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Secure Collaborative Planning, Forecasting, and Replenishment

Vinayak Deshpande

Krannert School of ManagementPurdue University

Collaborators:

Mikhail Atallah, Marina Blanton, Keith Frikken, Jiangtao Li

Computer Sciences, Purdue University

Leroy B.Schwarz

School of Management, Purdue University

Research funded by NSF ITR Grant

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The Starting Point....

“Information Asymmetry” is one of the major sources of inefficiency in Managing Supply Chains

==> Wrong Investment in Capacity

==> Misallocation of Resources

==> “Bullwhip Effect”

==> Reduced Customer Service

==> Unnecessary Additional Costs

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Supply Chain Management Trends

• Collaboration between supply-chain partners to improve efficiencies

• Information sharing for collaborative decision making

• National program sponsored by VICS for establishing collaboration standards – called CPFR (Collaborative Planning, Forecasting and Replenishment)

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.... but, there are Very Good Reasons for Keeping Asymmetric Information

Asymmetric

• Fear that Supply-Chain Partner will Take Advantage of Private Information

• Fear that Private Information will Leak to a Competitor

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As a result…

• Reluctance to share private/proprietary info– Even when both sides would gain from sharing

• Consequence: Information asymmetry– Many inefficiencies

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Is it possible to enjoy the benefits of Information-Sharing without Disclosing Private Information?

Obvious Question…

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The Future

• Online interactions that give the benefits of sharing, without its drawbacks– “As if” information sharing had taken place, yet without

revealing one’s private/proprietary data

• Counterpart’s information is often needed only as partial input for computing a desired output

• Can two parties compute desired output without either learning the other’s input?

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An Example: Vickrey Auction

• Requires computation of the second highest bid value and identity of highest bidder from all submitted bids

• Secure Multi-party Computation (SMC) protocols can– Compute the second highest bid without revealing the

identity of the second highest bidder

– Identify highest bidder without revealing his bid

– Not reveal bids of any other bidders

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Secure multiparty computation

• Alice has private data x,• Bob has private data y,• They want to jointly compute f(x,y),• Only Alice (or Bob, or both) knows the result.

Alice Bob

x y

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Secure multiparty computation (SMC) Literature

• A decades old area– Yao, Goldreich, Micali, Wigderson, … (many others)

– Elegant theory

– General results • Circuit simulations, use oblivious transfer

– General results typically impractical

• Recently: Protocols for specific problems– More practical

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Mechanism Design Literature

• Studies how private information can be elicited from agents by providing incentives

• Mechanism design problem simplified through the revelation principle (principal announces a menu constructed to induce truth telling)

• No future or side consequences of participating in the mechanism and truthfully revealing private information

• Assumes that the entity implementing the mechanism is trustworthy

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Supply Chain Literature…

• Has quantified the benefit of information sharing (e.g. Lee, So and Tang; Cachon and Fisher)

• Has modeled Supply-Chain Collaboration, e.g. collaborative forecasting (Aviv 2001, 2003)

• Key obstacles: companies unwilling to share sensitive information, fear of information leakage

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We Propose to

marry three distinct disciplines

• Secure Multi-Party Computation from CS

• Mechanism Design from Economics

• Supply-Chain Management from OM

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Our Goal..

...we are developing protocols to enable Supply-Chain Partners to

Make Decisions that Cooperatively Achieve Desired System Goals without Revealing

Private Information

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A Supply Chain Problem..

• Collaborative Forecasting and Planning without revealing private forecast information

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Industry Backdrop

• Collaborative Planning, Forecasting, and Replenishment (CPFR), an initiative of the Voluntary Intra-Industry Collaboration Society (VICS)– buyer and supplier share inventory-status, forecast, and

event-oriented information and collaboratively make replenishment decisions

– pilot program between Wal-Mart and Warner-Lambert, called CFAR: (www.cpfr.org)

• Challenges to CPFR– fear that competitively-sensitive “private information”

will be compromised– Necessary to protect “sensitive” forecast information

such as sales promotions from “leaking”

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Business Scenario

• A supply-chain with two players, a supplier selling to a retailer.

• The retailer and the supplier receive independent “signals” about future market demand– e.g., a retailer has private information about “promotions”

that he may be planning to run in the future which can affect his forecast of demand;

– the supplier can receive signals about overall “market trends”

• Incorporating these “signals” can improve forecast accuracy

• But.. “signal” information should be kept private

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Demand Model

, ,1 1

T Tr s

t r t i s t i ti i

d

• dt – demand in period t (observed by the retailer only)

• t,ir – Retailer’s signal about period t observed in period t-i

(private information to the retailer)

• t,is –Supplier’s signal about period t observed in period t-i

(private information to the supplier)

• , r , s – unknown parameters to be estimated from past observations

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Forecasting Process

• In each period t, estimate , r , s by regressing the observations dt versus the observed signals t,i

r and t,i

s

• For the forecast horizon (T periods) construct the forecast using the following equation:

, , 1,...,

T Tr s

j r sj i j ii j t i j t

d j t t T

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Collaborative Inventory Planning Policy

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Secure Protocols Example: Average Salary

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Secure Protocols Building Blocks:

• Hiding numbers by additively splitting values

-x= xs + xr, Supplier has xs, while retailer has xr

- Modular arithmetic (xs+xr) mod N =x hides x in a information theoretic sense

Secure addition and subtraction

Homomorphic Encryption ( E(X) E(Y)=E(X+Y) )

Secure Split Multiplication

Secure Split Division

Secure Scalar Product

Secure Matrix Multiplication

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Advanced Building Blocks:• Secure Matrix Inversion

-Matrix A is split such that As+Ar = A.

- Output supplier learns Bs, retailer learns Br; Bs+Br = B

• Secure Binary Search

• Secure Comparison

-Supplier has X, Retailer has Y,

- Output reveals if X<Y, without revealing X to retailer and Y to supplier

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Secure Multiple Linear Regression Protocol

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Secure Process for Forecasting and Inventory Planning

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Step 1: Input cost parameters

1Rh 0.5Sh

19Rp 15Sp

Retailer Supplier

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Retailer Supplier

16.80td

7RtOH

Step 2: Input demand and inventory information

1,1 0.83Rt

0RtBO

22RtIT

13StOH

0StBO

19StIT

2,2 0.58Rt

3,3 0.88Rt

4,4 0.29Rt

1,1 1.84St

2,2 0.81St

3,3 0.69St

4,4 0.18St

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Retailer Supplier

Step 2(con’t): Regression

Supplier

ˆ 14.997

ˆ 0.996R

ˆ 0.996S

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Step 3: Leadtime demand forecast

Overall

,[ , ] 47.46Rt t t L

,[ , ] 5.02St t t L

,[ , ] 79.35R St t t L L

SupplierRetailer

,[ ] 8.28R St t L L

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Step 4: Determine base-stock levels

Overall

* 57.30Ry

* 67Sy

SupplierRetailer

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Step 5: Determine order quantities

28.30Rtq

44Stq

SupplierRetailer

44Stq

28.30Rtq

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Protocol Implementation Issues:

Protocols are verifiable

• The Logic of the Protocol is Auditable– Logic of Source Code Can be Audited

• Outputs Can be Tested– Outputs Can be Verified Given Known Inputs

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Protocol Implementation Issues:

Other Advantages

• Valuable even in Trusted e.g. (intra-corporate) interactions– “Defense in depth” ! – Systems are hacked into, break-ins occur,

viruses occur, spy-ware, bad insiders, etc– Liability Decreased

• “Don’t send me your data even if you trust me”

• Impact on Litigation and Insurance Rates

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We Have Only Just Begun...

• Tough Issues to Deal with:– SMC Complexities; e.g.,

• How to Deal with Collusion• Computational Complexity (e.g., simultaneity)

– Supply-Chain Modeling Complexities; e.g.• Contracting/Incentive Issues

– SSCC Complexities; e.g., • Inverse Optimization

• Bob’s Objective is fB(xA, xB); Alice’s is fA((xA, xB)

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Future Work

• Protocols for other supply-chain applications– Price-Masking

– Bullwhip Scenarios

– Capacity Allocation

• Protocol implementation issues– Collusion by a subset of parties

– Intrusion detection

– Incentive issues and mechanism design

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Questions?...

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Secure Regression

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Secure 3x3 Matrix Inverse Protocol

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Secure Demand Forecasting ProtocolInput: The supplier knows the j,i

s and the retailer knows the j,ir , for all j,

i such that j = t + 1, ..., t + T and i = j − t, ..., T. The parameters , r , s are available in additively split form.

Output: Both supplier and retailer learn the forecast dj for all j = t + 1, ..., t + T.

Protocol Steps: 1. For each j {t + 1, ..., t + T}, the supplier computes vj

s = j,i

s. This is a “local” computation, as the supplier has all the j,i

s values. The retailer similarly computes vj

r = j,i

r for all j {t + 1, ..., t + T}.2. For each j {t + 1, ..., t + T}, the supplier and retailer run a split

multiplication protocol twice, once to compute wrj = rvr

j and once to compute ws

j = svsj (both in split fashion).

3. For each j {t + 1, ..., t + T}, the supplier and retailer run a split addition protocol to compute µ+ wr

j+ wsj, which is equal to dj . They

exchange their shares of each dj so they both learn its value.