# statistics-and-probability-a-manufacturer-called-manufacturer-a-is-reviewing-its-stocking

Problem 2. (EOQ Model) (Total: 1.75 points)
A manufacturer (Called “Manufacturer A”) is reviewing its stocking and replenishment policy for
a commodity component used for production of lawn mowers. The annually demand rate of
this component is 5000 units per year. Components are shipped to the manufacturer in a truck,
and each time an order is placed it costs the manufacturer \$500 regardless the size of the order.
It costs \$50 to hold a unit of component in stock per year.
(a) Please calculate the optimal EOQ (Economic Order Quantity) that the manufacturer
should use for ordering the components.
The optimal EOQ Q*=

integer.)

(b) What is the minimum annual inventory-related cost associated with the optimal EOQ?
The optimal annual inventory-related cost C*=

. (0.25 points)

(c) How often will the manufacturer place an order?
The manufacturer needs to place an order every
in a year.) (0.25 points)

days. (There are 365 days

There is another manufacturer (called “Manufacture B”) located in the same industrial park.
Manufacture B also orders the same components from the same supplier with the same annual
demand rate 10000 units per year (twice of Manufacture A). Moreover, the holding cost and the
fixed ordering cost occurs to Manufacturer B are also the same as Manufacturer A.
Manufacturer A and B decide to combine their orders, i.e., they order the components together,
in which way the fixed ordering cost only occurs once for both of them. In other words, after
Manufacturer A and B combine their orders, the fixed ordering cost and the unit holding cost
remain the same, but the demand rate is tripled.
(d) Please calculate the optimal EOQ for the combined orders.
The optimal EOQ for the combined orders Q*=

units. (0.15 points)

(e) Please calculate the minimum annual inventory-related cost for the combined orders.
The minimum annual inventory-related cost C* =

. (0.15 points)

(f) The annual cost you calculated in (e) is the total cost paid Manufacturer A and
Manufacture B. The two manufactures decide to split the payment of this total inventory
cost based on the proportions of their demand sizes. After splitting the inventory cost,
how much money does Manufacturer A save from combining his orders with
Manufacturer B each year?

Manufacture A saves

every year from combining his orders with Manufacturer

B. (0.2 points)

(g) How can you explain the cost saving calculated in (f)? (0.25 points)

Problem 3. (Newsvendor Problem) (Total: 1.75 points)
Suppose you are a retailer of toys. This year you decide to bring a new toy to the market just in
time for Christmas. The supplier of the new toy only allows you to place order once due to its
limited capacity. The unit wholesale price of the toy is \$12 and the suggested selling price is
\$36. Any unsold inventory will be sold to a discounter at a salvage value of \$6. The demand of
the new toy follows a Normal distribution, with mean demand equals to 1,000 units and
standard deviation equals to 200 units.
(a) The underage cost u =

. (0.25 points)

(b) The overage cost o =

. (0.25 points)

(c) Based on your answers in (a) and (b), what fill rate should you target?
The target fill rate =
That means you would expect

. (0.25 points)
% of your consumers experiencing lost

sales. (0.2 points)

(d) How many toys should you order from the supplier?
The optimal order quantity Q* =

units. (0.5 points)

(e) Suppose everything remains the same, except the salvage value of the toy is reduced
to \$4. How should the optimal order quantity Q* be adjusted? (0.15 points)
A. increase Q*
B. decrease Q*
C. Q* remain the same

(f) Suppose everything remains the same, except the standard deviation of the demand
is reduced from 200 to 100. How should the optimal order quantity Q* be adjusted?
D. increase Q*
E. decrease Q*
F. Q* remain the same

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