1. Supply Chain Management
Managing the Supply Chain
Key to matching demand with supply
Cost and Benefits of inventory
Economies of Scale
Inventory management of a retailer: EOQ + ROP
Levers for improvement
Safety Stock
Hedging against uncertainty
Role of lead time
Improving Performance
Centralization & Pooling efficiencies
Postponement
Accurate Response

2. What is a Supply Chain? What makes a “good” Supply Chain?
The Procurement
or supply system
The Operating
System
The Distribution System
Raw Material
supply points
Movement/
Transport
Storage
PLANT 1
PLANT 2
PLANT 3
WAREHOUSE
MARKETS
Manufacturing
Finished Goods A B C
What makes a “good” Supply Chain?

3. Corporate Finance
CISCO
SELECTRON
Current Assets
BS/ 2000
BS/2000
Cash &
Equivalents
4,234
1,475.5
Short-term investments
1,291
958.6 AR
2,299
2,146.3
Inventories
1,232
%11
3,787.3
%44
Deferred Income
2,054
260.5
Total Current Assets
11,110
8,628.2
Inventories represent about %34 of current assets for a typical company in the US; %90 of working capital.
For each dollar of GNP in the trade and manufacturing sector, about 40cents worth of inventory was held.
Average logistics cost = 21c/dollar = %10.5 of GNP.

6. Solectron’s executive officer
compensation plan
Base compensation
Bonuses
“The Bonus Plan provides for incentive compensation ... based on certain worldwide, site and individual performance measures. Worldwide and site performance are measured based on targets w.r.t. profit before taxes, inventory turns, days sales outstanding and return on assets. The Compensation Committee believes that these factors are indicative of overall corporate performance and shareholder value.” [compensation committee report FY 96]
Long Term Incentive Compensation

7. Supply Chain Metrics

8. Costs of not Matching Supply and Demand Cost of overstocking
liquidation
obsolescence
holding
Cost of under-stocking
lost sales and customer goodwill
lost margin

9. Why hold Inventory? Economies of scale Cycle/Batch stock Uncertainty
Fixed costs of ordering/manufacturing
Quantity discounts
Trade Promotions
Uncertainty
Information Uncertainty
Supply/demand uncertainty
Seasonal Variability
Strategic
Flooding, availability
Cycle/Batch stock
Safety stock
Seasonal stock
Strategic stock

10. Cost of Inventory Physical holding cost (out-of-pocket)
Financial holding cost
(opportunity cost)
Low responsiveness
to demand/market changes
to supply/quality changes
Holding cost (H)

11. Costs Associated with Batches
Ordering costs (S)
Changeover of production line (Set-up)
Transportation (Delivery)
Receiving
Holding costs (H = r C)
Physical holding cost
Cost of capital (r)
Cost of obsolescence

12. Palü Gear: Retail Inventory Management
Annual jacket revenues at a Palü Gear retail store are roughly $1M. Palü jackets sell at an average retail price of $325, which represents a mark-up of 30% above what Palü Gear paid its manufacturer. Being a profit center, each store made its own inventory decisions and was supplied directly from the manufacturer by truck. For each order up to 5000 jackets, the manufacturer charges a flat fee of $2,200 for delivery. To exploit economies of scale, stores typically orders 1500 jackets each time it places an order. (Palü’s cost of capital is approximately 20%.) What order size would you recommend for a Palü store in current supply network?

13. Palü Gear: Evaluation of current policy of ordering 1500 units each time
What is average inventory I?
I =
Annual cost to hold one unit H =
Annual cost to hold I =
How often do we order?
Annual throughput R =
# of orders per year =
Annual order cost =
What is total cost?
TC =
Can we do better ?

14. Find the most economical order quantity
Method 1 : Enumerate

15. Economies of Scale: Inventory Build-Up Diagram
R: Annual demand rate (units/yr),
Q: Number of jackets per replenishment order
Number of orders per year = R/Q.
Average number of jackets in inventory = Q/2 .
Inventory
T = Q/R Q
R = Demand rate T
time between
orders
Time t
Order placed,
arrives immediately
Lead time=0
Order placed,
arrives immediately
Lead time=0

16. Economic Order Quantity EOQ
R : Demand per year,
S : Setup or Order Cost ($/setup; $/order),
H : Marginal annual holding cost ($/per unit per year), H = r C
Q : Order quantity.
C : Cost per unit ($/unit),
r : Cost of capital (% / yr),
Total annual costs
H Q/2: Annual holding cost
S R /Q:Annual setup cost
QEOQ
Batch Size Q

17. What do we learn from the EOQ formula
What do we learn from the EOQ formula ? How does the ordering policy change if …
The product is a success and the demand picks up, now we are selling 4 times the original demand…
The interest rates double up, so does our unit inventory holding costs …
After investing in IT, we manage to reduce our fixed ordering cost by half …

18. Optimal Economies of Scale:
For a Palü Gear retailer
R = 3077 units/ year C = $ 250 / unit
r = 0.20/year S = $ 2,200 / order
Unit annual holding cost = H = $50/unit-yr
Optimal order quantity = EOQ = 520 units
Number of orders per year = R/Q = 3077/520 = 5.91
Time between orders = Q/R = 8.78 weeks
Annual order cost = (R/Q)S = $13,018/yr
Average inventory I = Q/2 = 260 units
Annual holding cost = (Q/2)H = $13,018/yr
520

19. Take-Aways I Batching & Economies of Scale
Increasing batch size of production (or purchase) increases average inventories (and thus cycle times).
Average inventory for a batch size of Q is Q/2.
The optimal batch size trades off setup cost and holding cost.
To reduce batch size, one has to reduce setup cost (time).
Square-root relationship between Q and (R, S):
If demand increases by a factor of 4, it is optimal to increase batch size by a factor of 2 and produce (order) twice as often.
To reduce batch size by a factor of 2, setup cost has to be reduced by a factor of 4.

20. Role of Supply Leadtime L:
Palü Gear cont.
The lead time from when a Palü Gear retailer places an order to when the order is received is two weeks. If demand is stable as before, when should the retailer place an order?
I-Diagram:
ROP
Order
arrives
Order
placed
2wks
ROP =

21. Two Key Decisions of Inventory Management
How much to order ?
Answer: EOQ
2. When to place an order ?
Answer: ROP Reorder Point
represents the amount of inventory on hand when we place a new order .
Delivery Lead Time = 0 (Instantaneous Delivery) then ROP = …….
Delivery Lead Time > 0 then ROP = …….
ROP is driven by:
Delivery Lead Time
Demand Uncertainty
Customer Service Level

22. A Key to Matching Supply and Demand
When would you rather place your bet? A B C D
A: A month before start of Derby
B: The Monday before start of Derby
C: The morning of start of Derby
D: The winner is an inch from the finish line

23. Demand uncertainty and forecasting
Year Demand Forecast Error

24. Demand uncertainty and forecasting
Forecasts depend on
historical data
“market intelligence”
Forecasts are usually (always?) wrong.
A good forecast has at least 2 numbers (includes a measure of forecast error, e.g., standard deviation).
The forecast horizon must at least be as large as the lead time. The longer the forecast horizon, the less accurate the forecast.
Aggregate forecasts tend to be more accurate.

25. Palü Gear: Service levels & Inventory management
In reality, a Palü Gear store’s demand fluctuates from week to week. In fact, weekly demand at each store had a standard deviation of about 30 jackets  assume normally distributed. Recall that average weekly demand was about 60 jackets; the order lead time is 2 weeks; fixed order costs are $2,200/order and it costs $50 to hold one jacket in inventory during one year.
Questions:
If the retailer uses the ordering policy discussed before (ROP =120), what will the probability of running out of stock in a given cycle be?
The Palü retailer would like the stock-out probability to be smaller. How can she accomplish this?
Specifically, how does it get the service level up to 95%?

26. Example: say we increase ROP to 140 (and keep order size at Q = 520)
On average, what is the stock level when the replenishment arrives?
What is the probability that we run out of stock before a delivery arrives?
How do we get that stock-out probability down to 5%?

27. Lead Time Demand
Consider the lead time between the placement of an order and the arrival of the order. L=2 weeks.
Demand per week, R ~ (60, 30)
The mean demand during the lead time = 2*60 = 120
Standard deviation of demand during lead time
= (30)2 + (30)2 = 2
D lead time ~ N (120, )

28. Lead time demand distribution SAFETY STOCK ROP
120
Mean Demand
During Lead Time
IF ROP=120
Probability of stock out (i.e.,
Probability that the demand during
lead time is greater than 120 ) = ?
Lead time
demand distribution
ROP
Increase reorder point
above average demand during lead time, lower the probability of stockout! BETTER SERVICE LEVEL!
SAFETY STOCK
Safety stock increase with the service level.
e.g., % 95
Lower probability of runing out of stock, higher ROP.

29. Less demand variability Small variance / SD
120
%95
ROP
120
Higher Variability
Larger SD/ variance
%95
ROP
Safety stock increases
with the variance (SD) of lead time demand

30. Safety Stock
Safety stock increases (decreases) with an increase (decrease) in:
demand variability or forecast error,
delivery lead time for the same level of service,
delivery lead time variability for the same level of service.

31. Palü Gear: Determining the required Reorder Point for 95% service
DATA:
R = 60 jackets/ week sR = 30 jackets/ week
H = $50 / jacket, year standard deviation of weekly demand
S = $ 2,200 / order L = 2 weeks
QUESTION:
What should safety stock be to insure a desired cycle service level of 95%?
ANSWER:
Determine s lead time demand =
Required # of standard deviations z* = 1.64
3. Reorder Point = *42.42= 190 jackets
Safety stock Is = 1.64*42.42=70 jackets

32. The standard normal distribution F(z)
Review of Probability
The standard normal distribution F(z)
Transform X = N(m,s) to z = N(0,1)
z = (X - m) / s.
F(z) = Prob ( N (0,1) < z)
Transform back, knowing z*:
X* = m + z*s.
F(z) z

33. Safety Stocks ROP m = R L L EOQ EOQ Time t L L Inventory on hand R Is
I(t) R L
EOQ
EOQ
order
order
order
ROP
mean demand during supply lead time:
m = R L Is
safety stock Is
Time t L L

34. Comprehensive Financial Evaluation: Inventory Costs of Palü Gear
1. Cycle Stock (Economies of Scale)
1.1 Optimal order quantity =
1.2 # of orders/year =
1.3 Annual ordering cost per store = $13,009
1.4 Annual cycle stock holding cost. = $13,009
2. Safety Stock (Uncertainty hedge)
2.1 Safety stock per store = 70
2.2 Annual safety stock holding cost = $3,500
3. Total Costs for 5 stores = 5 (13, , ,500)
= 5 x $29,500 = $147.5K.

35. How to find service level (given ROP)
How to find service level (given ROP)? How to find re-order point (given SL)?
L = Supply lead time,
D =N(R, sR) = Demand per unit time is normally distributed
with mean R and standard deviation sR
DL =N(m, s) = Demand during the lead time is normally distributed
with mean m = RL and standard deviations s = sR L
Given ROP, find SL = Cycle service level = P(stock out)
= P(demand during lead time >ROP)
= 1-F(z*= (ROP- m)/s) [use table]
= 1- NORMDIST(ROP, m, s, True) [or Excel]
Given SL, find ROP = m + Is
= m + z* s [use table to get z* ]
= NORMINV(1-SL, m, s) [or Excel]
Safety stock Is = z* s Reorder point ROP = m + Is

36. Demand Uncertainty & Inventory Management
Take-Aways II
Demand Uncertainty & Inventory Management
Cycle Cost : EOQ: How much to order?
Balance the fixed costs of ordering with the average inventory holding cost.
Total Cycle Cost are quiet robust to misestimating the parameters
Growth brings scale economies, adjust operating policies as markets conditions change.
Safety Stock Cost: Reorder Point : When to place an order?
Uncertainty is nothing but forecasting error.
Determined by the Service Level P(D(lead time)>ROP)
ROP=RxL+Safety Stock

37. Improving The Supply Chain
How can we reduce supply chain costs without sacrificing customer service?
How can we improve customer service without increasing supply chain costs?
Distribution Centralization
Product Postponement (HP)
Process Postponement (Benetton)
Capacity Analysis (Benetton)

38. Improving Supply Chain Performance:. 1
Improving Supply Chain Performance: 1. The Effect of Pooling/Centralization
Is=100
Decentralized Distribution
Centralization Distribution
Is= 400
Is=400

39. Centralized vs. Decentralized Distribution
Pros
Cons

40. Palü Gear’s Internet restructuring: Centralized inventory management
Weekly demand per store = 60 jackets/ week
with standard deviation = 30 / week
H = $ 50 / jacket, year S = $ 2,200 / order
Supply lead time L = 2 weeks
Service level : 95% availability.
Palü Gear now is considering restructuring to an Internet store. So 5 local stores will be closed and a National DC will be opened to distribute direct to customers.

41. Compare the safety stock in the decentralized and centralized systems
Centralized – 5 stores
Demand R per week
for each store
ms=60
ss=30
Demand during Supplier lead time (L=2)
mltd=
sltd=
Safety Stock for each store (%95 availability)
Total Safety Stock
Demand R per week
for the centralized warehouse
mc=
sc=
Demand During Supplier Lead Time
(L=2)
mltd=
sltd=
Safety Stock for the centralized warehouse
(%95 availability)

42. Palü Gear’s Internet restructuring: comprehensive financial inventory evaluation
1. Cycle Stock (Economies of Scale)
1.1 Optimal order quantity =
1.2 # of orders/year =
1.3 Annual ordering cost of e-store = $29,089
1.4 Annual cycle stock holding cost = $29,089
2. Safety Stock (Uncertainty hedge)
2.1 Safety stock for e-store =
2.2 Annual safety stock holding cost = $7,800.
3. Total Costs for consolidated e-store = 29, , ,800
= $65,980

43. Learning Objectives: centralization/pooling
Different methods to achieve pooling efficiencies:
Physical centralization
Information centralization
Specialization
Raw material commonality (postponement/late customization)
Cost savings are sqrt(# of locations pooled).

44. Improving Supply Chain Performance:. 2
Improving Supply Chain Performance: Postponement & Commonality (HP Laserjet)
Generic Power
Production
Unique Power
Process I: Unique
Power Supply
Europe
N. America
Transportation
Process II: Universal
Make-to-Stock Push-Pull Boundary Make-to-Order

45. Benetton’s Production and Distribution Network

46. Tailored Inventories: Postponement
Simple solution
Produce all garments as Greige goods (Production cost is 10% higher)
Tailored solution
Base load manufactured from colored thread (cheaper but long lead time sourcing)
Safety stock held as Greige goods and manufactured on demand (10% more expensive but short lead times)

47. Process Postponement Dye to Order Make to Stock Knitting 2 wks Dyeing

48. Postponement and Re-assortment: The Advantage to Forecasting
Actual total sales
500
1000
1500
2000
2500
3000
3500
4000
500
1000
1500
2000
2500
3000
3500
4000
500
1000
1500
2000
2500
3000
3500
4000
Initial Forecast Updated Forecast after observing 20% of sales after 80%
Each data point represents the forecast and the actual season sales for a particular item (at the style-color level).

49. Two types of Production Capacities
Benetton:
Two types of Production Capacities
Speculative Capacity
Long Lead Time cheap
Reactive Capacity
Short Lead Time - expensive
Commit before
observing the demand
Gamble!
Commit after
observing the early sales data
How do we decide on the size of the speculative capacity?

50. Optimal Service Level and Accurate Response to Demand Uncertainty when you can order only once:
Palü Gear’s is planning to offer a special line of winter jackets, especially designed as gifts for the Christmas season. Each Christma-jacket costs the company $250 and sells for $450. Any stock left over after Christmas would be disposed of at a deep discount of $195. Marketing had forecasted a demand of 2000 Christmas-jackets with a forecast error (standard deviation of 500)
How many jackets should Palü Gear’s order? 1% 3% 6%
10%
13%
16% 0% 2% 4% 8%
12%
14%
18%
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000
3200
Demand forecast for Christmas jackets

51. Optimal Service Level and Accurate Response: with Excel (1)
Optimal Service Level and Accurate Response: with Excel (1) Performance for a given order Q, say Q = 2000

52. Optimal Service Level and Accurate Response : with Excel (2)
Optimal Service Level and Accurate Response : with Excel (2) Performance for all possible Q
 200
D  -55
= F(Q)

53. Towards the newsboy model
Suppose you placed an order of 2000 units but you are not sure about whether you should have ordered one more unit.
What is the contribution of ordering an additional unit?
Earn a margin (p-c) = B with propability (1-p)= P(D>2000)
DP = ..
Incur an overage cost of (c-s) = C with probability p = P(D<=2000)
DP = …..
So? ... Order more?
Marginal Benefit
Marginal Cost
Expected contribution of an additional unit
E(DP) = ………………..

54. Accurate Response: The newsboy model
In general: at the optimal Q
E(DP) <= 0 – no incentives to order more
(1-p)B = pC
Sell Do not sell
Equivalently, choose the smallest Q
such that
p = P(D<Q) = F(Q) >= B / (B+C)
Expected
Profit ($k)
120
130
140
150
160
170
180
190
200
210
220
230
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000
Order/Stock
Quantity Q
+ 200 = Cu
- Co = - 55
Example:
Critical fractile
B / (B+C) =
Find Q by rounding up!
Q =

55. Accurate response: Find optimal Q from newsboy model
Cost of overstocking by one unit = C
the out-of-pocket cost per unit stocked but not demanded
“Say demand is one unit below my stock level. How much did the one unit overstocking cost me?” E.g.: purchase price - salvage price.
Cost of understocking by one unit = B
The opportunity cost per unit demanded in excess of the stock level provided
“Say demand is one unit above my stock level. How much could I have saved (or gained) if I had stocked one unit more?” E.g.: retail price - purchase price.
Given an order quantity Q, increase it by one unit if and only if the expected benefit of being able to sell it exceeds the expected cost of having that unit left over.
Marginal Analysis: Order more as long as F(Q) < B / (B + C)
= smallest Q such that service level F(Q) > critical fractile B / (B + C)

56. Where else do you find newsboys?
Benefits: Flexible Spending Account decision
ATM
Perishable Products (Newspaper, Medical Supplies, Fashion Goods)
Weddings, Conferences…

58. How do we deal with uncertainty?