Secure Protocols for Supply Chain Collaboration: Capacity Allocation and Collaborative Forecasting

Secure Protocols for Supply Chain Collaboration: Capacity Allocation and Collaborative Forecasting Vinayak Deshpande Krannert School of Management Purdue University Joint Work With: Mikhail Atallah Leroy B.Schwarz Keith Frikken

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

Two Supply Chain Problems.. • Capacity Allocation without revealing retailer’s order quantities • Collaborative Forecasting without revealing private forecast information

A capacity allocation problem… • Supplier Often Puts Customers “On Allocation” • - Each customer gets some or all of its order, based on metrics (e.g., Past Sales, Days-of-Supply) • Examples: • Honda Odyssey • Flat Panel Monitors for PC’s • Our Goal: Construct Secure Protocols for implementing the Optimal capacity allocation mechanisms

The Business Scenario • Single supplier selling to N  2 independent retailers or manufacturers, whose orders are based on private demand information, and the supplier’s announced price and allocation policy • Focus on situation when total orders exceed supplier’s capacity or inventory

Model Framework Supplier Capacity K at unit cost c Price & Quantity Allocation {P(i), Q(i, -i)} ...... N Retailers Revenues Ri(qi,i) i– Retailer’s private information parameter

Linear Allocation Mechanism Index the retailers in decreasing order of their order quantities, i.e., q1 q2...  qN. Retailer i is allocated Qi(q,n) where Wherenis the largest integer such that Qi(q,n)  0 for all i. Example: Retailers face newsvendor problem with normal demand distribution with mean , with an exponential prior on .

Proportional Allocation Mechanism Retailer i is allocated Qi(q) where Example: Retailers face newsvendor problem with uniform demand distribution on [0, ] with Pareto prior

Can the linear and proportional allocation mechanisms be implemented without revealing the retailer order quantities (and hence the private information parameter  ) to the supplier?

Secure Protocol for determining if capacity is tight • Run the secure summation protocol to compute • X = R + i qi, where R is a random chosen by the supplier, and X becomes known to the retailers not the supplier. • 2. Supplier locally computes K+R • 3. Run a secure comparison protocol to determine whether Y<X • 4. If answer is yes, capacity is tight. Protocol determines if capacity is tight without revealing qi to the supplier, or K to the retailers.

Secure Proportional Allocation Protocol • N retailers cooperatively choose a large Random R’, not known to the supplier • Each retailer sends R’*qi to the supplier • Supplier sends D’ = i qi*R’/K to every retailer • Every retailer computes it’s allocation qi’ as follows • qi’ = R’*qi/D’ = qi* K/ i qi

SPAP: Who Knows What? • Supplier capacity known only to the supplier • Retailer orders known only to individual retailers • Retailer’s common random number not revealed to the supplier • Individual retailer’s allocated quantity revealed to both the supplier and the individual retailer • Sum of individual retailer orders not revealed to anyone

Secure Linear Allocation Protocol • Every retailer marks himself as “active”. Let  be the set of active retailers and n = | | • Repeat steps 2(a)-(d) till n ceases to change • Every Retailer generates a random Ri. Let R =  Ri; no single party knows R • Using secure summation protocols compute n and D =iPqi-K+R, such that D is known only to the supplier • If n is the same as in previous iteration, go to step 3. • Run a secure summation protocol to compute (D/ n) – (R/n) = (iP qi – K)/n which is the pain per active retailer. If this pain exceeds a retailers order quantity, he marks himself “passive” • 3. Every retailer computes it’s allocation equal to their order quantity minus the pain per active retailer

SLAP: Who Knows What? • Supplier capacity known only to the supplier • Retailer orders known only to individual retailers • Pain per active retailer revealed only to retailers • Individual retailer’s allocated quantity revealed to both the supplier and the individual retailer • Number of active retailers known to everyone

Secure Collaborative Forecasting • develop protocols for constructing a joint forecast without revealing the retailers or suppliers private information

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”

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

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

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:

Secure Regression

Secure 3x3 Matrix Inverse Protocol

Secure Multiple Linear Regression Protocol

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.

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

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

Future Work • Protocols for other supply-chain applications • Price-Masking • Bullwhip Scenarios • Protocol implementation issues • Collusion by a subset of parties • Intrusion detection • Incentive issues and mechanism design

Questions?...

Secure Protocols for Supply Chain Collaboration: Capacity Allocation and Collaborative Forecasting