12
Inventory
Management
Homework; 3, 22, 28ab,
31, Add1, Add2, Add3
Chapter 12, Additional Homework 1
Yellow Press Inc. buys slick paper in rolls for textbook printing. Annual demand
is 2500 rolls. The cost per roll is $800, and the annual holding cost is 15
percent of the cost. Each order costs $50. Yellow Press uses a fixed
quantity ordering model.
a. How many rolls should be ordered at a time?
b. What is the time between orders (assuming 250 working days in a year)?
Chapter 12, Additional Homework 2
Sam’s Cat Hotel operates 52 weeks per year, 6 days per week, and uses a fixed quantity
ordering model. It purchases kitty litter for $11.70 per bag.
Current on-hand inventory is 320 bags, with no open orders or backorders.
Demand = 90 bags / week, varies via a normal distribution
Order cost = $54 / order
Annual holding cost = 27% of cost
Desired service level = 80%
Lead time = 3 weeks (18 working days), constant
Standard deviation of weekly demand = 15 bags
a.
b.
c.
d.
What is the EOQ? What is the average time between orders in weeks?
What is the ROP?
An inventory withdrawal of 10 bags was just made. Is it time to reorder?
The store currently uses a lot size of 500 bags (i.e. Q=500). What is the annual
holding cost of this policy? Annual ordering cost? Without calculating the EOQ, how
could you conclude from these two calculations that the current lot size is too large?
e. What would be the annual cost saved by shifting from the 500-bag lot size to the
EOQ?
Chapter 12, Additional Homework 3
Petromax Enterprises uses a fixed quantity ordering system for one of its inventory items.
The firm operates 50 weeks in a year.
Demand = 50,000 units per year
Ordering cost = $35 per order
Holding cost = $2 per unit per year
Lead time is 3 weeks fixed
Standard deviation of weekly demand = 125 units
a. What is the EOQ?
b. If Petromax wants to provide a 90% service level, what should be the safety stock and
reorder point?
Outline, Two Major Models
Fixed Quantity Model
Order a fixed amount
Order cycle (time between orders) varies
EOQ, Q0, TC (holding and ordering costs)
ROP
- Constant demand, constant lead time
- Variable demand~N, constant lead time
Fixed Interval Model
Order various amounts
Order cycle is fixed or constant
Inventory Management
 Inventory is a stock of anything held to meet some
future demand. It is created when the rate of receipts
exceeds the rate of disbursements.
 A stock or store of goods.
 Inventory Turns (Turnover)
COGS/Avg. Inventory Investment
ABC Analysis
Percentage of dollar value
100 —
Class C
Class B
90 —
Class A
80 —
70 —
60 —
50 —
40 —
30 —
20 —
10 —
0—
10
20
30
40
50
60
70
Percentage of items
80
90 100
Fixed Quantity Model
Constant demand, constant lead time.
On-hand inventory (units)
Receive
order
Inventory depletion
(demand rate)
Q
Average
cycle
inventory
Q
—
2
1 cycle
Time
Fixed Quantity Model – Formulas
Constant demand, constant lead time.
2 DS
H
Q
D
TC  H  S
2
Q
Q
TBO 
D
ROP  d ( LT )
Q0 
Q0=Economic Order Quantity
Q=Order Quantity
D=Annual demand
S=Order cost per order
H=Annual holding cost per unit
TC=Total annual costs
TBO=Time between orders, order cycle time
ROP=Reorder Point, used when LT>0
d=demand rate
LT=Lead time
Constant means fixed or non-fluctuating.
Fixed Quantity Model – Total Costs
Constant demand, constant lead time.
Ex: Find Q0, TBO, and make cost comparisons
Constant demand, constant lead time, LT=0.
Suppose that you are reviewing the inventory policies on
an item stocked at a hardware store. The current
policy is to replenish inventory by ordering in lots of
360 units. Additional information given:
D = 60 units per week, or 3120 units per year
S = $30 per order
H = 25% of selling price, or $20 per unit per year
Ex: Determine ROP
Constant demand, constant lead time, LT>0.
On-hand inventory (units)
Q=300 units, LT=8 days, TBO=30 days.
R
Time
Fixed Quantity Model
Variable demand~N, constant lead time, LT>0.
ROP  d ( LT )  Z ( d ) LT
Cycle-service level = 85%
Probability of stockout
(1.0 – 0.85 = 0.15)
Average
demand
during
lead time
R
Ex: Determine EOQ, ROP
Variable demand~N, constant lead time, LT>0.
The Discount Appliance Store uses a fixed order quantity model. One of
the company’s items has the following characteristics:
Demand = 10 units/wk (assume 52 weeks per year, normally distributed)
Ordering and setup cost (S) = $45/order
Holding cost (H) = $12/unit/year
Lead time (L) = 3 weeks
Standard deviation of demand rate = 8 units per week
Service level = 70%
Fixed Interval Model
Variable demand~N, constant lead time, LT>0.
Q  d (OI  LT )  Z d OI  LT  A
OI=Time between orders
A=Amount on hand at order time
On-hand inventory
Fixed Interval Model
Order
received
Order
received
OH
OH
IP1
IP3
Order
placed
Order
placed
IP2
LT
LT
OI
LT
OI
Time
Ex: Fixed Interval Model, page 572
d=30 units per day
d=3 units per day
LT=2 days
Service level 99%
OI=7 days
A=71 units
Fixed Quantity Model vs. Fixed Interval Model