1. Types of Inventory Transit stock or pipeline inventory Cycle stock
Safety stock (buffer inventory)
Anticipation inventory
Others
Smoothing inventories
Hedge inventories
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

2. Four Inventory Drivers
Demand and Capacity Mismatches
Smoothing inventories
Demand and Process Volume Mismatches
Cycle stocks
Demand and Supply Uncertainties
Safety stocks
Demand and Process Lead-Time Mismatches
Anticipation inventories
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

3. Independent Demand Demand from outside the organization
Unpredictable  usually forecasted
Demand for tables . . .
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

4. 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?
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

5. Two “Classic” Systems for Independent Demand Items
Periodic review systems
Continuous (perpetual) review systems
Fixed order quantity (Q)
Reorder point (R)
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

6. Periodic Review System (Orders at regular intervals)
Inventory
level 2 4 6
Time
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

7. Continuous Review System (Orders when inventory drops to R)
How is the reorder
point R established? Q
Inventory
level R
Time
L-T
lead time to get a new order in
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

8. 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
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

9. Order Quantity Q and Average Inventory Level
As the order quantity doubles
so does the average inventory (= Q/2) Q2
Q2 2 Q1
Q1 2
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

10. 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?
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

11. Economic Order Quantity (EOQ) Model
Cost Minimizing “Q”
Assumptions:
Uniform and known usage rate
Fixed item cost
Fixed ordering cost
Constant lead time
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

12. 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?
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

13. Holding Cost $ Holding cost increases as Q increases . . . (Q/2)×H Q
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

14. Ordering costs per year decrease as Q increases$
Ordering costs per year
decrease as Q increases
(why?)
(Q/2)×H
(D/Q)×S Q
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

15. Total Annual Costs and EOQ
EOQ at minimum total cost
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

16. EOQ Solution
When the order quantity = EOQ, the holding and setup costs are the same
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

17. 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.
Answers: EOQ = 800; 1,131 (goes up as the square root of 2)
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

18. EOQ tells us how much to order...
…but when should we order?
Reorder point and safety stock analysis
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

19. Safety Stock
When both lead time and demand are constant, you know exactly when your reorder point is ... Q R L
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

20. 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
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

21. Safety Stock III (Uncertainties)
But what happens when either demand or lead time varies? Q R L1 L2
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

22. Safety Stock IV What causes this variance? Average demand
during lead time
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

23. Safety Stock V
Additional inventory beyond amount needed to meet “average” demand during lead time
Protects against uncertainties in demand or lead time
Balances the costs of stocking out against the cost of holding extra inventory
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

24. Shown Graphically … Now, what is the chance of a stockout? 93% 7%
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

25. Recalculating the Reorder Point to include Safety Stock
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

26. Determining “z” I
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?
Average inventory plus safety stock level
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

27. Determining “z” II
Typical choices for z: z =  90% service level z =  95% service level z =  99% service level
What do we mean by “service level”?
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

28. Reorder Point 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?
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

29. 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.
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

30. 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?
Slow season: 81 cases
Busy season: 114 cases
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

31. 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
Answer: 245 cases
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

32. Volume Discounts I What effect will volume discounts have on the EOQ?
D = 1,200 units (100×12 months)
K = 12% of unit cost
S = $8.00 ordering cost
Order Size Price
$35.00
75 and up $32.50
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

33. Volume Discounts II 1. Calculate the EOQ for the lowest price:
2. If we can order this quantity AND get the lowest price, we’re done. Otherwise ...
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

34. Volume Discounts III
3. Calculate EOQ at the next lowest price, and keep repeating until you find an EOQ that is “feasible”:
We could order 68 at $35.00 each
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

35. Volume Discounts IV
4. 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?
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

36. Volume Discounts V Total costs at an order quantity of 75:
(75/2)×(12%)×$ (1200/75)×$ ×$32.50 =
$ $ $39,000 = ??
Total costs at an order quantity of 68:
(68/2)×(12%)×$ (1200/68)×$ ×$35.00 =
$ $ $42,000 = ??
Quantity 75: $39,274.25
Quantity 68: $42,283.98
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

37. Conclusions:
When all costs are considered, it is cheaper to order 75 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.
Hence, more detailed analysis is required.
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

38. ABC Classification Method
IDEA
Companies have thousands of items to track
Methods like EOQ only justifiable for most important items.
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

39. ABC Method Determine annual $ usage for each item
Rank the items according to their annual $ usage
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 $
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

40. ABC Analysis Example Total $ Usage = $98,500 Item Cost Demand $ Usage
$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
$600 G7
$176
250
$44,000 H8
150
$900 I9
$10
$100
J10
$14
$700
Total $ Usage = $98,500
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

41. Ranking by Annual $ Usage
Item
$ Usage
Cumulative $ Usage
% of Total $ Usage
Class G7
$44,000
44.67% A C3
$33,400
$77,400
78.58% A1
$9,200
$86,600
87.92% B D4
$8,100
$94,700
96.14% E5
$1,100
$95,800
97.26% H8
$900
$96,700
98.17% C
J10
$700
$97,400
98.88% F6
$600
$98,000
99.49% B2
$400
$98,400
99.90% I9
$100
$98,500
100.00%
©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield