the process?
3. A company has been selling a new product for 5 months and wants to forecast the demand for the 6th
month. The company is considering different forecasting methods.
a. The first method in consideration is simple moving average with 𝑛𝑛 = 3. Please fill in the following
table.
b. The second method in consideration is exponential smoothing with 𝛼𝛼 of 0.30 and an initial forecast
𝐹𝐹1 of 31. Please fill in the following table.
c. The third method in consideration is double exponential smoothing with 𝛼𝛼 of 0.30, 𝛿𝛿 of 0.30, an
initial trend forecast 𝑇𝑇1 of 1, and an initial exponentially smoothed forecast (𝐹𝐹1) of 30. Please fill in
the following table.
d. Which method do you recommend? Explain within two sentences.4. Given the following information, formulate an inventory management system. The item is demanded
50 weeks a year.
Parameter
Value
Item cost
$10
Order cost
$250/order
Annual holding cost
33% of item cost
Annual demand
25,750 units
Standard deviation of weekly demand
25 units
Lead time
2 weeks
Service probability
0.95
a. State the order quantity and reorder point.
b. Determine the annual holding costs.
c. Please explain why the average inventory is calculated as 𝑄𝑄
2
+ safety stock.
5. Palin’s Muffler Shop has one standard muffler that fits a large variety of cars. The shop wishes to
establish a periodic review system to manage inventory of this standard muffler.
Use the information in the following table to determine the optimal inventory target level (or order-up
to level).
Annual demand
3,000 mufflers
Standard deviation of daily demand
6 mufflers per working day
Item cost
$30 per muffler
Annual holding cost
25% of item value
Review period
15 working day
Ordering cost
$50 per order
Service probability
90%
Lead time
2 working days
Working day
300 per year
a. What is the optimal target level (order-up-to level)?
b. If the service probability requirement is 95 percent, the optimal target level [your answer in part (a)]
will increase, decrease, or stay the same?
6. The local supermarket buys lettuce each day to ensure really fresh products. Each morning, any
lettuce that is left from the previous day is sold to a dealer that resells it to farmers who use it to feed
their animals. This week, the supermarket can buy fresh lettuce for $4.00 per box. The lettuce is sold
for $10.00 per box and the dealer that resells old lettuce is willing to pay $1.50 per box. Past history
says that tomorrow’s demand for lettuce is normally distributed with a mean of 250 boxes and a
standard deviation of 34 boxes.
a. How many boxes of lettuce should the supermarket purchase tomorrow?
b. If the dealer is willing to pay $1 more for per box of old lettuce, will your answer in part (a) increase,
decrease or stay unchanged? Please explain the practical intuition.7. The EastCoasters Bicycle Shop operates 364 days a year, closing only on Christmas Day. The shop
pays $300 for a particular bicycle purchased from the manufacturer. The annual holding cost per
bicycle is estimated to be 25% of the dollar value of inventory. The shop sells an average of 18 bikes
per week. The ordering cost for each order is $250.
a. Determine the optimal order quantity and the total minimum cost.
b. If the purchasing cost of the bicycle increases from $300 to $400 and everything else stays the same,
how will total cost, total inventory holding cost and total ordering cost change (assume the shop orders
optimally)?
8. Next week, Super Discount Airlines has a flight from New York to Los Angeles that will be booked
to capacity. The airline knows from past history that demand follows a normal distribution, and an
average of 25 customers (with a standard deviation of 15) cancel their reservation or do not show for
the flight. Revenue from a ticket on the flight is $125. If the flight is overbooked, the airline has a
policy of getting the customer on the next available flight and giving the person a free round-trip ticket
on a future flight. The cost of this free round-trip ticket averages $250. Super Discount considers the
cost of flying the plane from New York to Los Angeles a sunk cost.
a. How many seats should Super Discount overbook the flight?
b. What is the expected overage cost and the expected underage cost for Super Discount? By
comparing the two expected costs, what conclusion can you draw?
9. Compare the following factors in a centralized inventory system and a decentralized one. For each
factor, state in which system it is higher and explain why. Make any assumption that you think is
necessary.
a. Inventory holding cost
b. Overhead costs (e.g., employee salaries, office equipment and supplies)
c. Customer lead time (i.e., delivery time from warehouses to customers)
d. Inbound transportation costs
10. So, any final comments for the course before it ends? (optional)