1. Supply Chain Management Module
Operations Management:
Supply Chain Management Module
Managing the Supply Chain
Key to matching demand with supply
Cost and Benefits of inventory
Economies of Scale
Factors affecting optimal batch size: EOQ
Levers for improvement
Safety Stock
Factors affecting level of safety stock: ROP
Levers for reducing safety stock
Improving Performance
Centralization & Pooling efficiencies
Postponement
Accurate Response
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

2. 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 = 21c/sales dollar = 10.5% of GDP
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

3. The Supply Chain The Procurement or supply system The Operating System
The Distribution System
Raw Material
supply points
Finished Goods
Storage
Raw Material
Storage
Movement/
Transport
Manufacturing
Movement/
Transport
Movement/
Transport
Movement/
Transport
STORAGE
PLANT 1
WAREHOUSE A
Notes:
STORAGE
PLANT 2
WAREHOUSE B
STORAGE
PLANT 3
WAREHOUSE C
MARKETS
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

4. Key Financial Indicators of Supply Chain Performance
Return on Assets
Net Present Value …
These are LAGGING indicators. What must the supply chain do to achieve this?
Notes:
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/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:
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

6. Accurately Matching Demand with Supply is the Key Challenge: Inventories
... by 1990 Wal-Mart was already winning an important technological war that other discounters did not seem to know was on. “Wal-Mart has the most advanced inventory technology in the business and they have invested billions in it”. (NYT, Nov. 95).
WSJ, Aug. 93: Dell Computer stock plunges. The company was sharply off in forecast of demand resulting in inventory writedowns.
BW 1997:
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

7. 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
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

8. Where is the Flow Time? Operation Buffer Waiting Processing Notes:
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

9. 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
Prices, availability
Cycle/Batch stock
Safety stock
Notes:
Seasonal stock
Strategic stock
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

10. 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 over 3000 jackets, was charged a flat fee of $2,200. Stores typically ordered 1500 jackets at a time, twice a year. (Palü’s cost of capital is approximately 20%.)
What order size would you recommend for a Palü store in current supply network?
retailer
manufacturer
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

11. 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 jackets in
inventory over time.
R = Demand rate
Inventory
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

12. Costs Associated with Batches
Order costs (S)
Changeover of production line
Transportation
Receiving
Holding costs (H = rC)
Physical holding cost
Cost of capital
Cost of obsolescence
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

13. 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?
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

14. Find most economical order quantity:
Find most economical order quantity: Spreadsheet for a Palü Gear retailer
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

15. 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+h: Holding cost % (%/yr),
H = (r+h) C.
Batch Size Q
Total annual costs
H Q/2: Annual holding cost
S R /Q:Annual setup cost
EOQ
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

16. 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 = Q =
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 = I/R =
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

17. Learning Objectives: Batching & Economies of Scale
Average inventory for a batch size of Q is Q/2.
Increasing batch size of production (or purchase) increases average inventories (and thus cycle times).
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.
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/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?
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

19. Demand uncertainty and forecasting
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.
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

20. 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%?
J.A. Van Mieghem/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

21. 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?
How do we get that stock-out probability down to 5%?
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

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

23. 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(m, s) = Demand during the lead time
where m = RL and s = sR L
Given ROP, find SL = Cycle service level = P(no stock out)
= P(demand during lead time < ROP)
= F(z*= (ROP- m)/s) [use table]
= NORMDIST(ROP, m, s, True) [or Excel]
Given SL, find ROP = m + Is
= m + z* s [use table to get z* ]
= m + NORMSINV(SL)*s [or Excel]
Safety stock Is = z* s Reorder point ROP = m + Is
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

24. 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
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

25. 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. Determine s lead time demand =
2. Required # of standard deviations z* =
3. Answer: Safety stock Is =
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

26. 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.
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

27. Learning Objectives safety stocks
Levers to decrease safety stock without hurting level of service:
Decrease demand variability or forecast error,
Decrease delivery lead time,
Decrease delivery lead time variability.
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

28. Improving Supply Chain Performance:. 1
Improving Supply Chain Performance: 1. The Effect of Pooling/Centralization
Notes:
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

29. 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.
m =
s =
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

30. 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.
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

31. 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
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

32. Learning Objectives: Supply Chain Performance
Pooling of stock reduces the amount of inventory
physical
information
specialization
substitution
commonality/postponement
Benetton: Tailored response (e.g., partial postponement) can be used to better match supply and demand
Single product
Multi product
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

33. Optimal Service Level in Response to Demand Uncertainty 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 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
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

34. In reality, you do not know demand for sure… Impact of uncertainty if you order the expected Q = 2000
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

35. What happens if you change your order level to hedge against uncertainty? Performance for all possible Q using Excel
 200
D  -55
= F(Q)
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

36. Towards the newsboy model
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?
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

37. 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)
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

38. Where else do you find newsboys?
Deciding on economic service level
Benefits: Flexible Spending Account decision
ATM
Capacity Mgt
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

39. 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
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt

40. 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?
Information Uncertainty
S. Chopra/Operations/Supply Chain Mgt
S. Chopra/Operations/Supply Chain Mgt