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Procedia Engineering 174 ( 2017 ) 1229 – 1234

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1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the organizing committee of the 13th Global Congress on Manufacturing and Management
doi: 10.1016/j.proeng.2017.01.291

ScienceDirect

13th Global Congress on Manufacturing and Management, GCMM 2016

Mitigation of Bullwhip Effect in Supply Chain Inventory
Management Model

Jianhua Dai*, Shengbo Peng, Shibiao Li
School of Economics and Management, Communication University of China, Beijing, 100020, China

Abstract

This article starts with the reasons to bullwhip effect phenomenon, analyzes how to enhance inventory management strategy to
reduce the bullwhip effect in supply chain management. And then, we study the case of McDonald’s and its third-party logistics
system HAVI cooperation to explore the cooperation mode between the two companies. Assuming that McDonald’s stores as a
logistics activities supply chain leader adopts the upper and lower inventory management strategy, according to the HAVI’s
distribution for McDonald’s stores, we develop a one-multi distribution model, and build a mathematical model for reducing
inventory and improve service level.
© 2016 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the organizing committee of the 13th Global Congress on Manufacturing and Management.

Keywords: bullwhip effect; inventory management; one-multi distribution; control model;

1. Introduction

Bullwhip Effect refers to a kind of distortion occurring in the process of transmitting information upstream,
which is a bigger fluctuation in upstream quantity caused by the fluctuation of downstream demands. This is a
common phenomenon in supply chain. The existence of Bullwhip Effect makes it difficult for enterprises to grasp
market demands, causing an overstock and reducing the operational efficiency for the whole supply chain. The best
way to solve Bullwhip Effect is to reduce knots of supply chain as far as possible, thus to greatly ensure accuracy of
information. Using efficient supply chain management system can reduce Bullwhip Effect and realize real-time
response, directly reducing operating costs of enterprises. The factors causing Bullwhip Effect include the following

* Corresponding author. Tel.: 13811722338.

E-mail address: [email protected]

© 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the organizing committee of the 13th Global Congress on Manufacturing and Management

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1230 Jianhua Dai et al. / Procedia Engineering 174 ( 2017 ) 1229 – 1234

several aspects which are demand forecast amendment, fluctuations in prices, quantity decision, shortages
game, inventory imbalances, lead time, etc.

Guo Haifeng applies vendor managed inventory strategy to reforge the physical process of supply
chain(Sponsored by China Postdoctoral Science Foundation “A Study on Interconnection Charges during China’s
Integration of Telecommunications, Broadcasting and Internet Networks” (No.: 20110490258)) [1]. The simulation
demonstrates that the inventory strategy of vendor management is an effective way to reduce Bullwhip Effect. Based
on pre-existing documents on Bullwhip Effect problem research, this article analyzes and summarizes how to reduce
Bullwhip Effect by vendor control inventory strategy combined with cases.
Nomenclature

The time required for goods from distribution centers to stores
Daily average demand of the goods in the stores.
The standard variance of the goods in the stores.

wL Upper limit of the stores.

dL Lower limit of the stores.
Q Order Quantity of stores.

2. Vendor Control Inventory Strategies under Management of Supply Chain

Supply chain management is to realize optimization of supply chain operation with least costs, in to make
the supply chain efficiently operate in the whole process from purchasing to satisfying the final customers including
workflow, material flow, fund flow, information flow, etc. And customers get appropriate products with a
reasonable price accurately and timely. Its basic idea is “Horizontal Integration” and makes full use of external
resources [2].

Enterprises always manage their own stock independently in the operation and have their vendor control
inventory strategy in every knot of material flow chain. As everyone has their different but open inventory strategy,
it gives rise to a distortion in demands, causing to enlarge demand variation and not able to accurately master up
streaming customers’ demands for suppliers. As to this problem, there appear some new inventory control methods.
In the practical application, we can find that all kinds of vendor managed inventory strategies do not independently
exist, and different ideas can cross, in to better realize vendor managed inventory strategy.

2.1. Vendor Managed Inventory

Vendor managed inventory management system is a cooperative strategy between user and vendor with an
availability at lowest costs and optimizing products for both parties. And guided by an integrated target framework,
the vendor manages inventory, transferring inventory management function to be charged by vendor.

The key measures of VMI strategy are as follows.
The first one is team spirit. While implementing this strategy, both vendor and customer should have a better

team spirit, with mutual trust and information transparency being equally important.
The second one is to have the minimum cost for both parties. This strategy can be used to reduce the

inventory costs in the whole supply chain, which will benefit to both of them.
The third one is goal congruence principle. The two parties should know their own responsibility and reach

unanimous ideas.
The fourth one is continuous improvement principle. A closed-loop system is formed, has continuous

feedback and eliminates waste gradually.

2.2. Joint Managed Inventory Management

Joint managed inventory management is an effective method to solve a requirement amplification phenomenon
caused by mutual different inventory operation mode with node enterprises in supply chain system, and improve

1231 Jianhua Dai et al. / Procedia Engineering 174 ( 2017 ) 1229 – 1234

synchronization degree of supply chain. It emphasizes the two parties’ participation in the meantime to make
inventory plan together. Every inventory director (vendor, manufacturer and distributor) in the process of supply
chain should think about their mutual congruousness and keep pace with the expected requirements from inventory
director between the two nodes, in to eliminate the phenomenon of demand variation amplification. The
demand determination of every adjacent node is a result of coordination of both supply and demand parties. The
inventory management is no longer separate operation process but a link of supply and demand as well as
coordination center. Joint managed inventory management principle is a management mode of risks sharing [3].

2.3. Third Party Logistics System

Third party logistics system is a means of supply inheritance, providing all kinds of services like product
transportation, inventory management and choice for customers. Enterprises can be more focused on their own
core businesses by delegating some of the functions of inventory management to third party logistics system. Third
party logistics system takes a role as a bridge to contact vendor and user.

3. Model Establishment

About the policy conditions of “Universal build” wireless cities, a briefly analysis is as follows.

3.1. Case Study

The HAVI is a third-party logistics company for McDonald. The company works for McDonald’s restaurants,
ing, storage, transportation and distribution of a series of work, including information processing, inventory
control, labeling, production and quality control and other aspects. All of this can reduces the McDonald’s stock
greatly, and product inventory to meet the minimum principle [4].

What McDonald only need is to let the suppliers know their demand information continually and timely, and the
suppliers can forecast the future demand of the user by this demand information. According to this forecast,
suppliers develop their own production plans and delivery plans, take the initiative to small quantities frequency to
the user to supplement the inventory of goods, both to ensure to meet user demand and inventory of goods for at
least minimum waste. With the VMI purchasing the biggest beneficiaries is McDonald, it can get rid of the
cumbersome procurement business, freed from the Procurement, even the inventory and transport are also burden by
HAVI with elevated service rate [5].

HAVI is that, not only played the role of third party logistics companies, but also bear the responsibilities of
suppliers. McDonald’s has commissioned a third party logistics agent for their manufacture, storage, distribution and
management. On the other hand, he takes the form of suppliers, agents, master of McDonald’s stock by the vendor,
purchasing is done by HAVI, McDonald’s and its suppliers, HAVI, is completely became a partner Whether HAVI
as third-party logistics companies, or as a vendor, who is in the entire logistics operation has played an important
role in the process [6]. For more than 30 years, HAVI and McDonald’s cooperation without a contract, both the
long-term relationship of mutual trust cooperation between the two has the lowest cost of trust.

Partnership between McDonald’s and HAVI is good proof of the above deals to supply inventory management on
policy, the joint management of inventory strategy and strategy of third-party logistics. HAVI mainly rely on
information systems management to create value, its average inventory is much lower than its competitors. The
logistics products loss rate of McDonald’s is only one out of 10,000. The following papers will be analysis its
management model.

3.2. Upper and Lower Inventory Control Method

The automatic monitoring technology of McDonald’s stores is very advanced, from to achieve transparent
management of the stock has a set of automation equipment. Here we assume that the upper and lower inventory
control method has been used on the device.

1232 Jianhua Dai et al. / Procedia Engineering 174 ( 2017 ) 1229 – 1234

When the stores system detects the minimum store inventory down to dL , the so-called upper and lower inventory
control model will generated the s automatically with quantity Q to the distribution center
s. When goods have been delivered to the stores, the expected maximum inventory level Lw is achieved.

When calculate the upper and lower limits, we must calculate the sales forecast based on past sales data, this
article does not examine in detail the demand forecast.

1) The assumptions of model
Commodities daily sales data is a normal distribution, according to the principle of normal distribution

function, we know that the standard deviation and the mean ratio k is a constant, but due to the sample data
obtained k and k there is a deviation, thus allowing the presence of constant bias.

Distribution Center by FCL distribution to stores replenishment.
2) The description of mathematical symbol
The number of specifications of the goods per case. : The time required for goods from distribution centers to

stores. : Daily average demand of the goods in the stores. : The standard variance of the goods in the stores.

wL : Upper limit of the stores. dL : Lower limit of the stores. Q : Order Quantity of stores.
3) Model establishment
The average demand in the period is its standard deviation is and:
λμ =λ×μ , λ λσ μ σ / μ λ μ σ λk . (1)
Also recorded in the period t , the safety stock is SS so:

λSS=σ ( ) σ ( )z p z p . (2)
We can calculate the lower of the stores:
d λL μ SS λ μ σ λ z(p) . (3)
The of the stores:
dQ=[(L )/B] B-S [ / ] BS B . (4)
Upper of the stores:
wL Q SS λ μ / B B σ λ z(p) . (5)

3.3. Distribution center and 1-N distribution model of retail store

To abstract the distribution relationship between Havi Logistics Company and retail store of McDonalds,
virtually it is a distribution relationship between a distribution center and many retail stores (1-N). The
quantity of optimal inventory strategy can be obtained by mathematical model.

1) Hypothesis
Inventory fee is composed by inventory storage fee and shortage cost. This paper argues that retail stores

will lose selling profits directly if the commodities in the retail stores are out of stock. The loss costs of each
unit of commodities are the profits, shared by distribution center and retail stores in different proportion.

Customers’ requirements to retail stores are supposed to change randomly, but each requirement is
independent. The external customers’ requirements in t period are supposed to be ty , the density function to
be ( )tf y , and distribution function to be ( )tf y , besides they are continuous, transcending and
differentiable.

The retail stores of MacDonald adopt continuous checking ( , )j js Q inventory strategy, in which the

point is js , and the quantity is jQ jQ is constant .

Havi Distribution Center adopts the continuous checking 0S inventory strategy which holds inventory level.

2) Meaning of variable symbolic
jy : goods in the stores j day sales. ( )j jY L : goods in the stores j day sales, during period jL . 0( )jY L : goods

in the stores j day sales, during Period 0L . j : average daily sales of merchandise in the store j. 0L : lead time for

goods from suppliers to distribution centers. jL : lead time for goods from distribution centers to stores j. j :

production s of store j obeys to the Poisson distribution in which parameter is λ. : proportional share

1233 Jianhua Dai et al. / Procedia Engineering 174 ( 2017 ) 1229 – 1234

coefficient of the supply chain shortage cost. 0h : distribution centers per unit time inventory holding costs. jh : per

unit time inventory holding costs of store j. P: unit shortage cost no matter cost of goods out of stock in which
stores. jQ : each quantity of store j. js : inventory levels when store j generate an automatically. 0s :

the maximum inventory level of the distribution center. 0HC : inventory holding costs of distribution center during

period t. jHC : inventory holding costs of store j during period t. 0LC : distribution centers to share the cost of

inventory loss during period t. jLC : store j to share the cost of inventory loss during period t. 0TC : distribution

center inventory costs in period t. jTC : store j inventory costs in period t. TC : total inventory cost of the supply

chain system in period t. In all above, 1, 2,…,j N .

3) Model Establishment
Inventory holding costs of store j during period t:

1
( )
2

j j j j j jHC h Q s L , (6)

The shared cost of inventory loss during period t of store j:

[ ( ) ] [ ( )] ( )
j

j j j j j j j j
s

LC P Y L s f Y L dY L . (7)

We get:

1
( ) [ ( ) ] [ ( )] ( )
2 j

j j j

j j j j j j j j j j j js

TC HC LC

h Q s L P Y L s f Y L dY L
. (8)

We assume the distribution centers per unit time inventory holding costs is h0, so inventory holding costs of
distribution center during period t:

0 0 0 0 01

1
[ ( ) ]

2

N

jj
HC h S S L Q , (9)

And distribution centers to share the cost of inventory loss during period t:

0 (1 ) [ ( ) ] [ ( )] ( )
j

j j j j j j j
s

LC P Y L s f Y L dY L , (10)

So,

0 0 0

0 0 0 01

1
[ ( ) ] (1 ) [ ( ) ] [ ( )] ( ) .

2 j
N

j j j j j j j jj s

TC HC LC

h S S L Q P Y L s f Y L dY L
(11)

By the above formula, we can get the supply chain system, the total inventory costs in period t is:

0 1

0 0 0 01

1 1
[ ( ) ] ( ) [ ( ) ] [ ( )] ( ) .

2 2 j

N

jj

N

j j j j j j j j j j j j jj s

TC TC TC

h S S L Q h Q s L P Y L s f Y L dY L

(12)
We obtain a set of solutions 1 2 0( , ,… , )Ns s s s that makes the TC minimum.
When make the solution of the model. We can use the heuristic method, and select the value of a series of α,

compared to the actual supply chain inventory management, as long as that relative to an optimal solution.

1234 Jianhua Dai et al. / Procedia Engineering 174 ( 2017 ) 1229 – 1234

4. Summary

Starting from reasons for Bullwhip effect phenomenon, this article stresses the emphasis on analyzing how to
reduce Bullwhip effect under supply management circumstance. This article takes MacDonald and its third party
logistics Havi Company as an example, to discuss their ways of cooperation. Retail stores of MacDonald, as a
leading part for supply logistics activities, are supposed to adopt up and bottom limitation inventory management
strategy, and abstract the distribution situation between Havi Company and retail stores of MacDonald to 1-N
distribution Module, thus to build mathematics modeling, so as to reach the target of lowering stock as well as
improving service.

The special circumstance that distribution center stock S_0 is less than the total quantities of the entire
retail store isn’t taken into consideration in this article when minimizing in the 1-N distribution module, which is
worth to mention and needs to improve in the module. The more this module corresponds with the practical
condition, the better of the simulation results to data as well as the less of enterprises’ costs. At the same time, it is
an effective way for enterprises to raise profits by way of reducing nodes of supply chain, linearization of
information transmitting, and utilizing advanced information management system, thus to eliminate, to some extent,
Bullwhip effect phenomenon.

Acknowledgements

This paper was supported by the National Natural Science Foundation of China (No. 71203202), the Program for
Young Scholars of Beijing (No. YETP0633) and the Research Task of Communication University of China (No.
3132014XNG1458, CUC16A17).

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