Secure Collaborative Planning, Forecasting, and Replenishment

1. Secure Collaborative Planning, Forecasting, and Replenishment Vinayak Deshpande Krannert School of Management Purdue 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

2. The Starting Point.... “Information Asymmetry” isone 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

3. 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)

4. .... 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

5. As a result… • Reluctance to share private/proprietary info • Even when both sides would gain from sharing • Consequence: Information asymmetry • Many inefficiencies

6. Obvious Question… Is it possible to enjoy the benefits of Information-Sharing without Disclosing Private Information?

7. 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?

8. 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

9. Secure multiparty computation Bob Alice y x • 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.

10. 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

11. 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

12. 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

13. We Propose to marry three distinct disciplines • Secure Multi-Party Computation from CS • Mechanism Design from Economics • Supply-Chain Management from OM

14. Our Goal.. ...we are developing protocols to enable Supply-Chain Partners to Make Decisions that Cooperatively Achieve Desired System Goals without Revealing Private Information

15. A Supply Chain Problem.. • Collaborative Forecasting and Planning without revealing private forecast information

16. 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”

17. 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

18. Demand Model • 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

19. Forecasting Process • In each period t, estimate , r , sby regressing the observations dt versus the observed signals t,ir and t,is • For the forecast horizon (T periods) construct the forecast using the following equation:

20. Collaborative Inventory Planning Policy

21. Secure Protocols Example: Average Salary

22. 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

23. 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

24. Secure Multiple Linear Regression Protocol

25. Secure Process for Forecasting and Inventory Planning

26. Step 1: Input cost parameters Retailer Supplier

27. Step 2: Input demand and inventory information Retailer Supplier

28. Step 2(con’t): Regression Retailer Supplier Supplier

29. Step 3: Leadtime demand forecast Retailer Supplier Overall

30. Step 4: Determine base-stock levels Retailer Supplier Overall

31. Step 5: Determine order quantities Retailer Supplier

32. 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

33. 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

34. 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)

35. 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

36. Questions?...

37. Secure Regression

38. Secure 3x3 Matrix Inverse Protocol

39. Secure Demand Forecasting Protocol Input: The supplier knows the j,isand 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 , sare available in additively split form. Output: Both supplier and retailer learn the forecast djfor all j = t + 1, ..., t + T. Protocol Steps: 1. For each j  {t + 1, ..., t + T}, the supplier computes vjs = Tj,is. This is a “local” computation, as the supplier has all the j,isvalues. The retailer similarly computes vjr = Tj,ir 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 = rvrj and once to compute wsj = 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+ wrj+ wsj, which is equal to dj . They exchange their shares of each dj so they both learn its value.