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Supply Chain Management:Issues and Models

Lecture 4: Bullwhip Effect

Prof. Dr. Jinxing Xie

Department of Mathematical Sciences

Tsinghua University, Beijing 100084, China

http://faculty.math.tsinghua.edu.cn/~jxie

Email: jxie@ math.tsinghua.edu.cn

Voice: (86-10)62787812 Fax: (86-10)62785847

Office: Rm. 1308, New Science Building

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牛鞭效应（例）

销售总公司 分销商工厂 零售商 顾客

i) Barilla (意大利面条制造商 )

P&G 批发商3M (胶带 )

零售商

信息流 物流

顾客

ii) P & G

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Amplified Demand Distortion (the Bullwhip Effects)

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Four sources of the bullwhip effect: Demand signal processing Rationing game Order batching Price variation

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Bullwhip Effect: An Analytical Model

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Bullwhip effect

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Events in each period

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Variables

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Demand Process

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Results for demand signal processing

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Optimal order-up-to level

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Optimal order quantity

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Amplification of order variance

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Summary

Bullwhip effect exists even when the leadtime is zero

Other causes of bullwhip effects: omitted here

Sharing information is needed?

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Information sharing:Value of information

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Basic Assumptions

The demand is assumed to be a simple autocorrelated AR(1) process

(2.1) d > 0, -1<<1, and is i.i.d. normally distributed with mean

zero and variance 2. << d

ttt DdD 1

Supplier

(Manufacturer)

RetailerDemand

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Leadtimes

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Retailer’s ordering decision process

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Manufacturer’s decision

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Retailer’s Leadtime Demand

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Retailer’s Leadtime Demand

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Retailer’s Ordering Decision

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For manufacturer:ttt DdD 1

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Manufacturer’s leadtime demand

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Manufacturer’s leadtime demand: No information sharing

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Manufacturer’s order-up-to level: No information sharing

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Manufacturer’s leadtime demand: information sharing

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Manufacturer’s order-up-to level: information sharing

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Benefits of information sharing

Comparing (3.10) with (3.13), one can quantify the benefits of information sharing:

Inventory level; Cost evaluation

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Similar methods can be used to Analyze the case when forecasting is used

Raghunathan S. “Information sharing in a supply chain: a note on its value when demand is non-stationary”. Management Science, April 2001, 605-610.

Analyze the value of advance demand information (the value of time) Zhao X., Xie J. and Wei J. The Impact of Early Order Co

mmitment on the Performance of a Simple Supply Chain. Working paper, 2002, Chinese University of Hong Kong.