Value of Information Sharing in Multi-Retailer Setting with Inter-Correlated and Auto-Correlated Demands

05/14/2003By Çağrı LATİFOĞLU

Outline

IntroductionValue of Information SharingImpact of Demand CorrelationJoint Effect & Game Theory ExtensionsConclusion

Introduction

1 w/h – 1 retailer case

1 w/h – N retailer case

W/H

Retailer

W/H

Retailer Retailer...................

Demand 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 sharesDemand Inventory Inventory policyPromotion plan

The manufacturer shares InventoryCapacity

Information Sharing-Benefits

Helps manufacturer in ordering process and allocation process

Reduced variance to the manufacturer which leads to:

Reduced safety stock at the manufacturerReduced flexibility need at the manufacturerReduced 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 costsoffering 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 correlationNetessine 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 chainJung 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:Dn

j= (dn,nj , dn,n+1

j ,..., dn,n+M-1j , µj , µj ,...)

Where N is number of retailers,

j=1,2,..,N

dn,nj =demand realization of retailer j in period n and

dn,n+kj = demand forecast made in period n for period n

+ k

µj =meand demand of retailer j

Joint Effect-Examples

dn+1,n+M-1j = dn,n+M-1

j + εn,M-1j

έj =(έn1, έn

2,..., έnN)

έj ~ zero mean, multi-variate distributionCross-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: Dit

F retailer i’s forecast of period t using actual demand during Dit-1 period t-1.

DitF = d + ρ Dit-1 + εit where d >0, 1> ρ>-1, i € [1,2,...N]

εit ~ Normal(0, σ2). εit is correlated with εjt with coefficient pr

YitF = d + ρ Yit-1 + δit => 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 applyDeciding 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.

Q & A

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