1. Inventory Control Models
Due December 4th
Homework Assignment
Inventory Control Models
MGMT E-5065 Operations and Logistics Management

2. Operations and Logistics
The Toy Manufacturer
MGMT E-5065
Operations and Logistics
Management
Problem 1
A toy manufacturer uses forty eight thousand ( 48,000 ) wheels
per year for its popular dump truck series. The firm makes its
own wheels which it can produce at a rate of eight hundred ( 800 )
per day. The toy trucks are assembled uniformly over the entire
year. Carrying cost is one dollar ( $1.00 ) per wheel a year. Setup
cost for a production run of wheels is forty five dollars ( $45.00 ).
The firm operates two hundred and forty ( 240 ) days per year.

3. The Toy Manufacturer REQUIREMENT
Manually compute the optimal production run size.
Manually compute the total variable costs ( TVC ) for the above
production run size.
C. Manually compute the length of the production run period.

4. Office Supply Distributor
A firm buys a projector bulb at the rate of ten ( 10 ) per week.
The price charged by the manufacturer varies with the order
quantity as follows:
Order Quantity
Unit Price
0 - 99
$200.00
$180.00
$150.00
500 or more
$130.00
Problem 2
The firm estimates that it pays one hundred dollars ( $ ) for
each order of bulbs. It also believes that it costs eighteen percent
( 18% ) per year of a bulb’s unit price to hold it in inventory.

5. Office Supply Distributor
REQUIREMENT
A. Determine the most cost-effective number of bulbs to order
at one time.
B. Compute the TC ( total costs ) for such an ordering policy
as well as the candidate ordering policies.
NOTE: Assume a fifty-two ( 52 ) week year.

6. ABC Company
Problem 3
ABC Company is the exclusive North American distributor of a
portable sauna manufactured in Sweden. The saunas cost the
company two-thousand four-hundred dollars each ( $2, ) ,
and the company estimates the annual carry cost per unit for
this product is five-hundred and twenty-five dollars ( $ ) .
Because the saunas must be shipped in a containerized vessel,
the fixed ordering cost is fairly high at one-thousand two-hundred
and fifty dollars ( $1, ) . Lead time for delivery is four ( 4 )
weeks. ABC Company receives orders for an average of fifteen
( 15 ) saunas per week. Customers are willing to place orders for
the saunas when ABC is out of stock. However, the firm estimates
the cost of keeping a customer’s sauna on backorder is $1,040.00
one thousand and and forty dollars per year.

7. ABC Company REQUIREMENT
Determine the optimal order quantity ( Q* ) for the saunas.
Determine the optimal number of backorders ( S* ) .
Determine the reorder point ( ROP / R ) for the optimal
order quantity.
Note: The firm operates fifty-two ( 52 ) weeks a year.

8. The Retailer
Problem 4
A retailer buys a certain item from a distant supplier. Lead time
( L ) is normally distributed with a mean of thirty days ( µ = 30 )
and a standard deviation of fourteen days ( σ = 14 ).
Daily demand is also normally distributed with a mean of four
items ( µ = 4 ) and a standard deviation of one and one-half items
( σ = 1.5 ) .

9. The Retailer REQUIREMENT
Determine the safety stock and reorder point for an eighty-five
percent (85%) service level, that is, a 15% risk of a stockout.
B. Determine the safety stock and reorder point for a ninety-five
percent (95%) service level, that is, a 5% risk of a stockout.

10. XYZ Company
Problem 5
XYZ Company buys a component from a distant vendor seven
(7) times a year. It takes an average of ten (10) days to receive
an order from the time it is placed.
The units cost three dollars ( $3.00 ) each and have a carry cost
of seventy-five cents ( $.75 ). The firm estimates a stockout cost
of one dollar ( $1.00 ) per unit. The probability distribution of
demand during a ten ( 10 ) day period is as follows:
Demand
144
152
160
168
176
184
192
Probability
.01
.04
.20
.50

11. XYZ Company REQUIREMENT
Calculate the safety stocks ( SS ) for reorder points 168
and 176 ( units ).
Calculate the additional annual carry costs ( H ) for the
reorder points 168 and 176 ( units ).
3. Calculate the annual expected stockout costs ( Cs ) for
the reorder points 168 and 176.

12. Inventory Control Models
Homework Assignment
Inventory Control Models
MGMT E-5065 Operations and Logistics Management