Impact of cost uncertainty on supply chain competition under different confidence levels

• Author: Huiru Chen,Zhibing Liu,Chi Zhou,Ruiqing Zhao
• DOI: http://doi.org/10.1111/itor.12596
• Date: 01 May 2021
• Published date: 01 May 2021

Intl. Trans. in Op. Res. 28 (2021) 1465–1504

DOI: 10.1111/itor.12596

INTERNATIONAL

TRANSACTIONS

IN OPERATIONAL

RESEARCH

Impact of cost uncertainty on supply chain competition under

different confidence levels

Zhibing Liua, Chi Zhoub,∗, Huiru Chenaand Ruiqing Zhaoc

aCollege of Mathematics and Physics, HuanggangNormal University, Hubei 438000, China

bSchool of Management, Tianjin University of Technology, Tianjin 300384, China

cInstitute of Systems Engineering, Tianjin University, Tianjin 300072, China

E-mail: lzb8401552@hgnu.edu.cn [Liu]; czhou@tjut.edu.cn [Zhou]; chenhuiru@hgnu.edu.cn [Chen];

zhao@tju.edu.cn [Zhao]

Received 14 February2016; received in revised form 28 April 2018; accepted 31 August 2018

Abstract

This paper considers two competing supply chains that face cost uncertainty, each consisting of one supplier

and one retailer. To address the uncertain cost information, we propose a decision rule based on confidence

levels to measure the goals of the supply chain participants. We provide the new concept of the belief-degree

cost of a supply chain that embodies the decision maker’s ability to comprehensively address information

uncertainty and control the risk caused by information uncertainty. We find that regardless of which of the

three games it is in – integrated, hybrid, or decentralized – a chain should order more and thereby gain

more profit when its cost uncertainty increases or the competing chain’s cost uncertainty decreases.The chain

with a low or sufficiently low belief-degree cost gains a competitive advantage on both quantity and profit.

A chain’s competitiveness can be enhanced by either decreasing its confidence level or increasing its rival’s

confidence level. Furthermore,we demonstrate that supply chain integration is the dominant strategyfor given

confidence levels. Nevertheless, a prisoner’sdilemma occurs when the differences in the belief-degree costs of

the two supply chains are not significant and the competitive intensity is high. In addition, the magnitudes

of the confidence levels can be changed to avoid or cause a prisoner’s dilemma. Finally, under different

confidence levels, the Stackelberg model for competing hybrid or decentralized supply chains is extended to

the bargaining model, and the impact of bargaining power on supply chain competition is analyzed.

Keywords:supply chain competition; contract designing; confidence level; cost uncertainty; belief-degree cost

1. Introduction

With the rapid developmentof Internet technology, business competition between firms has reached

an unprecedented level. To be competitivein the marketplace, firms must work togetherand optimiz e

∗Corresponding author.

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1466 Z. Liu et al. / Intl. Trans. in Op. Res. 28 (2021) 1465–1504

the supply chain to achieve a substantial increase in performance that cannot be achieved by

optimizing individual processes. As a result, the classical competitive model of firm versus firm is

giving way to a new model: supply chain versus supply chain (Barnes, 2006; Ha and Tong, 2008).

On the one hand, different market structures, such as an integrated or a decentralized supply

chain, will affect supply chain competition. For example, the Chinese dairy market was worth

$40.6 billion in 2013 compared with only $20.7 billion in 2008. The two largest national players,

the Yili Industrial Group and Mengniu Dairy Company, had a combined market share of 41% in

2012, leaving the other players far behind. Both companies source from independent and exclusive

farms, and sell their products through specialized dealers, but in recent years, they have worked on

establishing their own farms and direct selling centers (Fang and Shou, 2015).

On the other hand, cost structures are crucial for measuring supply chain performance and

achieving market competitiveness. The existing competition literature in supply chain management

treats costs as the deterministic parameters (Ha and Tong, 2008; Fangand Shou, 2015). Nevertheless,

costs are uncertain in many actual supply chain competition problems. In fact, factors, such as

updated production equipment, a change in production scale, or price changes of raw materials,

directly affect the costs of products. Therefore, costs are usually uncertain, particularly over certain

intervals. For instance, the annual reports1from the Yili Industrial Group from 2011 to 2013 state

that its total net profits were ¥2.14 billion, ¥2.09 billion, and ¥3.06 billion and its total costs were

¥35.96 billion, ¥40.40 billion, and ¥45.25 billion, respectively. This implies that its cost–profit ratios

were 5.95%, 5.17%, and 6.77%, respectively. As per the statistical standard and the annual reports2

of the Mengniu Dairy Company from 2011 to 2013, its total net profits were ¥1.78 billion, ¥1.44

billion, and ¥1.84 billion and its total costs were ¥35.79 billion, ¥34.84 billion, and ¥41.43 billion,

respectively, representing respective cost–profit ratios of 4.97%, 4.13%, and 4.44%. Based on these

data, we see that the total cost of the products of the Yili Industrial Group continues to increase,

whereas the total cost of the Mengniu Dairy Company first decreases and then increases. The two

companies’ cost–profit ratios also first decreaseand then increase. The main reason for this change is

the lack of milk sources, resulting in a price increasefor raw milk and leading to uncertainty over the

cost of products. For this reason, both companies have sought to strengthen the base construction

of their milk sources to control the cost of raw milk. Even so, the costs of dairy products remain

uncertain because they are affected by many uncontrollable factors such as market demand and

production scale. For example, in 2015, the net profit of the Mengniu Dairy Company was ¥2.37

billion, which is only 50.8% of that of the Yili Industrial Group, at¥4.65 billion. One of the simplest

reasons for this difference is that the Yili Industrial Group increased its input cost, especially its

advertising cost, resulting in an increase in its marketshare and an expansion of its production scale.

Therefore, different scales of production, changes in market demand, and the uncertainty affecting

raw material cost lead to uncertain product costs.

Furthermore, there is little to no, or inaccurate, historical data about this uncertain information,

such as the cost of a new product or the cost of a productwhose yields change with external demand,

and it cannot be exactly predicted in advance. People can only offer subjective judgments about this

type of information. Thus, probability theory is not applicable to characterize this type of uncer-

tain information. Additionally, almost all work on supply chain competition problems considers

1http://www.yili.com/cms/rest/reception/files/list?categoryId=20

2http://www.mengniu.com.cn/about/tzzq/

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individuals’ goals to be the conventional expected utility maximization. However, Ellsberg (1961)

observes that it is not always appropriate to regard maximizing expected utility as an individual’s

decision rule.

Motivatedby these concerns, this paper investigateshow to characterize the uncertain information

from different market structures using uncertainty theory (Liu, 2007), which is an essential tool for

addressing experts’ subjective judgments about unknown information in supply chain competition

problems, and proposes a decision rule based on confidence levels instead of the conventional

expected value rule. The confidence level is the degree of belief in a successful result and can be

defined as a percentage. Its value reflects the individual’s attitude toward risk during a decision-

making process.The higher the confidence level is, the more believablethe result is and, therefore, the

more risk-averse the individual is. Conversely, a lower confidence level implies that the individual

is more risk-loving and bears more potential risk. Specifically, when the confidence level is one,

the individual is completely risk-averse, and when the confidence level is zero, the individual is

completely risk-loving. To investigate individuals’ risks in supply chain competition problems,

we maximize their profits based on their confidence levels and formulate the corresponding models

through chance-constrained programming.Specifically, we attempt to solvethe following questions:

(1) How do the confidence level and supply chain competition affect ordering decisions? (2) How

should the wholesale price in a decentralized supply chain be determined under different confidence

levels? (3) Does supply chain integration provide a competitive advantage when facing competition

and uncertain information under different confidence levels? (4) How does bargaining power affect

supply chain competition for competing hybrid or decentralized supply chains if the Stackelberg

model is extended to a bargaining model?

To address these questions, we study two competitive supply chains based on confidence lev-

els under three different market structures: First, both supply chains are integrated; second, they

are hybrid, that is, one supply chain is integrated while the other is decentralized; and finally,

both supply chains are decentralized. Each supply chain has a single supplier and a single re-

tailer. The two suppliers are heterogeneous in their cost structures. We assume that their costs are

uncertain and build the corresponding models based on confidence levels. The equilibrium deci-

sions are derived according to the retailer’s optimal order quantity and (for a decentralized supply

chain) the contract form. Comparing the three equilibria, we examine the value of integration.

Finally, we conduct some extensions and analyze the impact of bargaining power on supply chain

competition.

A significant new concept, the belief-degree cost of a supply chain (or supplier), which is derived

from the supplier’s uncertain cost and the uncertain noise of the market clearing price under a given

confidence level, is proposed to address a supply chain competition problem. Essentially, the belief-

degree cost of a supply chain is the cost under a given degree of belief, represented by a confidence

level, after considering the uncertainty of the cost and the noise of the market clearing price. In

a supply chain, the belief-degree cost comprehensively reflects the uncertainty of the product cost

and price noise and the decision maker’s risk attitude. It comprehensively embodies the decision

maker’s ability to address information uncertainty and control the risk caused by it. The belief-

degree cost depends only on and increases with the confidence level if the distribution functions of

uncertain cost and uncertain noise are given. This means that higher confidence levels imply higher

belief-degree costs with lower risk levels or less uncertainty of cost and noise, and vice versa. Thus,

an increase in the confidence level of one chain will decrease its risk level and reduce/control the

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2018 The Authors.

International Transactionsin Operational Research C

2018 International Federation of OperationalResearch Societies