1. OPSM 501: Operations Management
Koç University Graduate School of Business
MBA Program
OPSM 501: Operations Management
Week 10:
Supply Chain contracts
Newsvendor
Zeynep Aksin

2. Hamptonshire Express
Anna has a degree from journalism & operations research
She has started a daily newspaper in her hometown
She used a leased PC: lease cost $10 per day
A local printer prints newspapers at 0.20 per copy
Sales the next day between 6 am and 10 am
Newsstand rental $30 per day
Express sold to customers at $1 per copy
Copies not sold by 10 am are discarded
Anna estimates daily demand to be distributed N(500,100)

3. Question 1 Optimal stocking quantity?
Profit at this stocking quantity?

4. Ordering Level and Profits in Vertically Integrated Channel
h=1; Anna sells to market directly:
i* = 584; E[Profit] = $331.33; Fill rate 98%

5. Improving demand through effort
After 6 weeks of operation, Anna thinks she can improve demand by adding a profile section
Experiments indicate that demand is a function of time she invests in preparing the section
She thinks D=

6. Question 2
How many hours should she invest daily in the creation of the profile section? Assume the opportunity cost of her time is $10 per hour.
Compare optimal profits to previous scenario

7. Optimal Level of Effort in Vertically Integrated Channel
Demand potential increases by 50
Expected profit increases by 0.8*50
h  h+1
0  1 40
1  2
16.56
2  3
12.71
3  4
10.71
4  5
9.44
i* = 684
E[Profit] =
371.33

8. Delegating sales to Ralph
Anna is really busy, so asks Ralph to take-over the retailing portion of her job.
Ralph agrees to run the newsstand from 6 AM to 10 AM and pay the daily rent of $30
He estimates demand the next day based on viewing a copy of the paper the previous night at 10 PM
He buys the papers from Anna at $0.8 per copy
Ralph is responsible for unsold copies at the end of the day

9. Question 3
Assuming h=4 try to determine the optimal stocking quantity for Ralph?
Why is this quantity different than the one in Question 2?
Now vary h in spreadsheet 3c which calculates the optimal newsboy quantity for the differentiated channel, i.e. to maximize Ralph’s profit.
How would changing the transfer price from the current value of 0.8 impact Ann’s effort level and Ralph’s stocking decision? (Spreadsheet 3d)
Compare an integrated (centralized) firm to a differentiated (decentralized) one.

10. Ordering Level and Profits in Differentiated Channel
Case 1. h=4; Anna sells to market directly:
i* = 684; E[Profit] = $371.33; Fill rate 98%
Case 2. h=4; Anna sells thru Ralph:
i* = 516; E[Total Profit] = $322
Anna makes $260
Ralph makes $ 62
Fill rate 84%
Why??

11. Effect of Transfer (Wholesale) Price in Differentiated Channel

12. Optimal Effort in Decentralized Channel
Optimal effort level for Anna is h=2 (and not 4).
h=2 h=4
Stocking quantity: $487 $516
Anna’s profit: $262 $260
Ralph’s profit: $56 $ 62
Total profit: $318 $322
Fill rate: 83% 84%
Why??

13. Inefficiencies in a Differentiated Channel
Supplier chooses w, retailer chooses i*
Retail ignores +ve effect of stocking one more unit on supplier
Supplier ignores +ve effect of cutting wholesale price/increasing effort on retailer
Supplier prices above marginal cost/exerts low effort
Retailer stocks less
Supply chain profits shrink

14. Contracts
Specifies the parameters within which a buyer places orders and a supplier fulfills them
Example parameters: quantity, price, time, quality
Double marginalization: buyer and seller make decisions acting independently instead of acting together; both of them make a margin on the same sale – gap between potential total supply chain profits and actual supply chain profits results
Buyback contracts can be offered that will increase total supply chain profit

15. Returns policies
Rationale: set buyback price b so that
(retailer cost structure
= supply cost structure)
Supplier can use both w and b
Supplier is bundling insurance with the good

16. Example

17. Reasons for return policies
Supplier is less risk averse than retailers
Supplier has a higher salvage value
Safeguarding the brand
Signalling information
Avoiding brand switching

18. Costs of Return Policies
Extra transportation and handling
Extra depreciation
Getting the return rate wrong
Retailer incentives

19. The case of books Returns as in Hamptonshire Express…
…However publisher has no control of return quantities
No control of inventory-shelf arrangements
No control over private-label
No control of retail price
Key difference: power has shifted from publisher to retailer

20. What’s the problem? Bad forecasting? Inefficient replenishment?
Video sales
Hollywood: video rentals and sales $20B business, and largest source of revenue
Rentals slipping
Competition from direct services
Customer dissatisfaction (20% cannot rent video they want on a typical trip)
What’s the problem? Bad forecasting? Inefficient replenishment?

21. Reduce wholesale price in return for a share of revenues
Revenue Sharing
Reduce wholesale price in return for a share of revenues
Encourages retailers to stock more
$60 a tape
$3/rental – rent each tape 20 times to break even
$9 a tape, studio receives half revenue
$3/rental – rent each tape 6 times to break even
Retailer stocks more

22. Revenue sharing When does it work?
marginal cost of increasing inventory low
administrative burden low
for price-sensitive products

23. The Impact of Revenue Sharing
Blockbuster Instituted the “Go Home Happy” marketing initiative
Results
Store traffic went up
Market share 4th quarter 98 = 26%
Market share 2nd quarter 99 = 31%
Revenue in 2nd quarter 99: +17% from 98
Cash flow in 2nd quarter 99: +61% from 98

24. Customers,
demand
centers
sinks
Field
Warehouses:
stocking
points
Sources:
plants
vendors
ports
Regional
Warehouses:
stocking
points
Supply
Inventory &
warehousing
costs
Production/
purchase
costs
Transportation
costs
Transportation
costs
Inventory &
warehousing
costs

25. Supply Chain Management: the challenge
Global optimization
Conflicting Objectives
Complex network of facilities
System Variations over time
Managing uncertainty
Matching Supply and Demand
Demand is not the only source of uncertainty

26. The newsvendor is all around us
Newspaper
Apparel industry
The flu shot

27. Recall Marks & Spencer Perfect forecast Excess demand Excess stock
Expected demand
Actual demand

28. Recall Zara’a Approach to Demand uncertainty
Excess stock and unmet demand are avoided by
stopping production when market saturates
Expected demand
Actual demand
Small batches

29. Flu vaccine example
Each year’s flu vaccine is different: can’t produce ahead or keep from last year
Flu vaccine production requires growing strains: there is a lead time
Factories have limited capacity
Demand is uncertain
Need to commit to production before flu season starts
Result: frequent shortage of vaccine or left overs at the end of the season

30. The Newsvendor Model Develop a Forecast: How did Anna come up with N(500, 100) for example?
11-30

31. O’Neill’s Hammer 3/2 wetsuit

32. Historical forecast performance at O’Neill
Forecasts and actual demand for surf wet-suits from the previous season

33. Empirical distribution of forecast accuracy

34. Normal distribution tutorial
All normal distributions are characterized by two parameters, mean = m and standard deviation = s
All normal distributions are related to the standard normal that has mean = 0 and standard deviation = 1.
For example:
Let Q be the order quantity, and (m, s) the parameters of the normal demand forecast.
Prob{demand is Q or lower} = Prob{the outcome of a standard normal is z or lower}, where
(The above are two ways to write the same equation, the first allows you to calculate z from Q and the second lets you calculate Q from z.)
Look up Prob{the outcome of a standard normal is z or lower} in the Standard Normal Distribution Function Table.
11-34

35. Converting between Normal distributions
Start with
= 100,
= 25,
Q = 125
Center the distribution over 0 by subtracting the mean
Rescale the x and y axes by dividing by the standard deviation
11-35

36. Using historical A/F ratios to choose a Normal distribution for the demand forecast
Start with an initial forecast generated from hunches, guesses, etc.
O’Neill’s initial forecast for the Hammer 3/2 = 3200 units.
Evaluate the A/F ratios of the historical data:
Set the mean of the normal distribution to
Set the standard deviation of the normal distribution to
11-36

37. O’Neill’s Hammer 3/2 normal distribution forecast
O’Neill should choose a normal distribution with mean 3192 and standard deviation 1181 to represent demand for the Hammer 3/2 during the Spring season.
11-37

38. Empirical vs normal demand distribution
Empirical distribution function (diamonds) and normal distribution function with
mean 3192 and standard deviation 1181 (solid line)
11-38

39. Demand Scenarios for a Jacket

40. Costs Profit = Revenue - Variable Cost - Fixed Cost + Salvage
Production cost per unit (C): $80
Selling price per unit (S): $125
Salvage value per unit (V): $20
Fixed production cost (F): $100,000
Q is production quantity, D demand
Profit = Revenue - Variable Cost - Fixed Cost + Salvage

41. Best Solution
Find order quantity that maximizes weighted average profit.
Question: Will this quantity be less than, equal to, or greater than average demand?

42. What to Make?
Question: Will this quantity be less than, equal to, or greater than average demand?
Average demand is 13,100
Look at marginal cost Vs. marginal profit
if extra jacket sold, profit is = 45
if not sold, cost is = 60
So we will make less than average

43. Scenarios Scenario One: Scenario Two:
Suppose you make 12,000 jackets and demand ends up being 13,000 jackets.
Profit = 125(12,000) - 80(12,000) - 100,000 = $440,000
Scenario Two:
Suppose you make 12,000 jackets and demand ends up being 11,000 jackets.
Profit = 125(11,000) - 80(12,000) - 100, (1000) = $ 335,000

44. Scenarios and their probabilities
Demand
Expected Profit
Production quantity

45. Expected Profit

46. Expected Profit

47. Expected Profit

48. Important Observations
Tradeoff between ordering enough to meet demand and ordering too much
Several quantities have the same average profit
Average profit does not tell the whole story
Question: 9000 and units lead to about the same average profit, so which do we prefer?

49. Probability of Outcomes

50. Key Insights from this Model
The optimal order quantity is not necessarily equal to average forecast demand
The optimal quantity depends on the relationship between marginal profit and marginal cost
Fixed cost has no impact on production quantity, only on whether to produce or not
As order quantity increases, average profit first increases and then decreases
As production quantity increases, risk increases. In other words, the probability of large gains and of large losses increases

51. Example Demand Probability 1 0.10 2 0.15 3 0.20 4 0.20 5 0.15 6 0.10
Mean demand=3.85 How much would you order?
Demand Probability
Total 1.00

52. Single Period Inventory Control
Economics of the Situation Known:
1. Demand > Stock --> Underage (under stocking) Cost Cu = Cost of foregone profit, loss of goodwill
2. Demand < Stock --> Overage (over stocking) Cost Co = Cost of excess inventory
Co = 10 and Cu = 20 How much would you order? More than 3.85 or less than 3.85?

53. Incremental Analysis Co = 10 and Cu = 20
Probability Probability Incremental
Incremental that incremental that incremental Expected
Demand Decision unit is not needed unit is needed Contribution
1 First (0.00)+20(1.00)
=20
2 Second (0.10)+20(0.90)
=17
3 Third
4 Fourth
5 Fifth
6 Sixth
7 Seventh
Co = 10 and Cu = 20

54. Generalization of the Incremental Analysis
Cash Flow Cu
-Co
nth unit needed
Pr{Demand  n}
Stock n-1
Decision
Point
Stock n
Base Case
Chance
Point
nth unit not needed
Pr{Demand  n-1}

55. Generalization of the Incremental Analysis
Chance
Point
Stock n-1
Decision
Stock n
Base Case
Expected Cash Flow
Cu Pr{Demand  n} -Co Pr{Demand  n-1}

56. Generalization of the Incremental Analysis
Order the nth unit if
Cu Pr{Demand  n} - Co Pr{Demand  n-1} >= 0 or
Cu (1-Pr{Demand  n-1}) - Co Pr{Demand  n-1} >= 0
Cu - Cu Pr{Demand  n-1} -Co Pr{Demand  n-1} >= 0
Pr{Demand  n-1} =< Cu /(Co +Cu)
Then order n units, where n is the greatest number that satisfies the above inequality.

57. P(Demand  n-1)  Cu /(Co +Cu)< P(Demand  n)
Incremental Analysis
Incremental
Demand Decision Pr{Demand  n-1} Order the unit?
1 First YES
2 Second YES
3 Third YES
4 Fourth YES
5 Fifth YES
6 Sixth NO -
7 Seventh NO
Cu /(Co +Cu)=20/(10+20)=0.66
Order quantity n should satisfy:
P(Demand  n-1)  Cu /(Co +Cu)< P(Demand  n)

58. Order Quantity for Single Period, Normal Demand
Find the z*: z value such that F(z)= Cu /(Co +Cu)
Optimal order quantity is:

59. The Standard Normal Distribution
Transform
X = N(mean,s.d.) to
z = N(0,1)
z = (X - mean) / s.d.
F(z) = Prob( N(0,1) < z)
Transform back, knowing z*:
X* = mean + z*s.d.
F(z) z

60. Example If we want to have cum. probability of 95% z=1.64 For demand:
Mean=20
std dev=10
Then:
Q= *10=36.4

61. Example: Anna’s first stocking decision
Cu = 1-0.2=0.8 and Co = 0.2; P ≤ 0.8 / ( ) = .8
Z.8 = .84 (from standard normal table or using NORMSINV() in Excel)
therefore Anna needs (100) = 584 papers

62. Example: What about Ralph’s first stocking decision?
Anna sets h=4 D=N(500+50*2, 100)
Cu = 1-0.8=0.2 and Co = 0.8; P ≤ 0.2 / ( ) = .2
Z0.2 = - Z0.8 =-0.84 (from standard normal table or using NORMSINV() in Excel)
therefore Anna needs (100) = 516 papers

63. Example 2: Finding Cu and Co
A textile company in UK orders coats from China. They buy a coat from 250€ and sell for 325€. If they cannot sell a coat in winter, they sell it at a discount price of 225€. When the demand is more than what they have in stock, they have an option of having emergency delivery of coats from Ireland, at a price of 290.
The demand for winter has a normal distribution with mean 32,500 and std dev 6750.
How much should they order from China??

64. Example 2: Finding Cu and Co
A textile company in UK orders coats from China. They buy a coat from 250€ and sell for 325€. If they cannot sell a coat in winter, they sell it at a discount price of 225€. When the demand is more than what they have in stock, they have an option of having emergency delivery of coats from Ireland, at a price of 290.
The demand for winter has a normal distribution with mean 32,500 and std dev 6750.
How much should they order from China??
Cu=75-35=40
Co=25
F(z)=40/(40+25)=40/65=0.61z=0.28
 q= *6750=34390

65. Example 3: Single Period Inventory Management Problem
Manufacturing cost=60TL,
Selling price=80TL, Discounted price (at the end of the season)=50TL
Market research gave the following probability distribution for demand.
Find the optimal q, expected number of units sold for this orders size, and expected profit, for this order size.
Demand Probability
P(D<=n-1)
0.1
0.3
0.5
0.7
0.8
0.9
Cu=20 Co=10
P(D<=n-1)<=20/30=0.66
<=0.66
q=800
For q=800:
E(units sold)=710
E(profit)=13,300