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19. SuperPart, an auto parts distributor, has a large warehouse in the Chicago region
and is deciding on a policy for the use of TL or LTL transportation for inbound
shipping. LTL shipping costs $1 per unit. TL shipping costs $800 per truck plus $100
per pickup. Thus, a truck used to pick up from three suppliers costs
800 3 100 $1,100+ =
. A truck can carry up to 2,000 units. SuperPart incurs a fixed
cost of $100 for each order placed with a supplier. Thus, an order with three distinct
suppliers incurs an ordering cost of $300. Each unit costs $50, and SuperPart uses a
holding cost of 20 percent. Assume that product from each supplier has an annual
demand of 3,000 units. SuperPart has thousands of suppliers and the company must
decide on the number of suppliers to group per truck if using TL.
a. What is the optimal order size and annual cost if LTL shipping is used? What is the
time between orders?
b. What is the optimal order size and annual cost if TL shipping is used with a
separate truck for each supplier? What is the time between orders?
c. What is the optimal order size and annual cost per product if TL shipping is used
but two suppliers are grouped together per truck?
d. What is the optimal number of suppliers that should be grouped together? What is
the optimal order size and annual cost per product in this case? What is the time
between orders?
e. What is the shipping policy you recommend if each product has an annual demand
of 3,000? What is the shipping policy you recommend for products with an annual
demand of 1,500? What is the shipping policy you recommend for products with an
annual demand of 18,000?
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shown in the Table below:
20. PlasFib is a manufacturer of synthetic fibers used for making furniture upholstery.
PlasFib manufactures fiber in 50 colors on one line. When changing over from one
color to the next, part of the line has to be cleaned, leading to a loss of material. Each
changeover costs $200 in lost material and changeover labor. Assume that each
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changeover requires the line to shut down for 0.5 hour. When it is running, the line
produces fiber at the rate of 100 pounds per hour.
The fibers sold by PlasFib are divided into three categories. There are five fast-
moving colors that average sales of 30,000 pounds per color per year. There are 10
medium-moving colors that average sales of 12,000 pounds per color per year. The
remaining are slow-moving products and average sales of 2,400 pounds per year each.
Each pound of fiber costs $5 and PlasFib has a holding cost of 20 percent.
a. What is the batch size that PlasFib should produce for each fast-, medium-, and
slow-moving color? How many days of demand does this translate into?
b. What is the annual setup and holding cost of the policies you suggested in part (a)?
c. How many hours of plant operation will the above schedule require in a year
(include a half-hour of setup per batch)?
This analysis is shown in worksheet Ex 11-20.
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21. TopOil, a refiner in Indiana, serves three customers near Nashville, Tennessee, and
maintains consignment inventory (owned by TopOil) at each location. Currently,
TopOil uses TL transportation to deliver separately to each customer. Each truck
costs $800 plus $250 per stop. Thus, delivering to each customer separately costs
$1,050 per truck. TopOil is considering aggregating deliveries to Nashville on a
single truck. Demand at the large customer is 60 tons a year, demand at the medium
customer is 24 tons per year, and demand at the small customer is 8 tons per year.
Product cost for TopOil is $10,000 per ton, and it uses a holding cost of 25 percent.
Truck capacity is 12 tons.
a. What is the annual transportation and holding cost if TopOil ships a full truckload
each time a customer is running out of stock? How many days of inventory is
carried at each customer under this policy?
b. What is the optimal delivery policy to each customer if TopOil ships separately to
each of them? What is the annual transportation and holding cost? How many days
of inventory is carried at each customer under this policy?
c. What is the optimal delivery policy to each customer if TopOil aggregates
shipments to each of the three customers on every truck that goes to Nashville?
What is the annual transportation and holding cost? How many days of inventory
are carried at each customer under this policy?
d. Can you come up with a tailored policy that has lower costs than the policies in (b)
or (c)? What are the costs and inventories for your suggested policy?
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Truckload and are as follows:
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22. Crunchy, a cereal manufacturer, has dedicated a plant for one major retail chain. Sales
at the retail chain average about 20,000 boxes a month and production at the plant
keeps pace with this average demand. Each box of cereal costs Crunchy $3 and is
a. Given that it is trying to minimize its ordering and holding costs, what lot size will
the retailer ask for in each order? What is the annual ordering and holding cost for
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the retailer as a result of this policy? What is the annual ordering and holding cost
for Crunchy as a result of this policy? What is the total inventory cost across both
parties as a result of this policy?
b. What lot size minimizes the inventory costs (ordering, delivery, and holding)
across both Crunchy and the retailer? How much reduction in cost relative to (a)
results from this policy?
c. Design an all unit quantity discount that results in the retailer ordering the quantity
in (b).
d. How much of the $1,000 delivery cost should Crunchy pass along to the retailer for
each lot to get the retailer to order the quantity in (b)?
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23. A steel service center sources products from an integrated steel mill at a cost of
$2,000 per ton. Demand for steel at the service center is 50 tons per month. The
service center has a holding cost of 25 percent and incurs a fixed cost of $2,000 for
each order. How many tons of steel should the service center order per replenishment?
What is the annual ordering and holding cost incurred by the service center?
The integrated steel mill incurs a fixed cost of $4,000 for each order placed by the
steel service center. Steel costs the mill $1,000 per ton and the mill has a holding cost
of 20 percent. Assuming that the mill builds up its steel (for the service center) at the
rate of 50 tons per month, what is the annual fixed cost and holding cost incurred by
the mill as a result of the service centers ordering policy? What is the annual cost
incurred by both the service center and the steel mill?
If the steel mill and the service center could work in a coordinated manner, what is the
optimal order size that minimizes their joint fixed and holding costs? What annual
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savings could the supply chain expect as a result of coordination? Design an all unit
quantity discount that the integrated steel mill could use to get the service center to
order the coordinated amount without increasing annual costs at the service center.
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24. The Orange company has introduced a new music device called the J-Pod. The J-Pod
is sold through Good Buy, a major electronics retailer. Good Buy has estimated that
demand for the J-Pod will depend on the final retail price p according to the demand
curve
Demand 2,000,000 2, 000Dp=−
The production cost for Orange is $100 per J-Pod.
a. What wholesale price should Orange charge for the J-Pod? At this wholesale price,
what retail price should Good Buy set? What are the profits for Orange and Good
Buy at equilibrium?
b. If Orange decides to discount the wholesale price by $40, how much of a discount
should Good Buy offer to customers if it wants to maximize its own profits? What
fraction of the discount offered by Orange does Good Buy pass along to the
customer?
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25. The Orange company prices J-Pods at $550 per unit. Good Buy sells the J-Pods at
$775. Annual demand at this retail price turns out to be 450,000 units. Good Buy
incurs ordering, receiving, and transportation costs of $10,000 for each lot of J-Pods
ordered. The holding cost used by the retailer is 20 percent.
a. What is the optimal lot size that Good Buy should order?
b. The Orange company has discounted J-Pods by $40 for the short term (about the
next two weeks). Good Buy has decided not to change the retail price but may
change the lot size ordered from Orange. How should Good Buy adjust its lot size
given this discount? How much does the lot size increase because of the discount?
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26. MCParts, an MRO distributor, sources products from three different suppliers in
the Atlanta region. Currently, MCParts uses TL transportation to source separately
from each supplier. Each truck costs $1,000 plus $400 per stop. Thus, delivering to
each customer separately costs $1,400 per truck. MCParts is considering aggregating
sourcing on a single truck. Demand for the fastest selling product is 120,000 units a
year, demand for the medium selling product is 60,000 units per year, and demand for
the slowest moving product is 12,000 units per year. Each product costs $10 and
MCParts incurs an annual holding cost of 25 percent. Truck capacity is 12,000 units.
a. What is the annual transportation and holding cost if MCParts sources a full
truckload from each supplier in each order? How many days of inventory is carried
for each product under this policy?
b. What is the optimal order quantity of each part if MCParts sources separately from
each supplier? What is the annual transportation and holding cost? How many days
of inventory is carried for each part under this policy?
c. What is the optimal order quantity for each product if MCParts aggregates
shipments from each of the three suppliers on every truck that arrives from
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Atlanta? What is the annual transportation and holding cost? How many days of
inventory are carried at each customer under this policy?
d. Can you come up with a tailored policy that has lower costs than the policies in (b)
or (c)? What are the costs and inventories for your suggested policy?
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27. AZOR, a European detergent manufacturer, has dedicated a plant for one major
retail chain. Sales at the retail chain average about 10,000 jugs of detergent a month
and production at the plant keeps pace with this average demand. Each jug of
detergent costs AZOR €5 and is sold to the retailer at a wholesale price of €10. Both
AZOR and the retailer use an annual holding cost of 25 percent. For each order
placed, the retailer incurs an ordering cost of €100. AZOR incurs the cost of
transportation and loading that totals €1,600 per order shipped.
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a. Given that it is trying to minimize its ordering and holding costs, what lot size will
the retailer ask for in each order? What are the annual ordering and holding costs
for the retailer as a result of this policy? What are the annual ordering and holding
costs for AZOR as a result of this policy? What is the total inventory cost across
both parties as a result of this policy?
b. What lot size minimizes the inventory costs (ordering, delivery, and holding)
across both AZOR and the retailer? How much reduction in cost relative to (a)
results from this policy?
c. Design an all unit quantity discount that results in the retailer ordering the quantity
in (b).
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