1. (60 points) Answer the following questions; 4 points each.
a. Consider that the demand for Product A per month as normally distributed with mean 500 units and
s.d. 0.1 units and Product B as normally distributed with mean 100 units and s.d. 10 units. Both have
an expected lead time of 4 days with s.d. of 0.01 days. Why is it reasonable to use EOQ for Product
A and not for Product B? Be precise and concise.
b. Which is not a valid statement about the Newsvendor Model?
i. demand is stochastic and IID
ii. single product and single period
iii. critical ratio takes on any continuous value
iv. can be applied to multi-period settings
c. For a mixed model used for forecasting, which includes level, trend, and seasonality, what would be
likely values of trend and seasonal factors for a non-seasonable product with demand growing at the
rate of 25%?
i. T = 0, S = 0 iii. T > 0, S = 1
ii. T = 1, S > 1 iv. T > 0, S = 0
d. Fill in the forecast and error columns in the table below for a 2-period moving average forecasting
model. (Hint: Your answer for each empty cell could be either ‘unknown’ or a calculated value.)
Period Observed demand Forecast Forecast
Error
1 10
2 15
3 20
4 15
5 –
e. Which of the following does not possess the Wagner-Whitin property?
i. Lot-for-lot iii. Fixed order quantity
ii. Fixed order period iv. Order once a week
f. To manage the inventory of a part, a continuous review system is used. The lead time is 1 week, and
the mean and s.d. of the demand during lead time are 23 and 50, respectively. Stockouts are
backordered. Management believes that an appropriate level of service is 95%. What is the
corresponding safety stock? (Show your work.)
i. 83 iii. 106
ii. 23 iv. 56

g. Calculate the total bias for the demand and forecast information provided below. (Hint: You may use
empty columns to calculate intermediate values. Your answer for each empty cell in the Biast column
could be either ‘unknown’ or a calculated value. Biast = Biast-1 + Et.)
Period Demand Dt Forecast Ft
1 96 106
2 119 117
3 96 114
4 102 114
h. State clearly at least two differences between the newsvendor model and the (Q,r) model.
i. Consider the table below resulting from lot sizing by the Wagner-Whitin algorithm (for the data
provided below). Specify the optimal six-month production schedule (i.e., when to produce and how
much to produce).
t 1 2 3 4 5 6
Dt 1000 1200 500 200 800 1000
j. Which costs are considered in the newsvendor model? Also indicate why is/are other cost(s) not
considered.
ISE 4810/IHE 6810 Production and Service Systems Parikh
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k. State two benefits and two limitations of the Winter’s forecasting model.
l. Demand for an item in a month (4 weeks/month) is iid and normally distributed with mean of 100
units and standard deviation 10 units. The lead time is 2 weeks. Suppose that the reorder point is 100.
Compute the probability of a shortage in an order cycle.
m. What is the difference between Fixed Order Quantity and Fixed Order Period inventory policies?
How would you characterize EOQ and Wagner-Whitin with respect to these two policies?
n. Clearly differentiate between Aggregate Production Planning and Capacity Requirements Planning.
o. What is the key difference between the MRP and Kanban systems? When would you use a 2-card
system compared to a 1-card system?
ISE 4810/IHE 6810 Production and Service Systems Parikh
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2. (12 points) An apparel company prints novelty T-shirts for a football event. The T-shirts cost $5 to
make and get sold for $20. Company policy is to dispose any excess inventory after the event by
discounting the T-shirts by 80% (i.e., sells now for $4). It estimates the demand of shirts for this event
to be 12,000 shirts, with a significant amount of uncertainty. What would you recommend the optimal
number of shirts this company should print, and when, to minimize their costs?

3. (12 points) Jill estimates that the annual demand of a part can be approximated as a Poisson distribution
with parameter value of 15. It takes 50 days to receive a replenishment order. The firm uses an annual
interest rate of 10% and each unit of this part costs $100. The ordering cost is $20 per order. A shortage
causes the customer to buy from competition, the cost of which is estimated to be $50. Suggest an
appropriate inventory model that Jill should use, indicate the reasons for your choice, and solve for the
corresponding ‘how much’ and ‘when’ questions?
ISE 4810/IHE 6810 Production and Service Systems Parikh
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4. (16 points) Bolts are consumed at a factory at a steady rate of 60 per week. Each bolt costs 2 cents. It
costs the factory $12 to initiate an order and holding costs are based on an annual interest rate of 25%.
a. (4 points) When and how many bolts should this factory order?
b. (4 points) What would be the percentage increase in total annual cost if the forecast of 60 per week
had 100% error? That is, the actual is 120 bolts per week.
c. (8 points) If the orders must be placed according to the power-of-2 rule (1, 2, 4, 8, … months) to
permit truck-sharing with orders of other parts, how much ($ and %) would this policy add to the
total cost compared to the cost found in (a)?