Transcript Managing Inventory Throughout the Supply Chain

Managing Inventory
throughout the Supply
Chain
Chapter 11
Chapter Objectives
Be able to:
 Describe the various roles of inventory, including the different types of
inventory and inventory drivers.
 Distinguish between independent demand and dependent demand
inventory.
 Calculate the restocking level for a periodic review system.
 Calculate the economic order quantity (EOQ) and reorder point (ROP) for
a continuous review system.
 Determine the best order quantity when volume discounts are available.
 Calculate the target service level and target stocking point for a singleperiod inventory system.
 Describe how inventory decisions affect other areas of the supply chain.
In particular, be able to describe the bullwhip effect, inventory
positioning issues, and the impact of transportation, packaging, and
material handling considerations.
Inventory Management
• Functions, forms, and drivers of
inventory
• Inventory cost issues
• Tools:
Economic order quantity (EOQ)
Reorder point (ROP) and safety stock
Dealing with quantity discounts
Types of Inventory
•
•
•
•
Cycle stock
Safety stock (buffer inventory)
Anticipation inventory
Others
– Hedge inventories
– Transportation inventory (pipeline)
– Smoothing inventories
Four Inventory Drivers
1. Demand and Supply Uncertainties
 Safety stock, hedge inventory
2. Demand and Process Volume Mismatches
 Cycle stock
3. Demand and Capacity Mismatches
 Smoothing inventory
4. Demand and Supply Lead-Time Mismatches
 Anticipation inventory, transportation inventory
Independent Demand
• Demand from outside the organization
• Unpredictable  usually forecasted
Demand for tables . . .
Dependent Demand
• Tied to the production of another item
• Relevant mostly to manufacturers
Once we decide how many tables we want to
make, how many legs do we need?
Two “Classic” Systems for
Independent Demand Items
• Periodic review systems
• Continuous (perpetual) review systems
Factors
– Order quantity (Q)
– Restocking level (R)
– Inventory level when reviewed (I)
Restocking Levels
• Periodic Review
R  RP L  z RP L
• Continuous Review
R  dL
Periodic Review System
(Orders at regular intervals)
Inventory
level
2
4
6
Time
Continuous Review System
(Orders when inventory drops to R)
How is the reorder
point ROP established?
Q
Inventory
level
R
L-T
lead time to get
a new order in
Time
Comparison of Periodic and
Continuous Review Systems
Periodic Review
Continuous Review
•
•
•
•
•
• Varying order intervals
• Fixed order sizes (Q)
• Allows individual review
frequencies
• Possible quantity discounts
• Lower, less-expensive safety
stocks
Fixed order intervals
Variable order sizes
Convenient to administer
Orders may be combined
Inventory position only
required at review
Order Quantity Q and
Average Inventory Level
As the order quantity doubles
so does the average inventory (= Q/2)
Q2
Q1
Q2
2
Q1
2
What is the “Best” Order
Size Q?
Determined by:
• Inventory related costs
– Order preparation costs and setup costs
– Inventory carrying costs
– Shortage and customer service costs
• Other considerations
– Out of pocket or opportunity cost?
– Fixed, variable, or some mix of the two?
Economic Order Quantity
(EOQ) Model
• Cost Minimizing “Q”
• Assumptions:
Uniform and known demand rate
Fixed item cost
Fixed ordering cost
Constant lead time
What are the Total Relevant
Annual Inventory Costs?
Consider:
 D = Total demand for the year
 S = Cost to place a single order
 H = Cost to hold one unit in inventory for a year
 Q = Order quantity
Then:
Total Cost = Annual Holding Cost + Annual Ordering Cost
= [(Q/2) × H] + [(D/Q) × S]
How do these costs vary as Q varies?
Why isn’t item cost for the year included?
Holding Cost
$
(Q/2)×H
Holding cost increases
as Q increases . . .
Q
Ordering Costs
$
Ordering costs per year
decrease as Q increases
(why?)
(Q/2)×H
(D/Q)×S
Q
Total Annual Costs and EOQ
Holding Cost
Ordering Cost
Total Cost
1500
1000
500
41
0
37
0
33
0
29
0
25
0
21
0
17
0
13
0
90
50
0
10
Inventory Cost ($)
2000
Order Quantity Q
EOQ at minimum total cost
EOQ Solution
2DS
EOQ  Q 
H
*
When the order quantity = EOQ, the
holding and setup costs are equal
Sample Problems
• Pam runs a mail-order business for gym equipment.
Annual demand for the TricoFlexers is 16,000. The
annual holding cost per unit is $2.50 and the cost to
place an order is $50. What is the economic order
quantity?
• Using the same holding and ordering costs as above,
suppose demand for TricoFlexers doubles to 32,000.
Does the EOQ also double? Explain what happens.
EOQ tells us how much to
order...
…but when should we order?
Reorder point and safety stock analysis
Safety Stock
When both lead time and demand are
constant, you know exactly when your
reorder point is ...
Q
R
L
Safety Stock II
Under these assumptions:
Reorder point = total demand during the lead time
between placement of the order and its receipt.
ROP = d × L, where
d = demand per unit time, and
L = lead time in the same time units
Safety Stock III
(Uncertainties)
But what happens when either demand or
lead time varies?
Q
R
L1
L2
Safety Stock IV
What causes
this variance?
Average demand
during lead time
 d L
Uncertainty Drivers
1)
2)
3)
4)
The variability of demand
The variability of lead time
The average length of lead time
The desired service level
2) and 3) are determined by a company’s
choice of supply chain partners
Safety Stock
• Additional inventory beyond amount
needed to meet “average” demand
during lead time
• Protects against uncertainties in
demand or lead time
• Balances the costs of stockouts against
the cost of holding extra inventory
Shown Graphically …
Now, what is the
chance of a stockout?
7%
93%
d  L  SS
Recalculating the Reorder
Point to include Safety Stock
ROP  d L  SS  d L  z L  d2  d 2 L2
where :
d  average demand per time period
L  average lead time
 d2  variance of demand during time period
 L2  variance of lead time
z  number of standard deviations above the
average demand during lead time
Determining “z”
z = number of standard deviations above
the average demand during lead time
The higher z is:
 The lower the risk of stocking out
 The higher the average inventory level
What is the average inventory level when we
include safety stock?
Determining “z”
Typical choices for z:
z = 1.28
z = 1.65
z = 2.33
 90% service level
 95% service level
 99% service level
What do we mean by “service level”?
Reorder Point + Safety Stock
Formula:
ROP  d L  z L   d 
2
d




2
2
L
What happens if lead time is constant?
What happens if the demand rate is constant?
What happens if both are constant?
If you wanted to reduce the amount of safety stock
you hold, what is your best option?
Problems I
One of the products stocked by Sam’s Club is SamsCola.
 During the slow season, the demand rate is
approximately 650 cases a month, which is the same
as a yearly demand rate of 650×12 = 7,800 cases.
 During the busy season, the demand rate is
approximately 1,300 cases a month, or 15,600 cases a
year.
 The cost to place an order is $5, and the yearly
holding cost for a case of SamsCola is $12.
Problems II
According to the EOQ formula:
 How many cases of SamsCola should be
ordered at a time during the slow season?
 How many cases of SamsCola should be
ordered during the busy season?
Problems III
During the busy season, the store manager has decided
that 98 percent of the time, he does not want to run out
of SamsCola before the next order arrives. Use the
following data to calculate the reorder point for
SamsCola.
•
•
•
•
•
Weekly demand during the busy season:
Lead-time:
Standard deviation of weekly demand:
Standard deviation of lead-time:
Number of standard deviations above the
mean needed to provide a 98% service level (z):
325 cases per week
0.5 weeks
5.25
0 (lead-time is constant)
2.05
Quantity Discounts I
What effect will quantity discounts have on EOQ?
D = 1,200 units (100×12 months)
H = $10 per unit per year
S = $30.00 ordering cost
Order Size
0 - 89
90 and up
Price
$35.00
$32.50
Note: When H is a cost based on a percent of the value of
the item, these calculations become more complicated,
but are done in the same way.
Quantity Discounts II
1. Calculate the EOQ for the non discount price:
2 1200 $30
EOQ 
 85
$10
2. If we can order this quantity AND get the
lowest price, we’re done. Otherwise ...
Quantity Discounts III
Compare total holding, carrying, AND item
cost for the year at:
 Each price break
 The first feasible EOQ quantity
Do you understand why we must now look
at item cost for the year?
Quantity Discounts IV
Total costs at an order quantity of 85:
(85/2)×$10 + (1200/85)×$30 + 1200×$35.00 =
$425 + $423.53 + $42,000 = ??
Total costs at an order quantity of 90:
(90/2)×$10 + (1200/90)×$30 + 1200×$32.50 =
$450 + $400 + $39,000 = ??
Conclusions:
• When all costs are considered, it is cheaper to
order 90 at a time and take the price discount.
• When there are volume discounts, the EOQ
calculation might be infeasible or might not
result in lowest total cost.
• If holding cost is a percentage of the item value
(a common practice for more expensive items),
analysis is more complex, but done the same
way
Single-Period Inventory
(When safety stock is not an option)
• Inventory is perishable
– Newspapers, periodicals
– Fresh food, Christmas trees
• Must balance costs of
– Being short = profit lost
– Having excess = item cost + disposal cost – salvage value
• Requires a target service level that best
balances shortage and excess costs
Target Service Level
Sets expected shortage cost = expected excess cost
Or
(1–p) × Cshortage = p × Cexcess
Where p = probability of enough units to meet demand,
(1–p) = probability of shortage
Hence solving for p where the top equation is true
provides the target service level
SLT = Cshortage / (Cshortage + Cexcess)
Target Stocking Point
• Must know how demand is distributed
– Is it roughly the same every day?
– Are there different demand distributions?
• In all cases, develop the cumulative
probability distribution for the demand
levels in order of increasing demand and
select demand level whose corresponding
cumulative probability is nearest to the
target service level.
Text Example for SLT = 65%
Inventory in the Supply Chain
• Bullwhip Effect
– Small demand changes  large order variations
• Inventory Positioning
– Cost and value increases, flexibility decreases down the supply
chain  where do we hold inventory?
• Transportation, Packaging, Material Handling
– Physical size and quantity of lot, how it is packaged, handling
equipment needed,and disposal of packaging are all factors in
choosing appropriate supplier and distribution process
Demand versus Order Size
(Bullwhip Effect)
Case Study in Inventory
Management
Northcutt Bikes: The Service
Department
Supplement
ABC Classification Method
IDEA
Companies have thousands of items to
track
Methods like EOQ only justifiable for most
important items.
ABC Method
1. Determine annual $ usage for each item
2. Rank the items according to their annual $
usage
3. Let:
 Top 20%  “A” items  roughly 80% of total $
 Middle 30%  “B” items  roughly 15% of total $
 Bottom “50%  “C” item  roughly 5% of total $
ABC Analysis Example
Item
Cost
Demand
$ Usage
A1
$46
200
$9,200
B2
$40
10
$400
C3
$5
6680
$33,400
D4
$81
100
$8,100
E5
$22
50
$1,100
F6
$6
100
$600
G7
$176
250
$44,000
H8
$6
150
$900
I9
$10
10
$100
J10
$14
50
$700
Total $ Usage
= $98,500
Ranking by Annual $ Usage
Item
$ Usage
Cumulative $ % of Total $
Usage
Usage
Class
G7
$44,000
$44,000
44.67%
A
C3
$33,400
$77,400
78.58%
A
A1
$9,200
$86,600
87.92%
B
D4
$8,100
$94,700
96.14%
B
E5
$1,100
$95,800
97.26%
B
H8
$900
$96,700
98.17%
C
J10
$700
$97,400
98.88%
C
F6
$600
$98,000
99.49%
C
B2
$400
$98,400
99.90%
C
I9
$100
$98,500
100.00%
C