1. Supply Chain Management
SYST 4050 Slides
Supply Chain Management
Lecture 21
Chapter 3

2. Outline Today Friday Next week Finish Chapter 11 Start with Chapter 12
SYST 4050 Slides
Outline
Today
Finish Chapter 11
Sections 1, 2, 3, 7, 8
Skipping 11.2 “Evaluating Safety Inventory Given Desired Fill rate”
Start with Chapter 12
Sections 1, 2, 3
Section 2 up to and including Example 12.2
Friday
Homework 5 online
Due Thursday April 8 before class
Next week
Finish Chapter 12
Start with Chapter 14
Chapter 3

3. Managing Inventory in Practice
SYST 4050 Slides
Managing Inventory in Practice
India’s retail market
Retail market (not inventory) projected to reach almost $308 billion by 2010
Due to its infrastructure (many mom-and-pop stores and often poor distribution networks) lead times are long
ss = Fs-1(CSL)L
Chapter 3

4. Managing Inventory in Practice
SYST 4050 Slides
Managing Inventory in Practice
Department of Defense
DOD reported (1995) that it had a secondary inventory (spare and repair parts, clothing, medical supplies, and other items) to support its operating forces valued at $69.6 billion
About half of the inventory includes items that are not needed to be on hand to support DOD war reserve or current operating requirements
MRO Maintenance Repair and Operations
DoD mandates RFID
Chapter 3

5. SYST 4050 Slides
Safety Inventory
A new technology allows books to be printed in ten minutes. Borders has decided to purchase these machines for each store. They must decide which books to carry in stock and which books to print on demand using this technology. Would you recommend Borders to use the new technology for best-sellers or for other books?
If Borders must carry stock after purchasing this machine, they should carry items with a steady demand, bestsellers and the like. The fringe books that are rarely purchased would best be left to the 10 minute process which is effectively instantaneous production. The books with low demand would be too expensive to stock for sporadic demand; they would need only one of each, but the breadth of the product line would be overwhelming and prohibitively expensive to carry from month to month.
Chapter 3

6. Measuring Product Availability
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Measuring Product Availability
Cycle service level (CSL)
Fraction of replenishment cycles that end with all customer demand met
Probability of not having a stockout in a replenishment cycle
Product fill rate (fr)
Fraction of demand that is satisfied from product in inventory
Probability that product demand is supplied from available inventory
Order fill rate
Fraction of orders that are filled from available inventory
Product availability reflects a firm’s ability to fill a customer order out of available inventory. A stockout results if a customer order arrives when product is not available.
Chapter 3

7. Product Fill Rate fr = 1 – 10/1000 = 1 – 0.01 = 0.99 Q = 1000 ESC = 10
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Product Fill Rate
inventory
fr = 1 – 10/1000 = 1 – 0.01 = 0.99
Q = 1000
time
ESC = 10
inventory
fr = 1 – 970/1000 = 1 – 0.97 = 0.03
time
Q = 1000
ESC = 970
Chapter 3

8. Expected Shortage per Replenishment Cycle
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Expected Shortage per Replenishment Cycle
Expected shortage during the lead time
If demand is normally distributed
Does ESC decrease or increase with ss?
Chapter 3

9. SYST 4050 Slides
Product Fill Rate
fr: is the proportion of customer demand satisfied from stock Probability that product demand is supplied from inventory.
ESC: is the expected shortage per replenishment cycle (is the demand not satisfied from inventory in stock per replenishment cycle)
ss: is the safety inventory
Q: is the order quantity
ESC is expressed in number of products (not a probability) that is not satisfied from inventory.
Hence, ESC/Q is the fraction of demand (Q = the average demand per replenishment cycle) that is not satisfied from inventory/stock.
Fill rate is the opposite, hence fr = 1 – ESC/Q.
Chapter 3

10. Example 11-3: Evaluating fill rate given a replenishment policy
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Example 11-3: Evaluating fill rate given a replenishment policy
Recall that weekly demand for Palms at B&M is normally distributed, with a mean of 2,500 and a standard deviation of 500. The replenishment lead time is two weeks. Assume that the demand is independent from one week to the next. Evaluate the fill rate resulting from the policy of ordering 10,000 Palms when there are 6,000 Palms in inventory.
Chapter 3

11. Example 11-3: Evaluating fill rate given a replenishment policy
SYST 4050 Slides
Example 11-3: Evaluating fill rate given a replenishment policy
Lot size
Q =
Average demand during lead time
DL =
Standard dev. of demand during lead time
L =
Expected shortage per replenishment cycle
ESC =
Product fill rate
fr =
10,000
LD = 2*2,500 = 5,000
SQRT(L)D = SQRT(2)*500 = 707
-ss(1-Fs(ss/L))+Lfs(ss/L) = -1000*(1-Fs(1,000/707) + 707fs(1,000/707) =
1 – ESC/Q = 1 – 25.13/10,000 =
Chapter 3

12. Cycle Service Level versus Fill Rate
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Cycle Service Level versus Fill Rate
What happens to CSL and fr when the safety inventory (ss) increases?
What happens to CSL and fr when the lot size (Q) increases?
Chapter 3

13. Why do some firms have zero tolerance for early/late deliveries?
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Lead Time Uncertainty
Why do some firms have zero tolerance for early/late deliveries?
Chapter 3

14. Example 11-6: Impact of lead time uncertainty on safety inventory
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Example 11-6: Impact of lead time uncertainty on safety inventory
Inventory
Reorder point
Demand during lead time
Time
Lead time
L = SQRT(L2D + D2s2L)
Chapter 3

15. Example 11-6: Impact of lead time uncertainty on safety inventory
SYST 4050 Slides
Example 11-6: Impact of lead time uncertainty on safety inventory
Daily demand at Dell is normally distributed, with a mean of 2,500 and a standard deviation of 500. A key component in PC assembly is the hard drive. The hard drive supplier takes an average of L = 7 days to replenish inventory at Dell. Dell is targeting a CSL of 90 percent for its hard drive inventory. Evaluate the safety inventory of hard drives that Dell must carry if the standard deviation of the lead time is 7 days.
Chapter 3

16. Example 11-6: Impact of lead time uncertainty on safety inventory
SYST 4050 Slides
Example 11-6: Impact of lead time uncertainty on safety inventory
Demand
D =
Standard dev. of demand
D =
Lead time
L =
Demand during lead time
DL =
Standard dev. of lead time
sL =
Standard dev. of demand during lead time
L =
Safety inventory
ss =
2,500
500 7
LD = 5,000 7
SQRT(LD2 + D2sL2) = SQRT(7* *72) = 17,550
Fs-1(CSL)L = Fs-1(0.90)*17,550 = 22,491
Chapter 3

17. When lead time is constant When lead time is uncertain
SYST 4050 Slides
Summary
When lead time is constant
L: Standard deviation of demand during lead time
sL: Standard deviation of lead time
When lead time is uncertain
ESC is expressed in number of products (not a probability) that is not satisfied from inventory.
Hence, ESC/Q is the fraction of demand (Q = the average demand per replenishment cycle) that is not satisfied from inventory/stock.
Fill rate is the opposite, hence fr = 1 – ESC/Q.
Chapter 3

18. Summary Average Inventory = Q/2 + ss L: Lead time for replenishment
SYST 4050 Slides
Summary
L: Lead time for replenishment
D: Average demand per unit time
D:Standard deviation of demand per period
DL: Average demand during lead time
L: Standard deviation of demand during lead time
CSL: Cycle service level
ss: Safety inventory
ROP: Reorder point
Notes:
Average Inventory = Q/2 + ss
Chapter 3

19. SYST 4050 Slides
Summary
fr is the product fill rate (fraction of demand satisfied from inventory)
ESC is the expected shortage per replenishment cycle (the demand not satisfied from inventory per replenishment cycle)
ss is the safety inventory
Q is the order quantity
ESC is expressed in number of products (not a probability) that is not satisfied from inventory.
Hence, ESC/Q is the fraction of demand (Q = the average demand per replenishment cycle) that is not satisfied from inventory/stock.
Fill rate is the opposite, hence fr = 1 – ESC/Q.
Chapter 3

20. SYST 4050 Slides
Example Question
Weekly demand for canned fruit at a grocery store is normally distributed, with a mean of 250 and a standard deviation of 50. The lead time is two weeks. Assuming a continuous review replenishment policy, how much safety inventory should the store carry to achieve a CSL of 90 percent?
Chapter 3

21. SYST 4050 Slides
Example Question
You may use the table below to calculate the safety inventory
Fs-1(0.9)
F-1(0.9, 250, 50)
F-1(0.9, 250, 70.71)
F-1(0.9, 500, 50)
F-1(0.9, 500, 70.71)
Chapter 3

22. SYST 4050 Slides
Safety Inventory
Why is Amazon.com able to provide a large variety of books and music with less safety inventory than a bookstore chain selling through retail stores?
Amazon is able to provide a large variety of books and music with less safety inventory through the power of aggregation. By holding best-selling items in geographically dispersed warehouses, Amazon can hold less inventory and still meet customer demand. . A large centralized supply would need less safety inventory as the demand variances might cancel each other, e.g., high demand from one region is offset by low demand from another. Only if many regions had unanticipated high demand would the central supply be exhausted.
This change has greatly reduced the amount of safety inventory required as the paint store must now stock far fewer product lines. The reduction in safety inventory has simultaneously reduced safety inventory storage costs and increased responsiveness.
Chapter 3

23. ~500 Borders stores versus ~20 Amazon warehouses
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Borders versus Amazon
~500 Borders stores versus ~20 Amazon warehouses
ss = Fs-1(CSL)L
Chapter 3

24. SYST 4050 Slides
Amazon versus Borders
“Company-wide, Borders has knocked eight days off of its days inventory outstanding through improvements in its supply chain. Nevertheless, inventory stuck around 176 days in 1999, turning just over twice a year. That's not very often. Barnes & Noble turned its inventory 2.5 times last year, and Amazon managed nine turns. If Borders could turn its inventory as often as Barnes & Noble, it would free up an additional $400 million for use during the year.”
Soure: Brian Lund (TMF Tardior), May 19, 2000
Chapter 3

25. SYST 4050 Slides
Safety Inventory
In the 1980s, paint was sold by color and size in paint retail stores. Today paint is mixed at the paint store according to the color desired. What impact did this change had on safety inventories in the supply chain?
Amazon is able to provide a large variety of books and music with less safety inventory through the power of aggregation. By holding best-selling items in geographically dispersed warehouses, Amazon can hold less inventory and still meet customer demand. . A large centralized supply would need less safety inventory as the demand variances might cancel each other, e.g., high demand from one region is offset by low demand from another. Only if many regions had unanticipated high demand would the central supply be exhausted.
This change has greatly reduced the amount of safety inventory required as the paint store must now stock far fewer product lines. The reduction in safety inventory has simultaneously reduced safety inventory storage costs and increased responsiveness.
Chapter 3

26. Importance of the Level of Product Availability
SYST 4050 Slides
Importance of the Level of Product Availability
Product availability (also known as customer service level) is measured by
CSL (Cycle service level)
fr (Product fill rate)
Product availability affects supply chain responsiveness and costs
High levels of product availability  increased responsiveness and higher revenues
High levels of product availability  increased inventory levels and higher costs
Chapter 3

27. The Newsboy/Newsvendor Problem
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The Newsboy/Newsvendor Problem
Matching supply with demand is particularly challenging when supply must be chosen before observing demand (and demand is uncertain). Suppose you are the owner of a simple business: selling newspapers. Each morning you purchase a stack of papers with the intention of selling them at your newsstand at the corner of a busy street. Even though you have some idea regarding how many newspaper you can sell on any given day, you never can predict demand for sure.
Chapter 3

28. The Newsboy/Newsvendor Problem
SYST 4050 Slides
The Newsboy/Newsvendor Problem
One time decision under uncertainty
Demand is uncertain
Plan inventory for a single cycle
Trade-off
Ordering too much
(waste, salvage value < cost)
Ordering too little
(excess demand is lost)
Examples
Restaurants
Fashion
High tech
Matching supply with demand is particularly challenging when supply must be chosen before observing demand (and demand is uncertain). Suppose you are the owner of a simple business: selling newspapers. Each morning you purchase a stack of papers with the intention of selling them at your newsstand at the corner of a busy street. Even though you have some idea regarding how many newspaper you can sell on any given day, you never can predict demand for sure.
Chapter 3

29. The Christmas Tree Problem
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The Christmas Tree Problem
Sell price p = 100
Cost c = 20
Chapter 3

30. Cost of overstocking Co = c - s
SYST 4050 Slides
Ordering Too Much…
Cost c = 20
Salvage value s = 5
Cost of overstocking Co = c - s
Chapter 3

31. Versus Ordering Too Little…
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Versus Ordering Too Little…
Sell price p = 100
Cost c = 20
Cost of understocking Cu = p - c
Chapter 3

32. Factors Affecting the Optimal Level of Product Availability
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Factors Affecting the Optimal Level of Product Availability
Cost of overstocking (Co = c – s)
The loss incurred by a firm for each unsold unit at the end of the selling season
Cost of understocking (Cu = p – c)
The margin lost by a firm for each lost sale because there is no inventory on hand
Includes the margin lost from current as well as future sales if the customer does not return
Chapter 3

33. Product Availability Cost of overstocking Cost of understocking
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Product Availability
Cost of overstocking
Liz Claiborne experiences “unexpected earnings decline as a consequence of “higher-than-expected excess inventories”
The Wall Street Journal, July 19, 1993
“On Tuesday, the network-equipment giant Cisco provided the grisly details behind its astonishing $2.25 billion inventory write-off in the third quarter”
News.com, May 9, 2001
Cost of understocking
IBM struggles with shortages in ThinkPad line due to ineffective inventory management
The Wall Street Journal, August 24, 1994
Matching supply with demand (with demand uncertainty)
Chapter 3

34. Example: Parkas at L.L. Bean
SYST 4050 Slides
Example: Parkas at L.L. Bean
Cost c = $45
Price p = $100
Salvage value s = $5
What is the expected profit?
Notes: L.L. Bean is a mail order company deciding on the number of units of a red parkas to order. An estimate of demand using past information and expertise of buyers is given here. What should the appropriate order quantity be? In general distribution may not be known.
Under the old policy of ordering, the buyers would have ordered 1,000 parkas. However, demand is uncertain and the table shows that there is a 51% chance that demand will be 1,000 or less. Hence, ordering 1,000 parkas results in a cycle service level (CSL) of 51%. The buyers must decide on an order size and CSL that maximizes profits.
Expected demand = ∑Dipi = 1,026 parkas
Chapter 3

35. Example: Parkas at L.L. Bean
SYST 4050 Slides
Example: Parkas at L.L. Bean
Cost c = $45
Price p = $100
Salvage value s = $5
Notes: L.L. Bean is a mail order company deciding on the number of units of a red parkas to order. An estimate of demand using past information and expertise of buyers is given here. What should the appropriate order quantity be? In general distribution may not be known.
Under the old policy of ordering, the buyers would have ordered 1,000 parkas. However, demand is uncertain and the table shows that there is a 51% chance that demand will be 1,000 or less. Hence, ordering 1,000 parkas results in a cycle service level (CSL) of 51%. The buyers must decide on an order size and CSL that maximizes profits.
Expected profit = ∑profitipi = $49,900
Chapter 3

36. Example: Parkas at L.L. Bean
SYST 4050 Slides
Example: Parkas at L.L. Bean
(1 – CSL)(p – c)
CSL(c – s)
Notes: L.L. Bean is a mail order company deciding on the number of units of a red parkas to order. An estimate of demand using past information and expertise of buyers is given here. What should the appropriate order quantity be? In general distribution may not be known.
Under the old policy of ordering, the buyers would have ordered 1,000 parkas. However, demand is uncertain and the table shows that there is a 51% chance that demand will be 1,000 or less. Hence, ordering 1,000 parkas results in a cycle service level (CSL) of 51%. The buyers must decide on an order size and CSL that maximizes profits.
What is the optimal order quantity?
Chapter 3

37. Optimal Level of Product Availability
SYST 4050 Slides
Optimal Level of Product Availability
Expected marginal contribution of raising the order size from O* to O*+1 (1 – CSL*)(p – c) – CSL*(c – s)
p – c
p – s Cu
Cu + Co
CSL* = Prob(Demand  O*) = =
O* = F-1(CSL*, , ) = NORMINV(CSL*, , )
Chapter 3

38. Example 12-1: Evaluating the optimal service level for seasonal items
SYST 4050 Slides
Example 12-1: Evaluating the optimal service level for seasonal items
The manager at Sportmart, a sporting goods store, has to decide on the number of skis to purchase for the winter season. Based on past demand data and weather forecasts for the year, management has forecast demand to be normally distributed, with a mean 350 and a standard deviation of 100. Each pair of skis costs $100 and retails for $250. Any unsold skis at the end of the season are disposed of for $85. Assume that it costs $5 to hold a pair of skis in inventory for the season. How many skis should the manager order to maximize expected profits?
Chapter 3

39. Example 12-1: Evaluating the optimal service level for seasonal items
SYST 4050 Slides
Example 12-1: Evaluating the optimal service level for seasonal items
Average demand (mean)
 =
Standard deviation of demand (stdev)
 =
Material cost
c =
Price
p =
Salvage value
s =
Cost of understocking
Cu =
Cost of overstocking
Co =
Optimal cycle service level
CSL* =
Optimal order size
O* =
350
100
$100
$250
85 – 5 = $80
p – c = 250 – 100 = $150
c – s = 100 – 80 = $20
Cu/(Cu + Co) = 150/170 = 0.88
NORMINV(CSL*, , ) = 468
Chapter 3