A Newsvendor Problem with two Suppliers under Dual-Channel Supply Chain and Supply Disruption Lijing Zhu, Yumeng Zhang*, Xiaohang Ren Academy of Chinese Energy Strategy China University of Petroleum (Beijing) Beijing, China *E-mail address:
[email protected]
Abstract-In this paper, we consider a newsvendor model in which the retailer can source from two suppliers. One supplier sells products through a dual channel framework, which includes a direct channel and a retailer channel. The other supplier sells products only through the retailer. The wholesale price of the dual channel supplier is cheaper, but supply disruption may occur with a certain probability, whereas the other supplier is perfectly reliable with a higher wholesale price. We study a risk neutral retailer's decision-making on the optimal order quantities from both two suppliers. Then in numerical analysis, we examine the sensitivity of the disruption probability, the wholesale price, market shares of two channels and the direct price on the optimal decisions. Keywords-inventory;
dual
sourcing;
dual-channel;
supply
disruption; supplier relationship management 1.
INTRODUCTION
Supply chain management is increasingly complicated nowadays. Due to the globalization of market and complex international supply network relationships, decision makers are exposed to greater uncertainties now than years ago. There are many reasons for supply chain uncertainties. One is that unpredictable disasters, such as terrorist acts, natural hazards and massive accidents, may occur and cause unexpected disruptions. For example, the longshoremen strike in California in 2002 and the outbreak of SARS in 2003 cause great problems for supply chain flows and suspend trade and transportation [1]. Another point is that advanced technology can provide fIrms with diversifIed transaction channels and increased number of suppliers. Although these trends could reduce costs in supply chains, fIrms become more susceptible to disruptions because the bullwhip effect may be exacerbated in a complex supply chain network. More and more fIrms tend to pay increasing attention to supply disruption management in practice, and relative academic literature also has increased sharply in the past decade [2]. Some papers consider a single retailer with at least two unreliable suppliers. Reference [3] and [4] study dual sourcing models with supply uncertainty and find that the retailer may only order from the more expensive but more reliable supplier sometimes. Reference [5] and [6] develop a model integrating two types of supply uncertainty: one supplier
has recurrent and disruption uncertainties and the other one is perfect. Reference [7] build a newsvendor model with multiple unreliable suppliers and demonstrate that the optimal order quantity is larger with unreliable supplier than that of the classical newsvendor problem. This model is developed by allowing the supply uncertainty to be correlated among the suppliers and the result is that the fIrm should choose suppliers who have independent disruptions [8]. The above papers are based on the assumption that each supplier can only sell to the retailer through the traditional channel. Apart from brick-and-mortar fIrms, however, suppliers can sell directly to consumers through Internet nowadays. The tremendous development of Internet not only changes people's life-style, but also brings about a dramatic alteration among the structure of supply chain. Internet offers a way for suppliers to sell directly online besides the traditional method, such as DELL, HP, IBM, NIKE, MATTEL, etc. Therefore, a new distribution system, also called a dual channel supply chain, appears when a manufacturer sells the same products through both a retailer and a direct channel [9]. Some literature considered inventory decisions in dual-channel supply chain [10-12] and most of them indicate that suppliers and retailers tend to introduce direct channels as a benefIcial strategy. Moreover, disruptions cannot be ignored in a dual-channel supply chain. This is because the agents' relationship in this case is more interactive and the dual-channel forces fIrms to face both vertical and horizontal channel conflicts, thus they are more likely to suffer from disruptions. Therefore, a single disruption may cause enormous knock-on effects on their decision-making and firms in dual-channel system are more sensitive to risks. Research on their disruption management is of great significance. However, little literature focuses on disruption management in a dual-channel supply chain. As exceptions, Reference [13] and [14] address the disruption management in a dual-channel system under demand disruptions and cost disruptions, respectively. Then both demand disruptions and cost disruptions are considered in a dual-channel framework in [15]. Three papers mentioned above assume that there is only one supplier in the dual channel supply chain.
978-1-5090-2842-9/16/$31.00 ©Q016 IE
Motivated by these results, this paper aims to discuss the retailer's inventory decision-making and its change in different scenarios. We consider an inventory model consisting of one retailer and two suppliers: one supplier is unreliable and has another direct channel and other one is reliable and only sell products through the retail channel. Besides, we assume that the demand model depending linearly on the prices, market shares and substitutability of products in two channels. This paper contributes to the literature in two aspects. First, we consider a dual sourcing problem in a dual-channel supply chain with supply disruption. As far as we know, studies on supply disruptions with one or more suppliers usually consider the traditional retail channel; most research on the dual-channel supply chain assumes that there is only one dual-channel supplier and discusses the retailer's changes to decisions. Tn this paper, we assume a more complex situation that a dual channel supplier is also competing with a single-channel supplier. In addition, this paper concentrate on the changes to retailer's decision-making. Most studies on dual-channel supply chain management focuses on channel selection, channel conflict and channel coordination, little attention has been paid to the sensitively of retailers and suppliers' respond to supply disruption. Therefore, we illustrate how the wholesale price, the direct price, disruption probability and market share of each channel would impact the retailer's decision-making. The rest of this paper is organized as follows. Section II describes the problem under consideration and basic underlying assumptions. Section ITT provides agents' profit functions and their decision-making. Tn Section IV numerical results are presented to illustrate agents' optimal order quantities in different scenarios. Conclusions are given in Section V.
Supplier I
THE PROBLEM
In this paper we study a supply chain consisting of two suppliers (supplier 1 and supplier 2) and one retailer (see Fig.1). Supplier 1 is perfect and only sells through the retail channel. Supplier 2 is unreliable that a supply disruption may occur with a positive probability; apart from the retail channel, supplier 2 also have a direct channel. Due to supply disruption, the wholesale price of supplier 2 is cheaper than that of supplier 1. We assume that supplier 2 can sell through both the retail channel and the direct channel and cannot concentrate on the supply to the retailer, which can increase his supply disruption risk. Also, the retail channel is not supplier 2's sole source of income, therefore leading to his lower wholesale price.
Direct
Retailer
Channel
Retail Channel
"-------..1
Figure I.
Consumers
The supply chain model
The following notation is used in the model: X F(x) pI (x) 8 Pi qi Qi Wi c
II.
Supplier 2
a. 7[r 7[s2
stochastic customer demand; cumulative distribution function of x; inverse function of F(x) market share of the retail channel and the direct channel, i=r,d, and ur+ ud=1, o,;:-----"'-o:::-------------: 4000
�
.� �
oQ.
��
100
b
==
50
�
0
0.0
01
Figure 3. C.
t:: �
0.4
�� E(n) _.��=====�J 3600 (I)
k
0.6
0.8
1.0
e
Optimal results for different values of k.
Market Shares o{Two Channels
We now examine the sensitivity of channels' difference on agents' decision-making. As shown in Fig. 4, consumers' preference for the traditional retail channel benefits the retailer and increases his order quantity from each supplier. Supplier 2's quantity in direct channel also decreases sharply in this case. Another point is that the increase in order quantity from supplier 1 is larger than that from supplier 2. When the retail channel is dominant in the system, the retailer prefers to increase his order quantity mainly from supplier 1. This is because that the sufficient downstream demand ensures less unsold products and enables the retailer to afford a higher wholesale price. For example, large brick-and-mortar companies are more likely to choose a reliable, although little more expensive supplier to stock, which can maintain their brand images and brand satisfaction.
08
The Disruption Probability (0:)
Optimal results for different values of the disruption probability
(a).
The Differenct between Two Wholesale Prices We assume that supplier 2's wholesale price is cheaper and in this subsection we consider effects of various wholesale prices on decision-making. Considering wz=kwJ, k approaches 1 means that the wholesale price of the unreliable supplier (supplier 2) increases and is in closer proximity to the wholesale price of the perfect supplier (supplier 1). Then the price advantage of supplier 2 declines and the retailer tends to order more products from supplier 1 in this case (Fig. 3). According to slopes, Fig. 3 also shows that k values exert greater effects on the optimal order quantity from supplier 2. This means that the cheaper wholesale price is a significant advantage of supplier 2 who can maintain his sales scale by lowering costs under a certain degree of supply disruption. B.
Fig. 3 also illustrates that the increase in supplier 2's wholesale price can reduce the retailer's optimal utility.
Figure 4.
D.
Optimal results for different values of
U,.
The Direct Price
The higher direct price increases the retailer's order quantity from both suppliers and is beneficial to the retailer (Fig. 5). The lower sale price in the direct channel is a main predominance but this advantage becomes less obvious when the direct price approaches the retail price. Tn this case, the
retail demand would increase and promote sales in the retail channel. Apart from the retailer's order quantity, the quantity in the direct channel also increases in Fig. 5. When the direct price is higher, demand in direct channel correspondingly reduces, supplier 2 would try to satisty demand as much as he could to maintain his profit in direct channel and keep the products in a stockpile. Therefore, the quantity does not reduce and its slope becomes less with a higher direct price. .....
tj:l
rIl 11)
'-1=1 .....
140
�::s
120
C/ .... 11)
"'0
.... 0 ";j 8
8
tU
Christopher, Martin, and H. Lee. "Mitigating supply chain risk through improved confidence." International Journal of Physical Distribution & Logistics Management 34.5:388-396, 2004.
[2]
Snyder, 1. Y, Atan, Z., Peng, P., Rong, Y., Schmitt, A. 1., and Sinsoysal, B. "Or/ms models for supply chain disruptions: a review." Ssm Electronic Journal, 48(2), 2012.
[3]
Anupindi, Ravi, and R. Akella. "Diversification Under Supply Uncertainty." Management Science 39.8:944-963, 1993.
[4]
Swaminathan, J. M., and J. G. Shanthikumar. "Supplier diversification: eflect of discrete demand." Operations Research Letters 24.5:213221,1999.
5
.....
[5]
Chopra, Sunil, G. Reinhardt, and U. Mohan. "The importance of decoupling recurrent and disruption risks in a supply chain." Naval Research Logistics 54.5:544-555, 2007.
[6]
Giri, B. C. "Managing inventory with two suppliers under yield uncertainty and risk aversion." International Journal of Production Economics 133.1:80-85, 2011.
[7]
Dada, Maqbool, N. C. Petruzzi, and 1. B. Schwarz. "A Newsvendor's Procurement Problem when Suppliers Are Unreliable." Manufacturing & Service Operations Management 9.1:9-32, 2007.
[8]
Masih-Tehrani, B., Xu, S. H., Kumara, S., & Li, H. "A single-period analysis of a two-echelon inventory system with dependent supply uncertainty." Transportation Research Part B Methodological, 45(8), 1128-1151, 2011.
[9]
Xu, G., Dan, B., Zhang, X., & Liu, C. "Coordinating a dual-channel supply chain with risk-averse under a two-way revenue sharing contract." International Journal of Production Economics, 147(1), 171179, 2014.
0..
QJ*
0
3600
nrll
E(7T)
.... 3S8� ..... tU .... .
Q2*
60
Figure 5.
[1]
-
3620.
80
0
REFERENCES
364�
100
'-1=1 0..
a China University of Petroleum (Beijing) Grant (No. 2462014YJRC036).
356 10
12
14
16
Direct Price (Pd)
18
20
� 11)
.J:l �
Optimal results for different values of the direct price(pd)'
V.
CONCLUSIONS
In this paper we study the newsvendor problem in dual channel with an Internet channel and a traditional channel supposing agents are risk-neutral and aim to maximize their profits. The inventory model consists of one retailer and two suppliers: one supplier sells through both the retail channel and another direct channel and supply disruption may occur with a certain probability; other one is reliable and only sell products through the retail channel. The reliable supplier has a higher wholesale price than the unreliable one. We assume a demand model depending on prices in both channels, degree of substitution across channels and the market shares. From the numerical study it has been observed that the retailer should reach the balance between the order quantities from two suppliers and there exists a certain disruption probability to minimize the retailer's optimal profits. In addition, the change of unreliable supplier's wholesale price exerts greater effects on the optimal order quantity from the unreliable supplier and the increase in unreliable supplier's wholesale price can reduce the retailer's optimal utility. Moreover, when the retail channel is dominant in the system, the retailer prefers to increase his order quantity mainly from the reliable supplier. ACKNOWLEDGMENT
This research was supported by Ministry of Education in China (MOE) Project of Humanities and Social Sciences (Project No. 15YJC630195). This work was also supported by
[10] Yao, D.-Q., Yue, x., Mukhopadhyay, S. K., & Wang, Z. "Strategic inventory deployment for retail and e-tail stores." Omega, 37(3), 646658,2009. [11] Chiang, W.-y. K. "Product availability in competitive and cooperative dual-channel distribution with stock-out based substitution." European Journal of Operational Research, 200(1), 111-126, 2010. [12] Dumrongsiri, A, Fan, M., Jain, A, & Moinzadeh, K. "A supply chain model with direct and retail channels." European Journal of Operational Research, 187(3), 691-718, 2008. [13] Huang, Song, C. Yang, and X. Zhang. "Pricing and production decisions in dual-channel supply chains with demand disruptions." Computers & Industrial Engineering 62.1:70-83, 2012. [14] Huang, Song, C. Yang, and H. Liu. "Pricing and production decisions in a dual-channel supply chain when production costs are disrupted." Economic Modelling 30.1 :521-538, 2013. [15] Huang, Song, C. Yang, and J. Yang. "Pricing and production decisions in dual-channel supply chains with demand and production cost disruptions." Systems Engineering-Theory & Practice 34.5: 1219-1229, 2014. [16] Berman, B., & Thelen, S. "A guide to developing and managing a well integrated multi-channel retail strategy." International Journal of Retail & Distribution Management, 32(3), 147-156, 2004. [17] Noble, S. M., Griffith, D. A, & Weinberger, M. G. "Consumer derived utilitarian value and channel utilization in a multi-channel retail context." Journal of Business Research, 58(12), 1643-1651, 2005. [18] Verhoef, P. c., Neslin, S. A, & Vroomen, B. "Multichannel customer management: Understanding the research-shopper phenomenon." International Journal of Research in Marketing, 24(2), 129-148, 2007. [19] Nielsen. Nielsen Global E-commence and the New Retail, Q3, 2014.
