Chapter 14
Inventory Management
Independent vs. Dependent Demand Items
Independent demand inventory items
– demand cannot be computed, it is random (uncertain)
– items such as finished goods or end items
Dependent demand inventory items
– demand is directly related to that of another item
– items like raw materials or subcomponents (related to
end item)
Big Question  When and how much to order?
every day |-----------------------------------------------------| once a year
2 Basic Approaches to Ordering Inventory
Fixed order quantity
– always order same quantity
– order whenever inventory level gets low (order point)
Fixed order period
– always order every n days
– order a different quantity each time
Economic Order Quantity (EOQ) model is most
common fixed order quantity approach
Inventory Costs
Ordering Costs
– clerical costs, postage, material handling costs, etc.
– setup or changeover cost
# orders/year = D/Q
Annual ordering cost = S(D/Q)
where
D = annual units demanded (forecast)
Q = quantity of one order
S = average cost of processing one order
Carrying Costs
-- costs incurred to keep items in storage
average inventory level = Q/2
(for basic EOQ model)
Annual carrying cost = C(Q/2)
where C = carrying cost rate ($ per unit per year)
Acquisition Costs
– cost to purchase or produce the items
Annual acquisition cost = D(ac)
where
ac = cost to purchase or produce one
unit of the item
Stockout Costs
– estimated per unit cost of a stockout (running
out of items)
– extra paperwork, lost sales, late fees, lost
goodwill, etc.
Cost of Capital
Interest paid to bank to borrow money to finance inventory
Example:
8% annual interest rate
60,000 units annual demand
$20 per unit—cost
order size = 5000 units
average inventory on hand = 2500 units
How much interest should they expect to pay next year?
Balancing Carrying Costs Against Ordering Costs
Annual Cost of Stocking
a Material ($)
600
500
400
Minimum
Total Annual
Stocking Costs
300
x
200
100
0
0
200
400
EOQ
x
600
800
1000
Q = Quantity of Material per Order (Units)
1200
Time Graph of Inventory
Inventory
Levels
Q
OP
EDDLT
0
LT
LT
LT
Time
Average Inventory Level = Maximum Inventory + Minimum Inventory
2
= (Q + 0)/2
= Q/2
Time Graph of Inventory
Inventory
Levels
Q
OP
EDDLT
SS
0
LT
LT
LT
Time
Average Inventory Level = Maximum Inventory + Minimum Inventory
2
= [(Q+SS) + SS]/2
= Q/2 + SS
EOQ Assumptions
– Demand, ordering cost rate, carrying cost rate, unit cost,
and lead time are known constants
– An order arrives all at once
– No stockouts occur
– No safety stock is carried
Total annual inventory cost = ordering + carrying +
acquisition costs
TC = S(D/Q) + C(Q/2) + D(ac)
We want to find the order quantity that results in the
minimum total annual inventory cost.
At the minimum total cost, the slope of the total cost curve
is zero, so the derivative of TC with respect to Q is zero.
TC = S(D/Q) + C(Q/2) + D(ac)
d{TC} SD C
 2  0 0
d{Q}
Q
2
Solve for Q to get:
2DS
Q 
C
2

2DS
Q  EOQ 
C
*
Basic EOQ Example
Annual demand = 6000 units
Ordering cost rate = $100 per order
Acquisition cost = $24 per unit
Carrying cost rate = 25% of unit value per year
250 work days per year
What quantity should be ordered to minimize total annual
inventory cost?
EOQ =
2DS
C
What is the total annual inventory cost with this order
quantity?
TC = S(D/Q) + C(Q/2) + D(ac)
TC =
TC =
On average, how many orders per year should be
expected?
On average, how many work days should one order last?
What is the expected minimum, maximum, and average
inventory level?
EOQ with Quantity Discounts
Step 1: Calculate EOQ for each price
Step 2: For feasible EOQs, calculate total annual
cost
Step 3: Calculate total annual cost at the lowest
allowable quantity for each lower price
Step 4: Pick quantity with lowest total annual cost
Graph of EOQs and price break quantities
Example: An office supplies wholesaler sells copier paper
by the ream. Ordering cost is $20/order. Carrying cost
rate is 30% of the dollar value per year. Annual demand
is 1000 reams.
#Reams Cost/Ream
1-49
50-199
200-499
500+
EOQ3.90 =
EOQ3.75 =
EOQ3.65 =
EOQ3.60 =
3.90
3.75
3.65
3.60
Calculate TC for:
TC = SD/Q + CQ/2 + D(ac)
TC3.75 =
TC3.65 =
TC3.60 =
189 reams @ $3.75
200 reams @ $3.65
500 reams @ $3.60
Order Point
Perpetual inventory accounting – inventory records are
updated anytime inventory levels change (typically used
with fixed order quantity inventory systems)
Order point – the inventory level that triggers an order
Lead time – lead time is the amount of time between when
a replenishment order is placed until it is received
Stockout – inventory level drops to zero
For most fixed order quantity systems, stockouts can only
occur during the lead time
If demand is constant, set the order point equal to the
expected demand during the lead time
OP = EDDLT
Stockouts and Safety Stock
2 main reasons for a stockout:
-- demand during lead time is greater than expected
-- lead time is longer than expected
Safety stock is extra inventory held during the lead time
(beyond EDDLT amount) and is the most common
approach to reducing stockouts
OP = EDDLT + SS
What are the disadvantages of:
-- too little safety stock?
-- too much safety stock?
Setting Order Points
Problem: What inv. level should order point be set at?
2 common approaches
-- set OP to achieve a desired customer service level
-- set OP to minimize costs of to much or too little inv.
There are many ways to measure customer service.
We will define customer service level as:
-- the % of DDLT filled with stock on hand
(What is safety lead time?)
Order Point Example
Annual demand = 8000 units
Lead time = 4 working days
260 working days per year
Safety stock = 200 units
What inv. level should the order point be at?
Two-Bin System (for inventory control)
4 Examples of Setting the OP
•
Achieve a desired service level
–
–
•
discrete demand (small numbers)
continuous demand (normal distr.)
Example#
1&2
3
Minimize stockout and carrying costs
–
payoff table
4
1. Sue’s Jewelry orders 20 men’s Rolex watches (style
#41B) each time the inventory level of this item gets low.
There is a two week lead time once the order is placed
with the supplier. Sue’s records show that for the past
20 times an order has been placed, the demand during
the 2-week lead time has always been 3, 4, 5, 6, or 7
watches. The number of occurrences of these demands
has been 4, 7, 6, 2, or 1, respectively (a total of 20 DDLT
observations). Since the carrying cost for Rolex watches
is quite high, Sue wants to determine what order point to
use so that there are enough watches on hand during
the lead time to sell to 80% of the customers who
request one.
Sue’s Jewelry
DDLT
3
4
5
6
7
Frequency
4
7
6
2
1
20
Prob.
Find OP for an 80% service level
Service Level
2. So that it can get a volume discount, Kendall Ford
orders 20 F-150 extended cab pickup trucks each time it
places an order from the manufacturer. The lead time to
receive the trucks is 22 days. The frequency of different
demands during the lead time has been 3, 4, 7, 8, 9, 12,
and 5 occurrences for demands of 9, 10, 11, 12, 13, 14,
and 15 trucks, respectively. Due to the cost of having
extra trucks on hand, management has decided it is not
cost effective to try to avoid all stockouts during the lead
time. They would like to set the order point for the F-150
so that it is out of stock for no more than 30% of the
customers who would buy this truck. Kendall Ford
should place a new order when how many trucks are left
on the lot? How many trucks should they expect to sell
during the new lead time?
Kendall Ford Trucks
DDLT
9
10
11
12
13
14
15
Occurrences
3
4
7
8
9
12
5
48
Prob.
Service Level
3. A distributor of aircraft jet fuel orders 180,000
gallons each time its supply gets low. The lead
time is 3 days. The average daily demand for jet
fuel is 18,500 gallons. Past records show that
the standard deviation of demand during the
lead time is 12,500 gallons. Because of stiff
competition from another distributor, it is desired
to have enough fuel on hand so that a stockout
occurs no more than 5% of the times that
customers place orders during the lead time.
What should the level of safety stock be? How
many gallons should be on hand when an order
is placed?
Safety Stock and Order Point
Probability
of Stockout
SS = zσDDLT
EDDLT
OP
Actual
DDLT
Payoff Table:
Long cost – the cost of one unit left over on hand when an
order arrives
Short cost – the cost of being one unit short during the lead
time (stockout cost)
4. Each year the Payless Drug Store on Coburg road
places orders for cases of natural Christmas wreaths
and pays $20 for a case of ten wreaths. The sales price
is $5 per wreath. Records for the past 20 orders show
that demand during the lead time has been 6 cases on 2
occasions, 7 cases on 6 occasions, 8 cases on 10
occasions, and 9 cases on 2 occasions. Any wreath left
on hand when a new order arrives will be all dried out
and must be thrown away. What is the long cost and
short cost? What should the order point be? What
service level would this order point provide?
Payoff Table
Long cost =
DDLT
6
7
8
9
Freq.
2
6
10
2
20
Short cost =
Prob.
Next, fill in payoff table and compute expected costs (EC)
(Long cost or short
cost in table)
6
6
OP
7
8
9
Prob:
actual DDLT
7
8
9
EC
Reducing Lot Sizes
Cutting setup costs is key to reducing production lot sizes.
Setup reduction examples
•
•
•
•
•
•
•
•
Summary of Benefits of Reduced Lot Sizes
shorter lead times
less inventory investment
defectives are caught quicker – less scrap, rework, & future
errors
need less floor space – employees closer together – better
communication
processes more closely linked – encourages joint problem
solving
simplified inventory management
lower material handling costs
avoid lumpy workloads
Processing Schedule
Alternative 1: process batch size = 100 units; transfer batch size = 100 units
Machine
1
batch 1
2
batch 1
3
batch 1
4
3000
batch 1
5
batch 1
6
batch 1
0
500
1000
1500
Elapsed Time
(minutes)
2000
2500
3000
Processing Schedule
Alternative 2: process batch size = 100 units; transfer batch size = 50 units
Machine
1
batch batch
1
2
2
batch
1
batch
2
batch
1
3
batch
2
batch
1
4
batch
1
5
1750
batch
2
batch
2
batch
1
6
0
500
1000
batch
2
1500
Elapsed Time
(minutes)
2000
2500
3000