1. Supply Chain Management Module
Managing the Supply Chain
Key to matching demand with supply
Cost and Benefits of inventory
Economies of Scale
Palu Gear: Inventory management of a retailer: EOQ + ROP
Levers for improvement
Safety Stock
Hedging against uncertainty
Role of leadtime
Improving Performance
Centralization & Pooling efficiencies
Postponement
Optimal Service Level
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

2. What is a Supply Chain? What makes for a “good” SC? 1. Procurement
or supply system
2. Operating
System
3. Distribution System
4. Sales
or demand system
Raw Material
supply points
Movement/
Transport
Storage
PLANT 1
PLANT 2
PLANT 3
WAREHOUSES
(DCs)
MARKETS
Manufacturing
Finished Goods A B C
Notes:
What makes for a “good” SC?
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

3. US Vehicle Inventory Lin/Operations/Supply Chain Mgt

4. Corporate Finance
Inventories represent about 34% of current assets for a typical US company; 90% of working capital.
For each dollar of GNP in the trade and manufacturing sector, about 40% worth of inventory was held.
Average logistics cost = 21¢/sales dollar = 10.5% of GDP
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

5. Costs of not Matching Supply and Demand
Cost of overstocking
liquidation, obsolescence, holding
Cost of under-stocking
lost sales and resulting lost margin
Notes:
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

6. We never Talk anymore!
Magazine sales at newsstands as % of copies shipped to newsstands
In Style
People
Vanity Fair
Vogue
The New Yorker GQ
New York
Esquire
Rolling Stone Us
Talk
64.7%
54.5%
45.6%
42.1%
39.9%
39.4%
35.1%
31.0%
28.0%
23.9%
18.0%
Lin/Operations/Supply Chain Mgt
Data for Oct – Oct. 2000
Lin/Operations/Supply Chain Mgt

7. The Current Environment: The Grocery Industry 1985-1992
Number of products in average supermarket
,036
,486
,000
2004 ??
2,000
20,000
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

8. A Key to Matching Supply and Demand
When would you rather place your bet? A B C D
Notes:
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
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

9. Where is the Flow Time? Operation Buffer Waiting Processing Notes:
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

10. Flow time T = Inventory I / Throughput R
Operational Flows
Throughput R
Inventory I
FLOW TIME T
Notes:
I = R T
Flow time T = Inventory I / Throughput R
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

11. Why do Buffers Build? Why hold Inventory?
Economies of scale
Fixed costs associated with batches
Quantity discounts
Trade Promotions
Uncertainty
Information Uncertainty
Supply/demand uncertainty
Seasonal Variability
Strategic
Flooding, availability
Cycle/Batch stock
Safety stock
Notes:
Seasonal stock
Strategic stock
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

12. Palü Gear: Retail Inventory Management & Economies of Scale
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. A shipment up to a full truck load, which was about 3000 jackets, was charged a flat fee of $2,200. Typically, stores placed roughly two orders per year, each of about 1500 jackets. (Palü’s cost of capital is approximately 20%.)
What order size would you recommend for a Palü store in current supply network?
retailer
manufacturer
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

13. Economies of Scale: Inventory Build-Up Diagram
R: Annual demand rate,
Q: Number of jackets per replenishment order
Number of orders per year = R/Q.
Average number of jackets in inventory = Q/2 . Q
Time t
Inventory Profile:
# of wind breakers in
inventory over time.
R = Demand rate
Inventory
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

14. Palü Gear: evaluation of current policy of ordering Q = 1500 units each time
What is average inventory I?
I = Q/2 =
Annual cost to hold one unit H =
Annual cost to hold I = Holding cost × Inventory
How often do we order?
Annual throughput R =
# of orders per year = Throughput / Batch size
Annual order cost = Order cost × # of orders
What is total cost?
TC = Annual holding cost + Annual order cost =
What happens if order size changes?
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

15. Find most economical order quantity:
Find most economical order quantity: Spreadsheet for a Palü Gear retailer
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

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

17. 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 =
Optimal order quantity = QEOQ =
Number of orders per year = R/Q =
Time between orders = Q/R =
Annual order cost = (R/Q)S = $13,008.87/yr
Average inventory I = Q/2 =
Annual holding cost = (Q/2)H =$13,008.87/yr
Average flow time T =
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

18. Role of 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:
The two key decisions in inventory management are:
How much to order?
When to order?
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

19. Learning Objectives: 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.
If demand increases by a factor of 4, the flow time decreases by a factor of 2.
An inventory policy must specify when to order (the ROP) and how much to order (the batch size).
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

20. Demand uncertainty and forecasting
Year
Demand
1992
194
1993
251
1994
320
1995
267
233
1997
223
1998
266
1999
252
2000
2001
331
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

21. Demand uncertainty and forecasting
Forecasts depend on (a) historical data and (b) “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.
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

22. 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 roughly normally distributed. Recall that average weekly demand was about 59 jackets; the order lead time is two 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, 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%?
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

23. How find s of lead time demand?sR sR … sR
Sum of N independent random variables, each with
identical standard deviation sR, has
standard deviation =
Applications:
Demand over the leadtime L has standard deviation = sR  L
Pooled demand over N regions or products has standard deviation = sR  N
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

24. 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?
On average, what is the inventory profile?
What is the probability that we run out of stock?
How do we get that stock-out probability down to 5%?
100
200
300
400
500
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

25. Safety Stocks m = R L Q Q L L L ROP R Is Inventory on hand I(t) Time t
order
order
order
ROP R
mean demand during supply lead time:
m = R L Is
safety stock Is
Time t L L L
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

26. Safety Stocks & Service Levels: The relationship
Cycle Service Level (CSL)
Stock-out probability
F(z)
Is = z s
demand during
supply lead time
mean
ROP
Raise ROP until we reach appropriate SL
To do numbers, we need:
Mean and stdev s of demand during lead time
Either Excel or tables with z - value such that CSL = F(z)
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

27. 1. How to find service level (given ROP). 2
1. How to find service level (given ROP)? 2. 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(mL, sL) = Demand during the lead time
where mL = RL and sL = sR L
Given ROP, find SL = Cycle service level = P(no stock out)
= P(demand during lead time < ROP)
= F(z*= (ROP- mL)/sL) [use table]
= NORMDIST(ROP, mL, sL, True) [or Excel]
Given SL, find ROP = mL + Is
= mL + z*sL [use table to get z* ]
= NORMINV(SL, mL, sL) [or Excel]
Safety stock Is = z*sL Reorder point ROP = mL + Is
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

28. 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
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

29. Palü Gear: Determining the required Safety Stock for 95% service
DATA:
R = 59 jackets/ week sR = 30 jackets/ week
H = $50 / jacket, year
S = $ 2,200 / order L = 2 weeks
QUESTION: What should safety stock be to insure a desired cycle service level of 95%?
ANSWER:
1. Required # of standard deviations z* for SL of 95% =
2. Determine s lead time demand =
3. Answer: Safety stock Is =
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

30. Comprehensive Financial Evaluation: Inventory Costs of Palü Gear
Cycle Stock (Economies of Scale)
1.1 Optimal order quantity = 520
1.2 # of orders/year = 5.9
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.
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

31. Learning Objectives safety stocks
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.
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

32. 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
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

33. Palü Gear’s Internet restructuring: Centralized inventory management
Weekly demand per store = 59 jackets/ week
with standard deviation = 30 / week
H = $ 50 / jacket, year
S = $ 2,200 / order
Supply lead time L = 2 weeks
Desired cycle service level F(z*) = 95%.
Palü Gear now is considering restructuring to an Internet store.
Assuming Internet store is sum of the five stores and demands are independent.
R = 5  59 = 295 jackets/week  average total demand over lead time mL = 2  295 = 590.
sR = 5  30 = 67.1  STD of total demand over lead time sL = 2  67.1 = 94.9.
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

34. Palü Gear’s Internet restructuring: comprehensive financial inventory evaluation
1. Cycle Stock (Economies of Scale)
1.1 Optimal order quantity = 5 x 520 = 1163
1.2 # of orders/year = 5 x 5.9 = 13
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 = 156
2.2 Annual safety stock holding cost = $7,800
3. Total Costs for consolidated e-store = 29, , ,800
= $65,980 = 147.5/ 5
Note: This is 5  cost of safety inventory at one store.
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

35. 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).
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

36. 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
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

37. Consumer Hierarchy Score Technical Hierarchy Score
Variety and Marketing/Operations: Be smart with product differentiation
Braking system
Transmission
Electrical design
Chassis design
Exterior body panels
Engine block
Front & rear seats
Floor mats
Airbags & antilock system
Rear-view mirrors
Dashboard layout
Headlights
Cup holders
Remote keyless entry
Consumer Hierarchy Score
Technical Hierarchy Score
Low
High
Source: Mohan Sawhney
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

38. Learning Objectives: Supply Chain Performance
Pooling of stock reduces the amount of inventory
physical
information
specialization
substitution
commonality/postponement
Tailored response (e.g., partial postponement) can be used to better match supply and demand
The entire supply chain must plan to customer demand
Single product
Multi product
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

39. Finding the optimal service level: The newsvendor problem
Lin/Operations/Supply Chain Mgt

40. Optimal Service Level when you can order only once: Palü Gear
Palü Gear’s is planning to offer a special line of winter jackets, especially designed as gifts for the Christmas season. Each Christmas-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?
0.5%
0.9%
2.2%
4.5%
7.8%
11.6%
14.6%
15.9% 0% 2% 4% 6% 8%
10%
12%
14%
16%
18%
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000
3200
3400
Demand Forecast for Christmas jackets
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

41. In reality, you do not know demand for sure…Impact of uncertainty if you order the expected Q = 2000
THEN:
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

42. What happens if you change your order level to hedge against uncertainty? Performance for all possible Q using Excel:
- Co = - 55
+ 200 = Cu
Lin/Operations/Supply Chain Mgt

43. Towards the newsboy model Suppose you placed an order of 2000 units but you are not sure if you should order more.
What happens if I order one more unit (on top of Q = 2000)?
Sell the extra unit with
probability …
DP = …..
Do not sell the extra unit with probability …
DP = …..
Expected profit from additional unit
E(DP) =
So? ... Order more?
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

44. The Value-maximizing Service Level The newsvendor formula
In general: raise service level (i.e., order an additional unit) if and only if
E(DP) = (1-SL)Cu – SLCo > Sell Do not sell
Thus, optimal service level SL* (= Newsvendor formula)
Example: use formula for Palu-Gear Christmas order
SL* =
So how much should Palu order then?
How does this compare to forecasted demand of 2000?
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

45. Accurate response: Find optimal Q from newsboy model
Cost of overstocking by one unit = Co
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 = Cu
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) < Cu / (Co + Cu)
= smallest Q such that service level F(Q) > critical fractile Cu / (Co + Cu)
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

46. Where else do you find newsvendors?
Deciding on economic service level
Benefits: Flexible Spending Account decision
Capacity Mgt
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

47. Whistler Blackcomb Ski & Snowboard School
Has over 1,200 instructors (including part timers).
Organized into 36 pods.
Manager of a pod must determine today the number of instructors to call in for tomorrow’s lessons.
A master schedule is generated on a monthly basis but adjusted daily.
Skiers can pre-book (i.e., reserve) a lesson or can walk in.
Total demand depends on a number of factors: Day of the week, point in the season, US/Canadian exchange rate etc.
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

48. Whistler Blackcomb Economics of Individual Lessons
Tomorrow
Today
Pre-bookings made for today
3:00pm
Finish lessons for day
5:00pm
Determine forecast demand and instructor requirements for tomorrow
Begin morning lessons (demand realized)
9:00pm
Call instructors to fill in or to call off
12:00pm
Afternoon lessons begin
8:00am
If unable to staff a lesson, lose $320 in revenue.
Instructors are paid $40 per hour for lessons.
An instructor who gives a lesson is paid for three hours.
An instructor on stand by who does not give lesson is paid for two hours.
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

49. Whistler Blackcomb Staffing Decision
A forecasting model predicts that demand for individual lessons tomorrow is 56.
Error in forecast (i.e., standard deviation) is 3.12.
If demand is normally distributed, how many instructors should be called in?
Assume each instructors teaches just one individual lesson.
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

50. Whistler Blackcomb Analysis
If one too many instructors, must pay for two hours.
Co = 2 × 40 = $80.
If one too few instructors, lose margin on a lesson.
Cu = 320 – (3 × 40 ) = 320 – 120 = $200.
Critical fractile = Cu/(Co+Cu)=200/(200+80) = 71.4%.
z71.4 = Normsinv(0.714) =
Optimal decision for normal distribution:
Q = μ + z71.4 × σ = × 3.12 = 57.7 ≈ 58
Lin/Operations/Supply Chain Mgt
Lin/Operations/Supply Chain Mgt

51. Economies of Scale Uncertainty
Goal of a Supply Chain
Match Demand with Supply
It is hard … Why?
Economies of Scale
There are fixed costs of ordering/production
Q*=
Implications:
How fast cycle inventory grows if demand grows.
How much to invest in fixed cost reduction to reduce batch size.
Hard to Anticipate Demand
Forecasts are wrong… why?
There is lead time… why there is lead time?
Lead time (flow time) = Activity time+ Waiting Time
Because there is waiting time..
Why there is waiting time?
There is inventory in the SC (Little’s Law)
Implications:
Is z (service level appropriate)
Reduce Lead time
Reduce sR
Uncertainty
Forecast Error
Safety Stock Is= zsR
Why there is Inventory?
Seasonality
Lin/Operations/Supply Chain Mgt

52. Is z (service level appropriate)
Implications:
Is z (service level appropriate)
Reduce Lead time
Reduce sR
Balance overstocking and understocking
Newsboy Problem …
Critical Fractile = 1- P(stockout)
Customer Demand Uncertainty
Normal Variations…
How do we deal with it?
Aggregation
Physical
Information
Specialization
Component Commonality
Postponement
Where does sR come from?
Bullwhip Effect
Causes
Demand Signaling
Rationing
Batching
Promotions
How do we deal with it?
Make the SC more visible
Align Incentives
Lin/Operations/Supply Chain Mgt