Inventory Management
Class Examples
1.
EOQ Example: The Fill-er-Up gas station has found that demand for its unleaded gasoline is
fairly constant and uniform at the rate of 100,000 gallons per year. Fill-er-Up must pay $100 for
shipping per order of gasoline, which it currently buys for $0.75 per gallon. Inventory carrying
cost is 10 percent of unit cost per year. How many gallons should be ordered at a time?
Suppose that Fill-er-Up’s underground storage tanks can hold only 10,000 gallons of unleaded
gasoline. What is the extra cost incurred by ordering this quantity each time instead of the EOQ?
2.
Quantity Discounts Example: Burger-Farm is a fast-food restaurant that buys hamburger buns
from a local bakery. Those buns are used at the rate of 50,000 per year. The baker has just
offered Burger-Farm the following quantity discounts:
Buns Ordered
1-999
1,000-1,999
2,000 or more
Price per Bun
$0.030
$0.028
$0.027
(a) If it costs Burger-Farm $1 for each order placed and the inventory holding cost is 25 percent
of unit cost, determine how much should be ordered each time to minimize total annual variable
costs.
(b) Suppose that Burger-Farm is limited to ordering only one week’s worth of buns at a time due
to storage space limitations and spoilage problems. What impact will this have on total
annual variable cost?
3.
EOQ with Incremental Replenishment Example: The student development center at Marion
College has a student worker who copies and assembles a handbook for students whenever the
supply of these runs low. Past observation indicates that these handbooks are given out at the rate
of four per day. The student worker can copy and assemble 100 per eight-hour day. The student
worker is paid $3.75 per hour, and it takes 0.5 hours to prepare everything to produce a batch of
handbooks. The cost of carrying inventory is related to handbooks that are damaged or become
obsolete due to changes in degree requirements. On average, 10 percent of all handbooks become
unusable, and each one costs $1.00 in materials, labor, and copying costs.
(a) If the office is open 250 days per year, how many handbooks should the student worker
produce at a time?
(b) How many days of demand will be supported by this order quantity?
4.
Fixed Order Quantity Systems (ROP) Example: Sky gifts sells a variety of gift items
including sweatshirts. The manager has observed from past sales that the number of sweatshirts
sold each week varies but is normally distributed with mean 35 and standard deviation 6. Sky
places orders once inventory levels reach their order point. Sky would like to avoid keeping too
large an inventory of sweatshirts but also wishes to meet at least 90% of demand from stock in
order to prevent losing sales. Their supplier takes one week to deliver orders. How low an
inventory level should Duke’s allow before placing orders?
If the supplier’s delivery lead time was two weeks, how low an inventory level should Sky permit
before placing an order?
5.
Fixed-Order-Interval (Periodic) Model Example: The Corner Drug Store stocks a popular
brand of sunscreen. The average demand for the sunscreen in 6 bottles per day, with a standard
deviation of 1.2 bottles. A vendor for the sunscreen producer checks the drugstore stock every
60 days. During one visit, the drugstore had 8 bottles in stock. The lead time to receive an
order is 5 days. Determine the order size for this order period that will enable the drugstore to
maintain a 95 percent service level.
6.
ABC Inventory Classification Example: A company maintains inventories of the following
nine items. Based on this information, determine which are A items, B items, and C items.
Item #
209
4914
37
387
3290
235
48
576
14
Value
$14.76
5.98
1.15
6.48
2.17
75.00
23.95
4.32
932.00
Annual Usage
2,000
15,000
297,000
6,000
6,000
300
7,000
5,000
1,000