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© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 2
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 single-
period 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.
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 3
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
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 4
Types of Inventory
• Cycle stock• Safety stock (buffer inventory)• Anticipation inventory• Others
– Hedge inventories– Transportation inventory (pipeline)– Smoothing inventories
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 5
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
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 6
Independent Demand
• Demand from outside the organization
• Unpredictable usually forecasted
Demand for tables . . .
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 7
Dependent Demand
• Tied to the production of another item
• Relevant mostly to manufacturers
Once we decide how many tables we want tomake, how many legs do we need?
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 8
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)
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 9
Restocking Levels
• Periodic Review
• Continuous Review
LRPLRP zR
dLR
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 10
Periodic Review System(Orders at regular intervals)
Inventorylevel
Time2 4 6
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 11
Continuous Review System(Orders when inventory drops to R)
L-T
Q
R
How is the reorder point ROP established?
Inventorylevel
Timelead time to get a new order in
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 12
Comparison of Periodic and Continuous Review Systems
Periodic Review• Fixed order intervals• Variable order sizes• Convenient to administer• Orders may be combined• Inventory position only
required at review
Continuous Review• Varying order intervals• Fixed order sizes (Q)• Allows individual review
frequencies• Possible quantity discounts• Lower, less-expensive safety
stocks
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 13
Order Quantity Q and Average Inventory Level
As the order quantity doublesso does the average inventory (= Q/2)
Q1
Q2
Q22
Q12
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 14
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?
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 15
Economic Order Quantity (EOQ) Model
• Cost Minimizing “Q”
• Assumptions:
Uniform and known demand rate
Fixed item cost
Fixed ordering cost
Constant lead time
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 16
What are the Total Relevant Annual Inventory Costs?
Consider:D = Total demand for the yearS = Cost to place a single orderH = Cost to hold one unit in inventory for a yearQ = 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?
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 17
Holding Cost
$
Q
Holding cost increasesas Q increases . . .
(Q/2)×H
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 18
Ordering Costs
$
Q
Ordering costs per yeardecrease as Q increases
(why?)
(Q/2)×H
(D/Q)×S
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 19
Total Annual Costs and EOQ
0
500
1000
1500
2000
10 50 90 130
170
210
250
290
330
370
410
Order Quantity Q
Inve
nto
ry C
ost
($)
Holding Cost Ordering Cost Total Cost
EOQ at minimum total cost
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 20
EOQ Solution
HDS
QEOQ2*
When the order quantity = EOQ, the holding and setup costs are equal
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 21
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
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 23
Safety Stock
When both lead time and demand are constant, you know exactly when your reorder point is ...
Q
L
R
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 24
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
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 25
Safety Stock III(Uncertainties)
But what happens when either demand or lead time varies?
Q
L1
R
L2
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 26
Safety Stock IV
What causesthis variance?
Average demandduring lead time Ld
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 27
Uncertainty Drivers
1) The variability of demand
2) The variability of lead time
3) The average length of lead time
4) The desired service level
2) and 3) are determined by a company’s choice of supply chain partners
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 28
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
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 29
Shown Graphically …
Now, what is thechance of a stockout?
93%
SSLd
7%
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 30
Recalculating the Reorder Point to include Safety Stock
timeleadduringdemandaverage
theabovedeviationsdardtansofnumberz
timeleadofvariance
periodtimeduringdemandofvariance
timeleadaverageL
periodtimeperdemandaveraged
where
dLzLdSSLdROP
L
d
Ld
2
2
222
:
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 31
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?
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 32
Determining “z”
Typical choices for z: z
= 1.28 90% service level z = 1.65 95% service level z = 2.33 99% service level
What do we mean by “service level”?
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 33
Reorder Point + Safety Stock Formula:
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?
222Ld dLzLdROP
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 34
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.
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 35
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?
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 36
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: 325 cases per week• Lead-time: 0.5 weeks• Standard deviation of weekly demand: 5.25• Standard deviation of lead-time: 0 (lead-time is
constant)• Number of standard deviations above the
mean needed to provide a 98% service level (z): 2.05
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 37
Quantity Discounts I
What effect will quantity discounts have on EOQ?
D = 1,200 units (100×12 months)H = $10 per unit per yearS = $30.00 ordering cost
Order Size Price0 - 89 $35.0090 and up $32.50
Note: When H is a cost based on a percent of the value of the item, these calculations become more complicated, but are done in the same way.
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 38
Quantity Discounts II
1. Calculate the EOQ for the non discount price:
2. If we can order this quantity AND get the lowest price, we’re done. Otherwise ...
8510$
30$12002 EOQ
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 39
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?
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 40
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 = ??
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 41
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
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 42
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
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 43
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)
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 44
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.
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 45
Text Example for SLT = 65%
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 46
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
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 47
Demand versus Order Size(Bullwhip Effect)
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 49
SupplementABC Classification Method
IDEA
Companies have thousands of items to track
Methods like EOQ only justifiable for most important items.
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 50
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 $
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 51
ABC Analysis Example
Total $ Usage = $98,500
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
© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036
Chapter 14, Slide 52
Ranking by Annual $ Usage
Item $ UsageCumulative $
Usage% of Total $
Usage ClassG7 $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