Supply Contracts and Channel Coordination

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Supply Contracts and Channel
Coordination

• Yossi Sheffi
• Professor, MIT

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Agenda

• The Framework
• Wholesale contracts
• Buy-back contracts
• Revenue sharing contracts
• Using real options

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The Scenario
Supplier
Retailer

• Contract is negotiated
• Retailer places order (a single period)
• Supplier makes and sends the stuff
• The selling season takes place
• Accounting (sales, salvage, etc.)

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Consumer Demand
Average 811.54 Std Dev 154.23
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Notations
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Demand Distribution
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Wholesale Contract
Retailer profit

• If retailer orders Q and demand is x
• If x .LE. Q, then the retailers sells x at
  revenue x?r and he sells the rest at a salvage
  value of s for a revenue of (Q-x)?s
• If x .GE. Q, then the retailer sells Q items for
  revenue Q?r
• For all x less than or equal to Q, the retailers
  revenue is

• For all x greater than Q, the retailers revenue
  is

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Wholesale Contract
Retailers profit
-


Suppliers profit
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Participants Cost Functions
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Wholesale Contract
Optimal Quantity
A helpful formula
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Wholesale Contract
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Wholesale Contract
Collecting terms
Note that since r gt w gt s, the ratio is positive
and smaller then 1.
Critical Ratio
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Wholesale Contract
Another way to look at this

• Cost of overage (items ordered but not sold)

• Cost of underage (not enough items ordered the
  cost is lost sales)

• So

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The Ideal Situation

• If the channel operates as one
• w drops out and the only cost that matters is c

• Note since c lt w this quantity is larger than
  the previous one (when the retailer pays w).
• So the channel has to find a way to increase the
  order size!

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Wholesale Contract
When the channel operates as one
With a wholesale contract
So to coordinate the channel, the optimal
order quantity of the retailer has to be equal to
the optimal quantity under the one channel. This
will happen only if w c
The supplier has to set the wholesale price equal
to c this means it has no profit.
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Normal Approximation

• If the integral goes to ? we have the
  expectation.
• Without the x multiplier we have the cumulative
  distribution, ?(x).

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Wholesale Contract
Retailers profit
Suppliers profit
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Wholesale Contract
Retailers cost function
Where
Retailers cost function in spreadsheet
(s-r)? (zNORMDIST(z,0,1,TRUE)NORMDIST(z,0,1,FA
LSE))(r-w)Q
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Wholesale Contract (N. Approx.)
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Wholesale Contract
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Effects of Wholesale Price
The supplier will charge a wholesale price at the
maximum point, if it is a monopoly supplier
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Effects of Wholesale Price
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A Buyback Contract

• How does the supplier get the retailer to order
  more?
• One way offer to share the risk through a
  buyback offer b (the retailer will buy back all
  Q-x at the end of the selling season)
• Assume b gt s
• The supplier buys at b but can salvage at s

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A Buyback Contract
Retailers profit
Suppliers profit
Adding the terms, the buyback falls out and it is
the same as an integrated channel
The optimal order size
The retailer is ordering more since it
essentially has a higher salvage value (bgts).
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A Buyback Contract
Note w and b are not set to coordinate
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r 200 c 50 s 10 w 135 b 80
Note w and b are not set to coordinate
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A Buyback Contract

• The issue how do we set the buyback contract to
  induce the retailer to order enough to
  coordinate the channel?
• Make sure that the order quantity is equal to the
  optimal quantity under the single channel scenario

Or
All w and b that comply will coordinate the
channel (in other words, they will make the
retailer order the optimal Q)
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Buyback Contract
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Buyback Contract - Optimal
Note Channel, and each members profits are
higher.
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Revenue Sharing

• Supplier still needs to get the retailer to order
  more
• Another risk-sharing scheme supplier lowers the
  wholesale price but takes a percentage, (1-?), of
  the revenue
• Question how to choose w and ? so the retailer
  will order the optimal amount

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The Players
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Revenue Sharing
Suppliers Expected Gross Profits
Retailers Expected Gross Profits
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r 200 c 50 s 10 w 40 0.40
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Revenue Sharing
Solve for the retailer
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Revenue Sharing
Collecting terms
The optimal retailer order is
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Revenue Sharing


A single channel
Revenue sharing
Note for ? to be less than 1, w needs to be less
than c. This means that the supplier takes on a
significant risk.
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Coordination with Rev. Sharing
Retail Price 200 Supplier Costs 50 Salvage
value 10
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Real Options

• The retailer buys Q call options at a price w.
  The supplier makes Q items. Each option can be
  exercised at a unit price p. As demand
  materializes the retailer can take deliveries at
  a price p.

• Retailers profit

• Suppliers profit

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Real Options
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Coordination with Real Options
Retailers optimal order
Comparing to a single channel
Where
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Coordination with Real Options
r 200 c 50 s 10 w 25 p 81
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r 200 c 50 s 10 w 25 p 81
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Summary

• Wholesale contracts give too much risk and not
  enough expected reward to the retailer
• To make the retailer order more (and increase the
  channels profit) the supplier has to take on
  part of the risk
• Risk sharing mechanisms covered include
• Buybacks
• Revenue sharing
• Real options
• There are many other mechanisms
• Each mechanism can coordinate the channel with
  various allocations of the profit between the
  retailer and the supplier.

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Any Questions?
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Yossi Sheffi sheffi_at_mit.edu