To find the minimum point on the total cost line, take the first derivative of the total cost equation with
respect to Q and set the result equal to zero as follows:
Q =
28) The campus bookstore sells 4,000 sets of graduation regalia each year. Placing an order from their
supplier costs $25 regardless of order quantity, so they usually place a large order (a half year’s supply) at
a time. It costs $5 per year to hold a cap and gown in inventory, primarily insurance costs for the highly
flammable material. What is the difference in their holding cost if they order at their optimal order
quantity compared to their current policy?
29) A catfish bait manufacturer uses a secret blend of ingredients to make their infamous bait. One of
these ingredients, we’ll call it X for proprietary reasons, is the major component in the mixture. X is
ordered in 55 gallon barrels from out of state and is used at the rate of 800 barrels per year. Each order
that is placed with the supplier costs $45 to process. Storage space is at a premium on the manufacturing
floor and out in the yard, so their annual cost to hold inventory is $80 per barrel. The owner’s brother–in–
law provides transportation services and his record has been less than stellar, so lead time has averaged 6
days with a standard deviation of 3 days. Stopping the process would be disastrous, so the plant manager
has set a 99% service level on the reorder point.
What is the best order quantity?
What is the total cost at this reorder point?
What is the reorder point?
What is the cost of holding this safety stock?
30) Nothing is too good for my cats, so all their food is custom made at Catastic, who operates a specialty
organic food mill in an adjacent state. We need 500 pounds of food per year, distributed evenly
throughout the year. It costs $20 shipping and handling to place and receive an order for this delicious
food. The cats are fed only on week days, so the 500 pounds per year translates to 2 pounds per day (we
go out to restaurants on the weekends). Of course, my cats don’t always eat exactly 2 pounds per day,
their demand could more precisely be described as an average of 2 pounds and a standard deviation of
0.3 pounds per day. It takes ten days on average to receive an order for food once I place it. It costs $35 to
hold a pound of food in inventory for a year and the food costs $850 per pound. It’s expensive, yes, but
again, nothing is too good for my cats.
What amount should I order and when should I order it if I want only a 1% chance of running out of food
for my cats?
31) Willard offers infestation services for friendly tenants according to the following price schedule: for
up to 99 mice, the price is $1.02 each, for 100 up to 499 mice the price is $1.00 each, and for any order
exceeding 500 mice, the cost is $0.98. He has a flat $1 delivery fee regardless of order quantity. Crystal
will need 10,000 mice this year and face a $4 holding cost. What is her optimal order quantity and how
much does Crystal save using this order quantity versus the next best order quantity?
32) A small refrigeration shop stocks up on electric motors from a catalog supplier located in the
Midwest. The price of the motors varies depending on the quantity purchased; the price breaks are
shown in the table. The refrigeration shop knows it will need around 600 motors for the coming season
and that it will cost them about $40 to place an order. Storage cost for the motors is $10 each. In previous
years they have bought all 600 at once and they are considering doing this again. What order quantity
would you advise and how much can they save using your recommendation instead of their one order
per year strategy?
Quantity
Price/unit
1-49
$35.00
50–99
$34.00
100–499
$33.00
500 or more
$30.00
11.4 Single-Period Inventory Systems
1) The food engineers at Moria Foods have developed a new variety of banana they have named the
“mayfly banana” which holds perfect ripeness for exactly one day before becoming a black-skinned sack
of mush. Which of these actions will result in a lower order quantity from the many retail establishments
clamoring to stock up on this new foodstuff?
A) an increase in the price consumers are willing to pay for the mayfly banana
B) an increase in the standard deviation of the number of mayfly bananas demanded by consumers
C) a decrease in the salvage value of the mayfly bananas
D) a decrease in the disposal cost of the mayfly bananas
2) A local barbecue joint makes one massive batch of potato salad each day. If they run out of this savory
side before the end of the day, their last few customers are less than satisfied, but if they make too much,
they sell it to the local hog farmer for feed. Every serving costs an equivalent of $0.23 to make, but can be
sold for $1.50 to customers and for $0.08 to the hog farmer. The average daily demand is for 200 servings
with a standard deviation of 20 servings. How many servings should be made each day?
A) 220
B) 225
C) 230
D) 235
3) A local barbecue joint makes one massive batch of potato salad each day. If they run out of this savory
side before the end of the day, their last few customers are less than satisfied, but if they make too much,
they sell it to the local hog farmer for feed. Every serving costs an equivalent of $0.23 to make, but can be
sold for $2.50 to customers and for $0.12 to the hog farmer. The average daily demand is for 400 servings
with a standard deviation of 40 servings. How many servings should be made each day?
A) 467
B) 453
C) 462
D) 455
4) Geoff hesitated as he read the fast food menu, unsure whether he should supersize his order of
delicious golden French fries. Doing so would increase his cost from $0.99 to $1.59 and just might provide
him the nutrition he needed to make it through the second half of his day at the office. Of course, if he
finished his hamburger and the usual amount of fries, he would simply throw the extra ones away.
However, if he failed to supersize his order, he would have to take a candy bar break mid-afternoon and
they weren’t exactly giving them away in the break room vending machines. He would likely need two
candy bars, which sold for $0.95 each. What is Geoff’s target service level?
A) 0.29
B) 0.61
C) 0.76
D) 0.87
5) Warren hesitated as he read the fast food menu, unsure whether he should supersize the orders of
delicious golden French fries. As the office lunch boy, he was responsible for buying enough food to keep
his coworkers satiated during the rest of the work day. Supersizing would increase his cost from $0.99 to
$1.59 and just might provide his colleagues the nutrition they needed to make it through the second half
of their day at the office. Of course, if they finished their hamburger and the usual amount of fries,
Warren would simply throw the extra ones away. However, if he failed to supersize the orders, he would
have to purchase candy bars during the afternoon and they weren’t exactly giving them away in the
break room vending machines. Each hungry colleague would likely need two candy bars, which sold for
$1.25 each. With a demand that is normally distributed with a mean of 15 and standard deviation of five,
what is Warren’s optimal supersize decision?
A) 16.3
B) 17.3
C) 18.3
D) 19.3
6) Degan routinely drove the 400-mile round trip to his favorite grocery store to stock up on bread, which
cost $1.50 per loaf. Running out would be disastrous – an unplanned trip to this store would mean a
custom order that would run $7.75 per loaf. Overstocking wasn’t a big issue, he could sell it to his
teaching partner for $0.10 per loaf. With a demand that is normally distributed with a mean of 125 and
standard deviation of 15, what is Degan’s optimal purchase quantity on his next trip to the store?
A) 139
B) 173
C) 115
D) 128
7) The excess cost of an item is the profit you would have made on it.
8) A target service level is the point where the expected cost of a shortage equals the expected excess cost.
9) Buying advance tickets for the Giraffe Massacre concert on New Year’s Eve saves the buyer one-tenth
of one percent on the face value of the tickets. It would be wise to buy tickets well in advance of the
concert date.
10) In a single-period inventory system, as the average demand rises, the standard deviation of demand
falls.
11) In a single-period system, the target ________ is the balancing point between shortage costs and
excess costs.
12) Unsure whether he should pick up a bunch of cilantro before heading home, the commuter weighed
his options. If he bought a bunch and they didn‘t need it, he would likely have lost the 79 cents because it
would surely spoil. If he didn’t buy it, this would necessitate another trip to the grocery store, which
would cost $3.79 in gasoline. The ________ cost is $3.79.
13) Unsure whether he should pick up a bunch of cilantro before heading home, the commuter weighed
his options. If he bought a bunch and they didn‘t need it, he would likely have flushed the 79 cents
because it would surely spoil. If he didn‘t buy it, this would necessitate another trip to the grocery store,
which would cost $3.79 in gasoline. The ________ cost is $0.79.
14) Three Chums Fish Company buys fresh salmon daily from the fishermen that ply the deep waters of
Puget Sound. Salmon are purchased for $2.50 per pound and sold to the public at $8.50 per pound. The
salmon are kept fresh by displaying them on ice but at the end of the day, any unsold fish have a
noticeable odor and are sold to a nearby chowder stand for $1 per pound. The past year’s demand for
salmon on Saturdays is shown in the table. Based on this information, what should their target service
level and stocking point be? What is the significance of the target stocking level?
Daily Demand (pounds)
# Days at This Level
300
3
320
4
340
6
360
9
380
9
400
8
420
6
440
5
460
2
15) Tickets for the gala Opening Night festivities in Oklahoma City are available for $80 in advance at a
couple of area businesses. If you wait until you arrive at the venue, you will pay full face value of $100
per ticket to enjoy the same festivities. If you buy a ticket and don’t use it, you can buy $25 worth of
chemicals and treat the ticket so that it can be used the following year. You have been taking orders from
your friends for a few years and historically demand has been normally distributed with a mean of 50
tickets and a standard deviation of 10. What’s the best quantity of tickets to purchase for this year’s event?
16) A local barbecue joint makes one massive batch of potato salad each day. If they run out of this savory
side before the end of the day, their last few customers are less than satisfied, but if they make too much,
they sell it to the local hog farmer for feed. Every serving costs an equivalent of $0.23 to make, but can be
sold for $2.50 to customers and for $0.12 to the hog farmer. The average daily demand is for 400 servings
with a standard deviation of 40 servings. How many servings should be made each day? One day the hog
farmer cancels the contract – evidently there are some things that even hogs won’t eat. With no fallback
position, how many servings of potato salad should the barbecue joint make? Discuss the discrepancy
between the two numbers.
11.5 Inventory in the Supply Chain
1) The factory produces product and ships it to the distributor. The distributor sends it to the wholesaler
when they receive an order. The wholesaler ships the product to the retailer as the retailer requests
replenishment. The customer visits the retailer’s bricks and mortar store to purchase the product when
they run out. According to the bullwhip effect, which of these supply chain members is most likely
subjected to the greatest variability in customer demand?
A) retailer
B) wholesaler
C) distributor
D) factory
2) Supply chain inventory:
A) increases in cost as materials move downstream.
B) decreases in value as materials progress downstream.
C) increases in flexibility as materials progress upstream.
D) is governed by the bullwhip effect, which says a small change upstream can cause a large change
downstream.
3) The bullwhip effect says that a small change in demand downstream in the supply chain causes a large
change in demand upstream.
4) The flexibility of inventory increases as materials move down the supply chain.
5) The value of goods on a “per unit” basis upstream in a supply chain is greater than the value of those
same goods downstream in a supply chain.
6) Order quantity decisions are typically made in isolation from considerations of transportation,
packaging, and material handling.
7) The ________ is an extreme change in the supply position upstream generated by a small change in
demand downstream.
8) Define the bullwhip effect. What can supply chain members do to mitigate its effects?
9) Discuss the advantages of holding inventory far upstream or downstream in the supply chain.