Spring 2025_ISOM2700_Prof.
Lu Lijian
ISOM2700 Spring 2025
Additional Practice Questions (the 2nd-half semester)
(1) In the EOQ model, if the lead-time increases from 5 to 10 days, the optimal order size will ____________
(A) Double
(B) Increase by a factor of 4
(C) Increase by a factor of square root of 2
(D) Increase by a factor that cannot be determined
(E) Remain the same
(2) Which statement about safety stock is NOT correct? ____________
(A) Safety stock is zero if the demand is deterministic.
(B) For normally distributed demand, safety stock is negative if the cycle service level is below 50%.
(C) To determine the safety stock we need to know the variance of demand in the lead time.
(D) To determine the safety stock we need to know the mean of demand in the lead time.
(E) Safety stock may be zero if demand is random.
(3) Which one of these products is NOT a newsvendor-type product? ____________
(A) Flu vaccine
(B) Fashion ski wear
(C) Airplane seats
(D) Job interview suits
(E) Hotel rooms
(4) A company operates four identical warehouses, each serving a geographic region with the same cycle service
level 95%. Demands in these regions are random and independent of each other. Now the company is
considering a consolidation of these four warehouses into one to serve the four regions. The demands in these
regions are estimated to remain the same. Order lead times also remain the same. Suppose the consolidated
warehouse will carry the same amount of safety stock as previously in four warehouses combined. The cycle
service level of the consolidated warehouse will be ____________
(A) higher than 95%
(B) equal to 95%
(C) lower than 95%
(D) Cannot be determined
(5) Regarding the principles of demand forecasting, which of the following is NOT true? ____________
(A) There is no perfect forecast
(B) Forecasts are more accurate for groups rather than individuals
(C) Forecast accuracy increases as time horizon increases
(D) Along with complex forecasting models, simple forecasting models can also make good forecasts
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Spring 2025_ISOM2700_Prof. Lu Lijian
Questions (6) and (7) relate to the following paragraph.
Given the following sales data, use the exponential smoothing model with α = 0.5 to perform forecasting.
Month 1 2 3
Actual sales 530 576 550
Forecast sales 555
(6) What is the forecast sales number (round to the nearest integer) for month 3? ____________
(A) 550
(B) 555
(C) 559
(D) 565
(E) 570
(7) The MAD for months 1 to 3 is ____________.
Questions (8) and (9) relate to the following paragraph.
On a given Hong Kong-Singapore flight, there are 300 seats. Suppose the ticket price is $450 and the number of
passengers who reserve a seat but do not show up for departure is normally distributed with mean 40 and standard
deviation 14. You decide to overbook the flight and estimate that the cost of an involuntary boarding denial (if the
number of passengers exceeds the number of seats) is $1350 (including full refund of purchase).
(8) The optimal number of reservations that you should accept (rounded to the nearest integer) is ___________.
(A) 328
(B) 334
(C) 340
(D) 346
(E) 352
(9) Suppose you have decided to accept the above optimal number of reservations computed in (8). Then what is
the probability that you won’t need deal with bumped passengers? (*Note: The number of no shows is discrete).
(A) 33%
(B) 43%
(C) 57%
(D) 69%
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Spring 2025_ISOM2700_Prof. Lu Lijian
Questions (10) to (12) relate to the following paragraph.
Weekly demand for a product has a normal distribution with a mean of 100 and a standard deviation of 20. Demands
from week to week are independent. The order lead-time is 5 weeks.
(10) What is the distribution of the demand during lead-time? ____________
(A) Mean = 500, standard deviation = 28.28, normally distributed
(B) Mean = 500, standard deviation = 44.72, normally distributed
(C) Mean = 500, standard deviation = 100, normally distributed
(D) Mean = 500, standard deviation = 2000, normally distributed
(11) The safety stock (rounded to the nearest integer) needed to achieve a cycle service level of 97% should be
________.
(12) The reorder point (rounded to the nearest integer) for a cycle service level of 97% should be ________.
Questions (13) to (15) refer to the following paragraph.
Patricia sells ice cream at $5 per scoop at the Piazza on the university's Outreach Day that will be held on Sept 20. As
her supplier requires firm orders by the afternoon of Sept 19, Patricia must make a commitment before the demand is
known. The supplier's wholesale price is $3 per scoop. Patricia forecasts that the demand is normally distributed with
mean 1,000 scoops and standard deviation 150. Any ice cream left by the end of the Outreach Day can be sold for $2
per scoop.
(13) How much should Patricia order from the supplier on Sept 19? ____________
(A) 1000
(B) 1065
(C) 1126
(D) 1150
(E) 2000
(14) Patricia’s supplier now offers a revenue sharing contract with the supplier such that Patricia has to pay $0.5
to the ice-cream supplier for each scoop sold at the regular price of $5. Compared with the original wholesale
price contract, the new contract changes (other parameters remain as before): _______________
(A) The overage cost
(B) The underage cost
(C) The fixed ordering cost
(D) The best inventory model to use
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Spring 2025_ISOM2700_Prof. Lu Lijian
(15) Patricia’s supplier now offers to buy back all unsold ice-cream from Patricia at the end of the day at a buy-
back price of $2.5 each. Compared with the original wholesale price contract, the new contract changes (other
parameters remain as before): ____________
(A) The overage cost
(B) The underage cost
(C) The fixed ordering cost
(D) The best inventory model to use
(16) Consider a paint retailer who sells 4 different colors of paints (red, blue, yellow and green). Assume that
weekly demand for each color is independent, and the weekly demand for each individual color has the
following distribution:
• Red: Normal distribution with mean 40 and standard deviation 10;
• Blue: Normal distribution with mean 100 and standard deviation 30;
• Yellow: Normal distribution with mean 80 and standard deviation 15;
• Green: Normal distribution with mean 120 and standard deviation 40;
The replenishment lead time from the paint factory is 2 weeks and the retailer aims for a CSL=0.95.
(a) How much safety stock in total will the retailer have to hold if paint is mixed at the factory and held in
inventory at the retailer as individual colors?
(b) How much safety stock in total will the retailer have to hold if the retailer holds base and mixes colors on
demand?
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Spring 2025_ISOM2700_Prof. Lu Lijian
(17) A vaccine marketed by a drug company has a known and constant demand of 1,200 units per year (or 100 per
month). The production cost is $720 per unit, the fixed setup cost is $2,400 per batch, and the holding cost
per unit per year is $144. Lead time for production is half a month.
(a) What is the optimal production quantity per batch?
(b) Now assume that the company's demand averages 100 units per month but is no longer constant. The monthly
demand is normally distributed with mean 100. The company has been using a reorder point that provides a
cycle service level of 90.32%. Suppose the management wants to provide a better service and is thinking of
doubling the amount of safety stock. What would be the service level if the safety stock is doubled?
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Spring 2025_ISOM2700_Prof. Lu Lijian
(18) Handi Inc., a maker of cell phones, procures a standard display from LCD Inc. via an options contract, where
the options contract grants Handi the right to exercise the option and buy displays in the future at a given price.
Here is how it works:
At the start of Quarter 1 (Q1), Handi pays LCD Inc. $4.5 per option. At that time Handi’s forecast of demand
in Q2 is normally distributed with mean 25000 and standard deviation 8000. At the start of Q2 Handi learns its
exact demand for Q2 and then exercises options at the fee of $3.5 per option (for every exercised option LCD
Inc. delivers one display to Handi). Assume Handi starts Q2 with no display inventory and displays owned at
the end of Q2 have zero salvage value. Should Handi’s demand in Q2 be larger than the number of options held,
Handi purchases additional displays on the spot market for $10 per unit.
For example, suppose Handi has purchased 30000 options (at $4.5 per option) at the start of Q1 but at the start
of Q2 Handi realizes that demand is 35000 units. Then Handi exercises all of its options (at $3.5 per option) and
purchases 5000 additional units (at $10 per unit) on the spot market. If, on the other hand, Handi realizes that
demand is only 28000 units, then Handi merely exercises 28000 options.
How many options should Handi purchase from LCD Inc. at the start of Quarter 1?
[Hint: This is an application of the newsvendor model.]
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Spring 2025_ISOM2700_Prof. Lu Lijian
(19) Short Answer Questions
I. Answer “True” or “False” to the following statements. If False, please explain the reason in one or two
sentences.
a. When the demand variability increases, the optimal newsvendor order quantity also increases.
b. All else equal, a higher underage cost per unit leads to a larger optimal newsvendor order quantity.
II. A newsvendor keeps careful records of the number of papers he has sold each day. He uses this information to
estimate his demand distribution. For what reason might his results be inaccurate?
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Spring 2025_ISOM2700_Prof. Lu Lijian
(20) Umbra Visage (UV) is a retailer of Zamatia, an upscale maker of eyewear. UV purchases each pair of
sunglasses from Zamatia for $75 and sells them for $115. Zamatia’s production cost per pair is $35. At the end
of the season, UV offers deep discounts to sell remaining inventory. The estimate is each pair will only have
$25 salvage value if not sold by the end of the season. UV’s forecasting department believes the demand for
this pair of sunglasses is:
Demand 800 1,000 1,200 1,400 1,600 1,800
Probability 0.11 0.11 0.28 0.22 0.18 0.10
(a) What is the optimal order quantity for UV?
(b) What is Zamatia’s expected profit when UV orders its optimal order quantity in part (a)?
(c) What would be the integrated supply chain’s optimal order quantity if there’s a centralized decision
maker?
(d) The manager at Zamatia is thinking about how to achieve first-best solution, as an advisory consulting for
Zamatia, can you give an advice on proposing a contract between Zamatia and UV to achieve the first-best
solution?
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