**Price
competition model in decentralized and centralized supply chains with
demand
disruption**

Chai
Wenlong^{1 }, Sun Huijun^{1}, Wei Wang^{ 1},
Jianjun Wu^{
2}

^{1}*Moe
Key
Laboratory for Urban Transportation Complex Systems Theory, ^{2}State
Key
Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong
University (China)*

Received November 2012

Accepted February 2013

Wenlong,
C.,
Huijun, S., Wang, W., & Wu, J. (2013). Price competition model in
decentralized and centralized supply chains with demand disruption. *Journal
of Industrial Engineering and Management, *6(1), 16-24. http://dx.doi.org/10.3926/jiem.616

*---------------------*

*Abstract**：*

** Purpose:**
The paper studies the price
competition of a supply
chain with one supplier and two competing retailers under occasional
demand
disruption.

** Design/methodology/approach:**
The supply chain is either
decentralized or
centralized. The demand disruption
for
two retailers occurs with different probability. We analyze the effect of occurrence
probability of
demand disruption on the optimal prices of the supplier and two retailers.

** Findings:**
We find
that the profits of supplier, retailers and supply chain are decreasing
with
the occurrence probability of demand disruption.

** Originality/value:**
It
is helpful for supply chain members to adjust the original contracts to
demand disruption.

** Keywords:
**Demand
disruption; Probability; Price competition; Profit

*---------------------*

**1.
Introduction**

The market demand is often disrupted by some haphazard events, such as the promotion of sale, the raw material shortage, the new tax or tariff policy, machine breakdown, and so on. All the retailers and suppliers in the entire supply chain will be severely affected by these demand disruptions (Qi, Bard & Yu, 2004; Huang, Yu, Wang & Wang, 2006; Xiao & Yu, 2006). Therefore, the issue of supply chain management under demand disruptions has been an active research topic in recent years.

This paper focus on the supply chain under demand disruptions when retailers compete. Xiao, Yu, Sheng & Xia (2005) studied the coordination of a supply chain system with one manufacturer and two competing retailers when there are demand disruptions. A price-subsidy rate contract is considered to coordinate the investments of the competing retailers with sales promotion opportunities and demand disruptions. Xiao, Qi and Yu (2007) studied the coordination of the supply chain with demand disruptions in the cases of a linear quantity discount schedule or an all-unit quantity discount schedule. Xiao and Qi (2008) investigated how to coordinate a supply chain with one manufacturer and two competing retailers using an all-unit quantity discount or an incremental quantity discount after the production cost of the manufacturer was disrupted. Chen and Xiao (2009) considered two coordination schedules, a linear quantity discount schedule and a Groves wholesale price schedule, to coordinate a supply chain consisting of one manufacturer, one dominant retailer and multiple fringe retailers after demand disruptions. Zhang, Fu, Li and Xu (2012) investigated how to coordinate a supply chain with one manufacturer and two retailers under demand disruptions by revenue-sharing contracts.

The above papers mainly focused on the competition and coordination of a supply chain after demand disruptions. These researches all assumed that the demand disruption of a supply chain would occur in the future. However, the occurrence of demand disruption cannot be determined (Xu, Qi, Yu, Zhang & Gao, 2003; Yu & Qi, 2004; Yang, Qi, & Yu, 2005).

In this paper, we will consider the demand disruption of a supply chain with a single supplier and two retailers who compete in the market. Our particular interest is the occurrence probability of demand disruption on each retailer. We explore the effects of demand disruption uncertainty on the supply chain.

The rest of the paper is organized as follows. Section 2 introduces the basic model when demand disruption occurs. Section 3 studies the demand disruptions in decentralized and centralized supply chains. Some numerical examples are given in Section 4 to elaborate our results. Finally, Section 5 provides conclusions.

**2.
Basic model**

We
consider a supply chain consisting of one supplier and two competing
retailers.
It is either integrated where the manufacturer ‘owns’ her two exclusive
retailers or decentralized where the manufacturer sells its product to
the
market through retailers. The supplier is a leader and the retailers
are
followers. We have the following notations (*i=*1,2):

*w _{o}*:
the unit wholesale price of supplier;

a_{i}:
the market scale for retailer *i*;

*d _{i}*:
the degree of substitutability between retailers, 0<

*d*<1;

_{i}*p _{i}*:
the retail price of retailer

*i*;

*q _{i}*:
the market demand for retailer

*i*;

j* _{i}*:
the probability of demand disruption on retailer

*i*;

p* _{i}*:
the profit of retailer

*i*;

p* _{0}*:
the profit of supplier;

P: the total profit of the supply chain;

We
assume that the demand function of retailer *i* is:

The
substitutability coefficient *d _{i}* is a measure of the
sensitivity of the ith retailer’s sales to the change of jth retailer’s
price.
When the demand disruption occurs, the market scale or the demand for
retailer

*i*will change. Then the demand function of retailer

*i*is:

where
a_{i}’
is the market scale for retailer* **i*
after demand disruption, *d _{i}’*
is
the substitutability coefficient under demand disruption.

We
assume that the new market scale a_{i}’
for retailer *i*
is:

with
a positive Da_{i}
representing an increased market demand, and a negative Da_{i}
representing a decreased market demand. Similarly, the new
substitutability
coefficient is:

**3.
Demand disruptions in decentralized and centralized supply chains**

**3.1.
Demand disruptions in a decentralized and centralized supply chain**

We consider a supply chain consisting of one supplier and two competing retailers. For a decentralized supply chain (DSC), the supplier produces goods with a unit production cost and sells the product through the retailers. After purchasing the product from the supplier with a unit wholesale price, retailers add some values to the product with a unit selling cost, and then determine his retail price to sell the product. For simplicity, we assume that the costs above are normalized to zero.

By substituting Eqs. (9) and (10) into (6) and (7), we can obtain the profit of each supply chain member.

**3.2.
Demand disruption in a centralized supply chain**

For a centralized supply chain (CSC), the supplier ‘owns’ the two exclusive retailers. Her problem is to determine the retail price of each retailer so as to maximize the total profit of the centralized supply chain.

**4.
Numerical examples**

To
explore the
effects of the demand disruption uncertainty of the decentralized and
centralized supply chains, we give some numerical examples in this
section. Consider
the following example with parameters: *a _{1}=a_{2}=20,
d_{1}=0.5,
d_{2}=0.4, *Da

_{1}=Da

_{2}=-3, Dd

_{1}=Dd

_{2}=0.05.

Fig.
1 and Fig.
2 illustrate how the optimal wholesale price of the supplier in
decentralized
supply chain and the optimal retail price of two retailers in
decentralized or
centralized supply chain depend on the occurrence probability of demand
disruption. In Fig. 1, we assume that j_{1} is
changing from 0 to 1, and j_{2}=0.1.
In Fig. 2, we assume that j_{2} is
changing from 0 to 1, and j_{1}=0.1.

Figure 1. The optimal wholesale and retail price versus the probability of demand disruption for retailer 1

Figure 2. The optimal wholesale and retail price versus the probability of demand disruption for retailer 2

From Fig. 1 and Fig. 2, we can see that the optimal wholesale price of supplier in decentralized supply chain and the optimal retail price of two retailers in centralized or decentralized supply chain are decreasing with the with the occurrence probability of demand disruption for retailer 2/retailer 1. Because the demand for retailer 1/retailer 2 drops, he would like to lower the retail price to sell more goods. For market competition, retailer 2/retailer 1 will also bring the retail price down. And the supplier will lower his wholesale prices and share the demand disruption.

Fig.
3 and Fig. 4 illustrate how the
profits of supplier, retailers and supply chain depend on the
occurrence probability
of demand disruption. In Fig. 3, we assume that j_{1}
is
changing from 0 to 1, and j_{2}=0.1.
In Fig. 4, we assume
that j_{2}
is changing from 0 to 1, and j_{2}=0.1.

Figure 3. The profit versus the probability of demand disruption for retailer 1

Figure 4. The profit versus the probability of demand disruption for retailer 1

From Fig. 3 and Fig. 4, we can see that the profit of CSC, members in DSC and DSC are all decreasing with the probability of demand disruption. The demand disruption reduces the profits of supply chain partners. The profit of centralized supply chain is always larger than the one of decentralized supply chain under the demand disruption.

**5.
Conclusion**

In this paper, we study the price competition of a supply chain with one supplier and two competing retailers under occasional demand disruption. We mainly focus on the price competition of the two retailers when the demands for them are disrupted with different probability. The optimal retail prices for the two retailers in the centralized and decentralized supply chains are obtained. We found that the profits of supplier, retailers and supply chain are decreasing with the occurrence probability of demand disruption.

The demand disruption management in the supply chain is a meaningful and interesting field. In our future study, we will consider how to coordinate the supply chain by contract when demand disruptions occur.

**Acknowledgements
**

This work is partly supported by the Beijing Natural Science Foundation (8102029), Beijing Science and Technology Star Plan (2009A15), the Fundamental Research Funds for the Central Universities (2012JBZ005) and FANEDD (201170).

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Journal of Industrial Engineering and Management, 2008-2020

Online ISSN: 2013-0953; Print ISSN: 2013-8423; Online DL: B-28744-2008

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