A Dynamic Mechanism for Achieving
Sustainable Quality Supply
Tracy Lewis Fang Liu1 Jeannette Song
Fuqua School of Business, Duke University
1Nanyang Business School, Nanyang Technological University
December 2014
Starbucks Growth
8
7
6
5
4
Fiscal Year End Store Counts
3
2
1
US
International
20
00
20
01
20
02
20
03
20
04
20
05
20
06
0
600
500
400
Net Earnings
($Millions)
300
200
100
0
'95 '96 '97 '98 '99 '00 '01 '02 '03 '04 '05 '06 '07
20
00
20
01
20
02
20
03
20
04
20
05
20
06
15000
14000
13000
12000
11000
10000
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
Annual Revenues
($Billions)
The Coffee Supply Chain
Worldwide, 25 million
small producers rely on
coffee for a living
Farmers/producers
50% Latin America
35% Pacific Rim
15% East Africa
Suppliers
Processors
Make green coffee
Areas of coffee cultivation
Exporters
Distributors
Mktg & financing
Technical expertise
Logistics
Retailers
Over 2.25 billion cups of
coffee are consumed in the
world every day
Commodity chain for the coffee industry
C.A.F.E. Practices
(Coffee and Farmer Equity Practices)
Coffee buying guidelines to support coffee buyers and coffee farmers
–
1.
Ensure high quality coffee and equitable relationship with farmers
Prerequisites for Starbucks suppliers
–
–
2.
Product quality: green preparation and cup quality
Economic accountability: financial transparency, viability, equity pay
Supplier grading/rewarding system on environmental and social criteria
(weighted scoring sheet, up to 100 points)
–
–
Social responsibility: Non-discrimination & employee quality of life,
occupational health, safety & living condition (60)
Environmental leadership: conservation of natural resources and impact on
environment, growing (20), processing (20)
4
Supplier Incentives
•
Level 1
Total score > 60 points
Preferred pricing & contract terms, prioritized purchases
•
Level 2
Total score > 80 points
Premium of $0.05 per pound on green coffee prices for first year
•
Level 3
Second year with 10% increase in scores over Level 2
Additional premium of $0.05 per pound
Sustainable Quality Supply
• Other examples
– Wal-Mart: local organic produce
– Coca-Cola: pure water
• Common features
– Demand for large quantity of high quality supply
– Foresee shortage in the near future
– Sequential investments to hedge against future risk
• Challenges
–
–
–
–
–
Supplier development
Long-term commitment
Changing environment / private information
Voluntary participation
Self-enforceability
Research Questions
• Are the existing industry guidelines such as C.A.F.E. sufficient for
achieving sustainable supply quality in the long run?
– Ex post efficiency
• Do they also encourage first-best initial and continued supplierdevelopment investments?
– Ex ante efficiency
• If the current practice is not successful, when to stop?
– Termination conditions
Approach: Dynamic mechanism design
Model Setting
Supplier (s)
Retailer (r)
Market
• Collaborate for T periods, discount factor d
• Product quality (prerequisite, fixed)
• Sustainability index 0 < x < 1 (current sustainability level)
– Single aggregated measure
• Social and environmental aspects (measured by score card)
• Weighted scores
– Commonly observed
• Third-party certified
– Jointly agreed with payments adjusted, so no rejections by retailer
(Additional) Production Cost and Investment
• In period t, supplier incurs an additional cost (over that for x=0)
C ( x t , q st )
– Increasing and convex in xt
t
– Increasing and concave in s
– Supermodular
t
•  s  0, s  : production conditions in period t
– Technological readiness, labor market conditions, soil and weather conditions
– Private information to supplier
– Morkov process, depending on improvement investment It and  st 1
 st ~ Fst  |  st 1 , I t 
t
t t 1
t
t
e.g.,  s   s s  I   s
Adjusted Market Revenue
• In period t, the retailer receives adjusted revenue
R ( x t , q rt )
–
–
–
–
Additional revenue + tax credit
Increasing and concave in xt
Increasing and convex in  rt
Supermodular
•  r  0, r  : current demand conditions in period t
t
– Consumer’s valuation of sustainability: environmental awareness, social
awareness, general economic conditions, tax credit
– Private information to retailer
– Markov process
 rt ~ Frt   |  rt 1 
e.g.,
 rt  rt rt 1   rt
Benchmark:
Supply-Chain Optimal Solution
• Optimal expected discounted supply-chain profit from period t on
• For any given
index:
, supply-chain ex-post optimal sustainability
• Optimal single-period supply chain profit
• Optimal ex-ante investment
Questions for Decentralized Chain
• Short term goal: How to provide incentives to achieve xt* in
each period?
– What should be the payment structure?
• We do not assume a fixed payment type
– How does the payment depend on market and production
environment?
– How to ensure long-term commitment?
• Long term goal: How to ensure optimal supply-chain
investments It*?
– Retailer invests to improve θst
– Supplier development
– Investment amount is private information, relationship specific
Literature Review
Methodology
o
Supply chain contracts: repeated interactions
o
o
o
Relational contracts
o Plambeck and Taylor (2006)
o Tunca and Zenios (2006)
o Taylor and Plambeck (2007a,b)
Investment efficiency
o Plambeck and Taylor (2007)
Dynamic mechanism design
o Lutze and Ozer (2008)
o Zhang, Nagarajan and Sosic (2010)
o Oh and Ozer (2012)
o Li , Zhang and Fine (2013)
Principal-agent framework – no full coordination
o
Dynamic mechanism design
o
o
o
Bergemann and Valimaki (2006, 2010) (w/o BB)
Athey and Segal (2007a, b) (w/o IR)
Lewis, Liu & Song (2012) – dynamic ownership
Ours: Partnership & commitment – full coordination
Modeling
• Quality as contract terms
– Baiman, Fischer & Rajan
(2000)
– Lim (2001)
– Iyer, Schwarz & Zenios (2005)
– Zhu, Zhang & Tsung (2007)
– Kaya and Ozer (2009)
Ours: Jointly decide index x,
dynamic model
Structure of the Mechanism
• A sequence of investment strategies I determines a
multi-period direct mechanism:
M x , | I
t
– Sustainability index
•
t
T
t 1
is the set of possible period t reported histories
– Payments
•
is payments to member i after material is supplied
• The mechanism induces a dynamic game
Sequence of Events
Stage 1: ex-ante
decision to
participate stage
Stage 2:
investment stage
Stage 3: ex-post decision to
participate stage
Stage 4: reporting stage
Period t
time
Period t+1
Supplier
stay?
Supplier
stay?
no
yes
no
yes
Retailer invests Itr
Supplier observes  st
Retailer observes  rt
~
Supplier reports  st 1) Select index, x t
~
Retailer reports  rt 2) Make payments, τt
1)
2)
3)
4)
Supplier quits without penalty
The partnership ends and cannot be fixed
Retailer invests 0 in the future
Retailer purchases from the market with
sustainability index 0
5) Supplier supplies the market with
sustainability index 0
Retailer decides whether to commit to M at the beginning of period 1
Payoffs of Each Player
Expected optimal profit to go given the other member’s reporting strategy
• Retailer
• Supplier
Desired Equilibrium
• Supply chain transparency (Bayesian incentive compatible BIC):
– Truth-telling is the mutual best response:
• First-best outcome
– Ex ante efficient investments (EE1):
– Ex post efficient sustainability index (EE2):
• Voluntary participation
– Ex ante Interim individual rational (IIR1):
– Ex post Interim individual rational (IIR2):
• Self-enforceability (Budget balancing BB):
and
Constructing the Mechanism
(Without Investment)
• To ensure BIC, let
expected supply chain profit – participation fee
• Member i will not lie -- he/she receives all the values he/she contributed
to the system
• For every realization of  st , supplier’s willingness to pay is
• Supplier’s willingness to pay under her worst off type is
• To ensure IIR2, supplier’s participation fee has to be less than her
willingness to pay under every possible st
Constructing the Mechanism (Cont.)
(Without Investment)
• To ensure BB, total participation fee must exceed supply chain
profit
• Thus, set
• To ensure EE2, set
Adjusting Transfer Payments
Net transfer payment for member i
Transfer that ensures
the first-best index
Expected participation
payment for t, ensures
self-enforceability
Expected participation
payment for t+1, ensures
supply chain transparency
Net transfer payment achieves ex-ante budget balance
Adjust to ensure ex-post budget balance
Payment Structure
•
Two-part nonlinear tariff
A bottom-line price fixed at the beginning of the period depending on the
previous period’s conditions
+
A real-time payment equals the current period supply chain profit based
on the current period’s sustainability index and the current period’s
environmental conditions
+
A real-time payment equals the expected continuation supply chain
profit based on the current period’s environmental conditions
Different from C.A.F.E.
Supply Chain Optimal Investments
and Retailer’s Commitment
T
• Modified mechanism M xt* , t*|I * specifies contract terms according to
t 1
production cost distribution under optimal investment

Fst*  Fst  |  st 1 ,I t*

• Retailer’s expected profit before he invests in period t
• Retailer’s best response is the supply chain optimal investment (EE1)
I rt*  I t*
t*
t*
• If It* is unique, then I r  I is the unique equilibrium
t* t* * T
• Retailer commits to M x , |I
if and only if
t 1
Sustainable Quality Supply Agreement (SQSA)
• The mechanism
–
–
–
–
–
   
~
M x  , h t | I *
*
t
*
T
t 1
ensures
Supply chain transparency (BIC)
Voluntary participation (IIR1, IIR2)
Optimal ex ante investments (EE1)
Optimal ex post sustainability index (EE2)
Budget balance: self-enforceability (BB)
Here,
Example: Coffee Supply Chain
time
Identical stationary distributions of the
production and market condition
•
Linear cost/revenue


R x t , rt  x t rt


C x t ,  st  x t st
•
•
Retailer invests in technological innovation, success rate is p
•
Let
•
Define
,
Coffee Example: SQSA Properties
Price of free will
Sustainable practice
Unsustainable practice
• Threshold policies on T, for fixed p
• Threshold policies on p, for fixed T
Region A + Region B = retailer
terminates the current
contract and start a new
sustainable practice
Coffee Example: Supplier Development Dynamics
Total collaboration: 1 - 10 years
Year 1
Year 10
Year 8
High cost years
• Years 1 to 7
• When x>0, production cost = 2
Starbucks: when x=1, market revenue = 1
time
Low cost years
•
• Years 8 to 10
Production cost = 0
Coffee Example: Supplier Development (cont.)
Total collaboration:10 years
Year 1
Year 10
Year 8
time
High cost years
Low cost years
• Year 1 to 7
• When x>0, production cost = 2
Starbucks: when x=1, market revenue = 1
• Year 8 to 10
• Production cost = 0
Cost of investment = 1
With probability p grower’s
cost reduce to zero
Year
1
2
3
4
5
6
7 8 9 10
V*t
(7p+2)v3
(6p+2)v3
(5p+2)v3
(4p+2)v3
(3p+2)v3
(2p+2)v3
3 3 2
Invest if p≥
1/7
1/6
1/5
1/4
1/3
½
1 1 1 1
1
Observations
• It is not necessarily optimal to select a high sustainability index in
every period because it may not be economically sustainable
• The real-time payments depend not only on the sustainability
index (the first transfer) but also on the market condition (the
third transfer)
• For any given success rate p, when the contract length T
increases, the retailer is more likely to invest in more periods
• With longer contract length T, the supplier is more likely to invest
in a wider range of suppliers (with smaller cutoff success rate)
• For any given success rate p, the retailer will continue SQSA if the
remaining contract length T is longer than a certain threshold
max(T0 ,T1), which is neither convex nor concave in p
Summary
• Designed a T-period agreement (SQSA) for the supply chain
members to collaborate to achieve supply-chain optimal
sustainability level and investment
– Suggesting new elements and payment calculations to add to
the existing sustainability initiatives
– Confirming long-term collaboration encourages investments
• Key:
– Shared-surplus type of mechanism – residual claimant
– Dynamically adjusted payment scheme, reflecting both
current performance and environmental effects
• Can be generalized to N members in series