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Supply Chain Contracts. Gabriela Contreras Wendy O’Donnell April 8, 2005. Outline. Introducing Contracts Example: ski jackets Buy-back Revenue-sharing Quantity-flexibility Newsvendor Problem Wholesale Buy-back Revenue-sharing Quantity-flexibility

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supply chain contracts

Supply Chain Contracts

Gabriela Contreras

Wendy O’Donnell

April 8, 2005

outline
Outline
  • Introducing Contracts
  • Example: ski jackets
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Newsvendor Problem
    • Wholesale
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Results for other problems and open questions
slide3

A contract provides the parameters within which a retailer places orders and the supplier fulfills them.

example music store
Example: Music store
  • Supplier’s cost

c=$1.00/unit

  • Supplier’s revenue

w=$4.00/unit

  • Retail price

p=$10.00/unit

  • Retailer’s service level

CSL*=0.5

question
Question

What is the highest service level both the supplier and retailer can hope to achieve?

example music store continued
Example: Music store (continued)
  • Supplier’s cost

c=$1.00/unit

  • Supplier’s revenue

w=$4.00/unit

  • Retail price

p=$10.00/unit

  • Supplier & retailer’s service level

CSL*=0.9

characteristics of an effective contract
Characteristics of an Effective Contract:
  • Replacement of traditional strategies
  • No room for improvement
  • Risk sharing
  • Flexibility
  • Ease of implementation
slide8
Why?

Sharing risk

increase in order quantity

increases supply chain profit

types of contracts
Types of Contracts:
  • Wholesale price contracts
  • Buyback contracts
  • Revenue-sharing contracts
  • Quantity flexibility contracts
outline10
Outline
  • Introducing Contracts
  • Example: ski jackets
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Newsvendor Problem
    • Wholesale
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Results for other problems & open questions
example ski jacket supplier
Example: Ski Jacket Supplier
  • Supplier cost

c = $10/unit

  • Supplier revenue

w = $100/unit

  • Retail price

p = $200/unit

  • Assume:
    • Demand is normal(m=1000,s=300)
    • No salvage value
formulas for general case
Formulas for General Case
  • E[retailer profit] =
  • E[supplier profit] =

q(w-c)

  • E[supply chain profit] =

E[retailer profit] + E[supplier profit]

results
Results:

Optimal order quantity for retailer = 1,000

Retail profit = $76,063

Supplier profit = $90,000

Total supply chain profit = $166,063

Loss on unsold jackets:

  • For retailer = $100/unit
  • For supply chain = $10/unit
optimal quantities for supply chain
Optimal Quantities for Supply Chain:
  • When we use cost = $10/unit, supply chain makes $190/unit
  • Optimal order quantity for retailer = 1,493
  • Supply chain profit = $183,812
  • Difference in supply chain profits = $17,749
outline15
Outline
  • Introducing Contracts
  • Example: ski jackets
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Newsvendor Problem
    • Wholesale
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Results for other problems
buy back contracts
Buy-Back Contracts

Supplier agrees to buy back

all unsold goods for

agreed upon price

$b/unit

change in formulas
Change in Formulas:
  • E[retailer profit] =
  • E[supplier profit] =

q(w-c)

3. E[overstock] =

+ bE[overstock]

– bE[overstock]

outline19
Outline
  • Introducing Contracts
  • Example: ski jackets
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Newsvendor Problem
    • Wholesale
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Results for other problems
revenue sharing contracts
Revenue-sharing Contracts

Seller agrees to reduce the

wholesale price and

shares a fraction f

of the revenue

change in formulas21
Change in formulas
  • E[supplier profit]=

(w-c)q+fp(q-E[overstock])

  • E[retailer profit]=

(1-f)p(q-E[overstock])+vE[overstock]-wq

slide23

“Go Away Happy”

“Guaranteed to be There”

outline24
Outline
  • Introducing Contracts
  • Example: ski jackets
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Newsvendor Problem
    • Wholesale
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Results for other problems
quantity flexibility contracts
Quantity-flexibility Contracts
  • Retailer can change order quantity after observing demand
  • Supplier agrees to a full refund of dq units
outline27
Outline
  • Introducing Contracts
  • Example: ski jackets
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Newsvendor Problem
    • Wholesale
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Results for other problems
contracts and the newsvendor problem
Contracts and the Newsvendor Problem
  • One supplier, one retailer
  • Game description:

Y

Accept Contract?

Q

N

Production

End

Product Delivery

Demand Recognition

Transfer payments

assumptions
Assumptions
  • Risk neutral
  • Full information
  • Forced compliance
profit equations
Profit Equations

pr = pS(q) – T

ps = T – cq

P(q) = pS(q) – cq = pr +ps

p= price per unit sold

S(q)= expected sales

c= production cost

Proof:

transfer payment
Transfer Payment

What the retailer pays

the supplier after

demand is recognized

T = wq

w = what the supplier charges the retailer per unit purchased

outline32
Outline
  • Introducing Contracts
  • Example: ski jackets
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Newsvendor Problem
    • Wholesale
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Results for other problems
newsvendor problem
Newsvendor Problem

Wholesale Price Contract

Decide on q, w

slide34
Let w be what the supplier

charges the retailer

per unit purchased

Tw(q,w)=wq

results37
Results:
  • Commonly used
  • Does not coordinate the supply chain
  • Simpler to administer
outline38
Outline
  • Introducing Contracts
  • Example: ski jackets
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Newsvendor Problem
    • Wholesale
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Results for other problems
buy back contracts39
Buy-back Contracts
  • Decide on q,w,b
  • Transfer payment

T = wq – bI(q)

= wq – b(q – S(q))

claim
Claim

A contract coordinates retailer’s and supplier’s action when each firm’s profit with the contract equals a constant fraction of the supply chain profit.

i.e. a Nash equilibrium is a profit sharing contract

slide41

Buy-back contracts coordinate

if w & b are chosen such that:

recall p r ps q t
Recall: pr = pS(q) – T

pr = pS(q) –

wq – b(q – S(q))

= (p – b)S(q) – (w – b)q

= lP(q)

recall p s t cq
Recall: ps = T - cq

ps = – cq

wq – b(q – S(q))

= bS(q) + (w – b)q – cq

= (1 - l)P(q)

results44
Results

Since q0 maximizes p(q),

q0 is the optimal quantity for both pr and ps

And both players receive a fraction of the supply chain profit

outline45
Outline
  • Introducing Contracts
  • Example: ski jackets
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Newsvendor Problem
    • Wholesale
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Results for other problems
newsvendor problem46
Newsvendor Problem

Revenue-Sharing Contracts

Decide on q, w, f

transfer payment47
Transfer Payment

Tr= wq

+ pS(q)

(1-f)

retailer s profit
Retailer’s Profit

pr= pS(q)- T

  • For l Є (0,1], let

fp= lp

w= lc

pr= lP(q)

f

similar to buy back
Similar to Buy-Back

From Previous Slide:

pr(q,wr,f)=lP(q)

Recall from Buy-Back:

pr(q,wr,b)=lP(q)

outline50
Outline
  • Introducing Contracts
  • Example: ski jackets
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Newsvendor Problem
    • Wholesale
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Results for other problems
quantity flexibility contracts51
Quantity-flexibility Contracts
  • Decide on q,w,d

Supplier gives full refund on dq unsold units i.e. min{I,dq}

retailer s profit function53
Retailer’s profit function

pr = pS(q) – wq + w

optimal q satisfies
Optimal q satisfies:

w = p(1 – F(q))

1 – F(q) + F((1 – d)q)(1 – d)

If supplier plays this w, will the retailer play this q?

supplier s profit function56
Supplier’s profit function

ps = wq – w

What is supplier’s optimal q?

key result
Key result
  • The supply chain is not coordinated if (1 – d)2f((1 – d)q0) > f(q0)

q0 is the minimum

result
Result
  • Supply chain coordination is not guaranteed with a quantity-flexibility contract
  • Even if optimal w(q) is chosen
  • It depends on d & f(q)
summary
Summary

You can coordinate the supply chain

by designing a contract

that encourages both players

to always want to play q0,

the optimal supply chain order quantity

outline60
Outline
  • Introducing Contracts
  • Example: ski jackets
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Newsvendor Problem
    • Wholesale
    • Buy-back
    • Revenue-sharing
    • Quantity-flexibility
  • Results for other problems and open questions
newsvendor with price dependent demand
Newsvendor with Price Dependent Demand
  • Retailer chooses his price and stocking level
  • Price reflects demand conditions
  • Can contracts that coordinate the retailer’s order quantity also coordinate the retailer’s pricing?
  • Revenue-sharing coordinates
multiple newsvendors
Multiple Newsvendors
  • One supplier, multiple competing retailers
  • Fixed retail price
  • Demand is allocated among retailers proportionally to their inventory level
  • Buy-back permits the supplier to coordinate the S.C.
competing newsvendors with market clearing prices
Competing Newsvendors with Market Clearing Prices
  • Market price depends on the realization of demand (high or low) & amount of inventory purchased
  • Retailers order inventory before demand occurs
  • After demand occurs, the market clearing price is determined
  • Buy-back coordinates the S.C.
two stage newsvendor
Two-stage Newsvendor
  • Retailer has a 2nd opportunity to place an order
  • Buy-back
  • Supplier’s margin with later production < margin with early production
open questions
Open Questions
  • Current contracting models assume on single shot contracting.
  • Multiple suppliers competing for the affection of multiple retailers
  • Eliminate risk neutrality assumption
  • Non-competing heterogeneous retailers