Value of Information Sharing in Multi- Retailer Setting with Inter-Correlated and Auto-Correlated Demands 05/14/2003 By Çağrı LATİFOĞLU

Outline Introduction Value of Information Sharing Impact of Demand Correlation Joint Effect & Game Theory Extensions Conclusion

Introduction 1 w/h – 1 retailer case 1 w/h – N retailer case W/H Retailer W/H Retailer Demand

Introduction Our aim is to find/construct a demand model for the quantifying the value of information sharing in a multi-retailer setting with auto-correlated and inter- correlated demands.

Information Sharing The retailer shares Demand Inventory Inventory policy Promotion plan The manufacturer shares Inventory Capacity

Information Sharing-Benefits Helps manufacturer in ordering process and allocation process Reduced variance to the manufacturer which leads to: Reduced safety stock at the manufacturer Reduced flexibility need at the manufacturer Reduced smoothing costs at the manufacturer

Information Sharing-Incentives No immediate benefits to retailer if infinite capacity at the retailer is assumed. There should be an arrangement between the manufacturer and retailers. Examples: Use of vendor managed inventory to save retailer’s overhead and processing costs offering discounts to retailer reducing lead time

Information Sharing-Examples Lee at al.(2000) Value of Information Sharing in a Two-level Supply Chain AR(1) demand process Inventory Reduction and Cost Reduction More valuable when: long lead times high demand variance within periods high auto-correlation over time

Information Sharing-Examples Cachon & Fisher(2000) Supply Chain Inventory Management and Value of Shared Information Stationary Stochastic Demand Process Inventory Reduction and Cost Reduction More valuable when: Different Retailers Unknown Demand

Information Sharing-Examples Improving supply-chain performance by sharing advance demand information (2001) U.W. Thonemann Expected cost is concave decreasing in the number of customers who share ADI. If the cost of obtaining ADI is also concave in the number of customers who share ADI, then either none or all customers share ADI in an optimal solution. We showed that all members of a supply chain benefit from sharing ADI. The manufacturer benefit from reduced cost customers benefit from lower prices or higher service levels It introduces variation in the base-stock levels and increases the variability of the production quantities.

Information Sharing-References Additional References: Benefits of information sharing with supply chain partnerships (2001) Yu ZX, Yan H, Cheng TCE Forecasting errors and the value of information sharing in a supply chain (2002) Zhao XD, Xie JX Information sharing in a supply chain (2000) Lee HL, Whang SJ Modeling the benefits of information sharing-based partnerships in a two-level supply chain (2002) Yu Z, Yan H, Cheng TCE Leveraging information in multi-echelon inventory systems (2002) Mitra et. al.

Demand Correlation Two types of demand correlation to be considered: Auto-correlation: That is the correlation of the demand with itself in a time period. Ex: You are less likely to buy a car tomorrow if you bought one today. Inter-correlation(or cross-correlation): That is the correlation of demands that are realized by different retailers. Ex:If you buy your car from one retailer,that means you won’t buy from another one in close future assuming you want to but only one car.

Demand Correlation-Examples Multistage Safety Stock Planning with Item Demands Correlated Across Products and Through Time (1995) Indefurth Autocorrelation of demands brings a tendency to hold SS at end item-level Intercorrelation of demands brings a tendency to hold SS at upper levels. An optimization approach for AR(1) is introduced An optimization approach for jointly correlated demands is also introduced

Demand Correlation-References Flexible service capacity: Optimal investment and the impact of demand correlation Netessine et. al. (2002) Time-dependent demand in requirements planning: An exploratory assessment of the effects of serially correlated demand sequences on lot-sizing performance Raiszadeh et. al. (2002) Impacts of buyers' order batching on the supplier's demand correlation and capacity utilization in a branching supply chain Jung et. al. (1999) Coordinated replenishments in inventory systems with correlated demands (2000) Liu et. al. Plus the paper’s that will be included in the joint-effect

Joint Effect A two-echelon allocation model and the value of information under correlated forecasts and demands. (1996) Güllü Impact of Demand Correlation on the value of and incentives for information sharing in a supply chain (2001) Raghunathan

Joint Effect-Examples In Güllü (1996) the depot-retailes environment considered in Eppen-Schrage(1981) is used. It extends Eppen & Schrage model to incorporate forecasts (for many periods and retailers) to be a part of the state of the system. Forecasts for future periods are updated in each period according to an evolution model Evolution model allows the incorporation of correlation of demands(both auto- and cross-) in the model.

Joint Effect-Examples Demand model: D n j = (d n,n j, d n,n+1 j,..., d n,n+M-1 j, µ j, µ j,...) Where N is number of retailers, j=1,2,..,N d n,n j =demand realization of retailer j in period n and d n,n+k j = demand forecast made in period n for period n + k µ j =meand demand of retailer j

Joint Effect-Examples d n+1,n+M-1 j = d n,n+M-1 j + ε n,M-1 j έ j =(έ n 1, έ n 2,..., έ n N ) έ j ~ zero mean, multi-variate distribution Cross-correlations are allowed.

Joint Effect-Examples Results: As fraction of variability leraned by keeping track of forecasts increases, the difference between ore-up-to-levels increases. Forecasts and demand across retailers become more negatively correlted as difference gets larger. Imbalance between forecasts and demands are captred progressively and total system stock is reduced. If correlation increases order-up-to-levels increase and difference(between consequent values of S) gets smaller. Forecasters are confident about the total mean to be observed but unsure about which retailer will receive what portion of demand.

Joint Effect-Examples Raghunathan (2001) Prior studies have shown manufacturer directly effected but the retailer’s won’t participate unless they receive some prize. Shapley value concept from Game Theory is used to distribute the surplus generated from information sharing.(a value employed frequently in n-person cooperative games) This paper is an extension of Lee at. al.(2000) Single retailer model is extended to N retailer model Retailers share their forecast and demand information with manufacturer.

Joint Effect-Examples Demand Model: D it F retailer i’s forecast of period t using actual demand during D it-1 period t-1. D it F = d + ρ D it-1 + ε it where d >0, 1> ρ>-1, i € [1,2,...N] ε it ~ Normal(0, σ 2 ). ε it is correlated with ε jt with coefficient p r Y it F = d + ρ Y it-1 + δ it => Manufacturer’s demand

Joint Effect-Examples Ordering decisions with and without information sharing is compared It is observed that if manufacturer’s service level is sufiiciently high, the benefit comes from primarily inventory reduction. Variance of manufacturer’s forecast is higher when More retailers share information, Correlation across time or retailers is higher, Variance of demand is higher.

Joint Effect-Examples Observations made: Value of information sharing is higher when cross- correlation and auto-correlation is high. When correlation is sufficiently high, marginal value of addition of a retailer to the coalition decreases In the case of negative correlation or independent demands, addition of a retailer to coalition members realize increasingly larger incremental value.

Joint Effect-Examples Under high correlation, retailers receive less Information sharing partnerships are to be formed withh less retailers under high correlation Accelarating physical flow of goods is more valuable than expanding the flow of information when capacity of manufacturer is limited. Higher correlation increases manufacturer surplus but the marginal value of manufacturer surplus decreases as number of retailers increase

Joint Effect-Examples Allocation of the surplus The members of the coalition do not compete rather colloborate to gain even more surplus when demands are independent When retailers are substituable, manufacturer’s bargaining power increase as retailer’s decrease.

Game Theoretic Extensions How reatilers behave when cross correlation and autocorrelation exists is an important issue for both Deciding the incentive to apply Deciding the structure of partnership So we can extend the subject by considering game theoretic approach

Game Theoretic Extensions Benefits of cooperation in a production distribution environment (1999) Gavirneni Grouping customers for better allocation of resources to serve correlated demands (1999) Tyagi et. al. Information sharing in a supply chain with horizontal competition (2002) Li LD Decentralization and Collusion (1998) Baliga et. al. Market collusion and the politics of protection (2001) Ludema Distributional assumptions in the theory of oligopoly information exchange (1998) Malueg et. al. Information sharing between heterogenous uncertain reasoning models in a multi-agent environement: a case study (2001) Luo et. al. Information disaggregating and incentives for non-collusive information sharing (1998) Novshek et. al.

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