1. Supply Chain Coordination with Contracts

2. A Typical Supply Chain

3. A Paradigm Shift
From optimization within an organization to optimization for a SC.
Design incentive structures (contracts) to coordinate various parties of the SC to achieve system optimization.

4. Why Coordination?
Each player (company) in the SC has different, and often time, conflicting objectives.
These individual objectives are usually not in line with that of the SC.
An incentive structure (contract) is needed to align the optimization action of each individual player for the interest of the SC (Contract Design)
Make the pie bigger then divide!

5. Popular SC Systems Studied in Literature:
Two levels: a supplier and a retailer (or multiple retailers).
Product: seasonal or stable (newsvendor v.s. EOQ)
Demand:
deterministic or stochastic
insensitive or sensitive to retail price
Objective Function: risk neutral or risk averse.
Other variations: information asymmetry, multiple replenishment opportunities, competing retailers, …

6. Contract Design and Evaluation
For a given SC structure, which contracts coordinate the SC?
How does the contract allocate profit among players of the SC?
Efficiency v.s. administrative cost for a given contract.

7. Newsvendor Problem
News paper demand unknown but distribution known with cdf F.
Underage cost (Price-Cost): Cu
Overage cost (Cost - Salvage): Co
How much to order to maximize the expected profit?

8. Newsvendor Solution At the best order quantity,
marginal underage = marginal overage
=> [1- F(Q)] ͯ Cu = F(Q) ͯ Co
=> F(Q) = Cu / (Cu + Co) (1)
If F is a Normal distribution with mean μ and std σ ,
=> Q = μ + σ ͯ z,
where z is the z-value based on (1).
Marginal underage cost for Qth product = marginal overage cost of Qth product.

9. Performance Measures Expected lost sales (for Normal dist.):
= σ ͯ [Normdist(z,0,1,0)-z ͯ (1-Normsdist(z,0,1,1)]
Expected sales:
= Exp demand – Exp lost sales
Expected leftover inv:
= Q – Exp sales
Expected profit:
= (Price-Cost)*Exp sales
– (Cost-Salvage)*Exp inv
Normdist(x,mean,std, cum or density)
Normsdist(x) = cum distribution of standard normal

10. A Sunglass Supply Chain
Sunglass designer and manufacturer (called supplier):
Manufacturing cost: $35
Whole sale price: $75
Sunglass retailer:
Retail price: $115
End-of-season price: $25
Estimated demand:
Normal ( =250, =125)
Should the retailer order more or fewer glasses than average?

11. Best Decision for Retailer
Underage cost Cu : $115 - $75 = $40
Overage cost Co : $75 - $25 = $50
Cu / (Cu + Co) = 40 / ( ) = 44.4%
z =
Q = ( )*125 = 233
Expected sale = 191
Expected leftover Inventory = 42
Expected profit = $40*191-$50*42 =$5,540

12. Supplier and System Profit
Supplier’s profit = 233*($75-$35) = $9,320
System profit = $5,540+$9,320 = $14,860.
Retailer takes all risk
Supplier assumes no risk
Can we do better for the supply chain (system)?

13. What’s Best for the System?
Underage cost Cu : $115 - $35 = $80
Overage cost Co : $35 - $25 = $10
Cu / (Cu + Co) = 80 / ( ) = 88.9%
z =
Q = *125 = 403
Expected sale = 243
Expected leftover = 160
Expected system profit = $17,840
=>19% profit increase!
Double marginalization. Retailer is more conservative than the system since his profit margin is smaller than the system.

14. How to Improve System Performance
Retailer needs to order more!
Option 1: Reduce whole sale price
What happened?
We need a win-win (not win-lose) mechanism
Option 2: How about buy back contract?
Specified by a whole sale price and a buy back price.

15. Option 1: Reduce whole sale price
What happened?
If the supplier reduce the whole sale price from $75 to $65, what happens?
Best Decision for Retailer
Underage cost Cu : $115 - $65 = $50
Overage cost Co : $65 - $25 = $40
Cu / (Cu + Co) = 50 / ( ) = 55.55%

16. Option 1: Reduce whole sale price
z =
Q = (0.1397)*125 = 267
Expected sale = 208
Expected leftover Inventory = 59
Expected profit = $50*208-$40*59 =$8,040
Supplier’s profit = 267*($65-$35) = $8,010
System profit = $5,540+$9,320 = $16,050.

17. Option 1: Reduce whole sale price
Conclusion: System total profit will increase but the supplier’s profit will decrease.
Supplier will not reduce selling price to retailer. NO COORDINATION.
In fact, at whole sale price of $85.5, the supplier’s profit maximized.

18. Option 2: How about buy back contract?
Assume that the supplier offers to buy back unsold items back at the price of $40 each, what happens?
Retailer:
Underage cost Cu : $115 - $75 = $40
Overage cost Co : $75 - $30 = $45
Cu / (Cu + Co) = 40 / ( ) =0.4707
z =

19. Option 2: How about buy back contract?
Q = ( )*125 = 241
Expected sale = 195
Expected leftover = 45
Expected profit = $5,775
Supplier:
Suppliers profit
= 241*($75-$35) - 45*($30-$25)=$9,415
System profit = $5,775+$9,415=$15,190
All better off.

20. Retailer’s Profit with BB Price at $65
Underage cost Cu : $115 - $75 = $40
Overage cost Co : $75 - $65 = $10
Cu / (Cu + Co) = 40 / ( ) = 80%
z =
Q = *125 = 355
Expected sale = 236
Expected leftover = 119
Expected profit = $8,250

21. Supplier’s and System Profit with BB Price at $65
Suppliers profit
= 355*($75-$35) - 119*($65-$25)=$9,440
System profit = $8,250 + $9,440=$17,690
System profit is higher
Both supplier and retailer are also better off (Win-Win).
How to improve system profit further?

22. Optimal Whole Sale and BB Price
Need to make sure retailer’s Q is optimal for the system.
System Q is determined by
(Price-Cost)/(Price-Cost + Cost-Salvage)
Retailer’s Q is determined by
(Price-Whole)/(Price-Whole + Whole-BuyBack)
Two ratios should equal to each other

23. Optimal Whole Sale and BB Price
Optimal Buy Back Price =
Price – (Price-Whole Sale Price)*
(Price-Salvage)/(Price-Cost)
Profit calculations

24. Optimal Whole Sale and BB Price
If the whole sale price is $75, the optimal BB price must be $70.
Retailer
Underage cost Cu : $115 - $75 = $40
Overage cost Co : $75 - $70 = $5
Cu / (Cu + Co) = 40 / (40 + 5) =
z =
Q = *125 = 403
Expected profit =$8,920

25. Optimal Whole Sale and BB Price
Supplier
Expected Profit =$8,920
Total Expected Profit = $17,840
Are they happy?
Not for supplier

26. Observation
To keep the Cu / (Cu + Co) = , when whole sale price (as well as BB price) increases, the supplier’s profit increases
When whole sale price is $85.5 and BB price is $81.81,
Retailer’s expected profit is $6,565.5
Supplier’s profit is $11,261.50
Both are better off

27. Observation
When whole sale price is $90.13 and the BB price is $87.02,
The retailer’s profit is $5,540 (same as before)
Therefore the whole sale price cannot be over $90.13!

28. Observations on Optimal Buy Back Contract
Optimal whole sale and buy back price pairs are not unique. All lead to optimal system profit.
All profit allocations are possible.
=> Buy Back contract is flexible!
Zero sum game, but based on the largest pie possible.
=> Achieve supply chain coordination.
When does retailer makes more profit?

29. Other Advantages of Buy Back Contract
Preserve brand name
Prevent strategic shoppers
Re-distribute inventories
Alleviate fears from product upgrade
Encourage supplier to promote its products

30. Disadvantages of Buy Back Contract
Cost of return and salvage
Irrational retailer
Dampen retailer’s incentive to sell

31. Quantity Discount Contract
Supplier offers lower price for larger orders
Increase underage cost and decrease overage cost
=> larger Q

32. Options Contract Retailer buy capacity option form supplier pre-season
Retailer exercise the option as season starts
Encourages supplier to build up capacity pre-season for uncertain market

33. Revenue Sharing Retailer pays lower whole sale price
Supplier shares revenue generated by retailer
=> both share risk of demand uncertainty
=> Q increases
Successfully used by Blockbuster

34. Quantity Flexibility Contract
Retailer order pre-season.
Retailer is obligated to buy at least a % and has an option of buying up to b% of pre-season order when season starts.
Risk sharing to courage supplier build sufficient capacity pre-season.

35. Price Protection
Retailer will be compensated by the price differences as product price drops.
Encourage retailer to order sufficient (hopefully close to system optimal) quantity.