Option contract strategies with risk‐aversion and emergency purchase

• Author: Xiaoyong Yuan,Yugang Yu,Baofeng Zhang,Gongbing Bi
• DOI: http://doi.org/10.1111/itor.12519
• Published date: 01 November 2020
• Date: 01 November 2020

Intl. Trans. in Op. Res. 27 (2020) 3079–3103

DOI: 10.1111/itor.12519

INTERNATIONAL

TRANSACTIONS

IN OPERATIONAL

RESEARCH

Option contract strategies with risk-aversion

and emergency purchase

Xiaoyong Yuan, Gongbing Bi,∗, Baofeng Zhang and Yugang Yu

School of Management, University of Science and Technology of China, Hefei,Anhui 230026, China

E-mail: yuanxy@mail.ustc.edu.cn [Yuan]; bigb@ustc.edu.cn[Bi]; zhangbf@mail.ustc.edu.cn [Zhang];

ygyu@ustc.edu.cn [Yu]

Received 9 July2017; received in revised form 15 November 2017; accepted 20 January 2018

Abstract

This paper considers a one-period supply chain consisting of a risk-averse retailer and a risk-neutral supplier.

As a Stackelberg leader, the supplier produces short life-cycle products to the retailer and determines the

option price. The newsvendor-like retailer orders call option from the supplier with an emergency order

opportunity. The analytical model shows that when the emergency purchase price is low, the risk-averse

retailer’s optimal order quantity is less than that of a risk-neutral retailer and independent of the retail price.

It is surprising that when it is moderate or high, the risk-averse retailer may order less than, equal to, or

more than a risk-neutral one. Computational studies are given to investigate the key parameters on optimal

decisions and profits. It shows a risk-averse retailer may get higher profit than a risk-neutral one.The retailer

benefits from a low emergency purchase price, while it harms the supplier.

Keywords:option contract; risk-averse; newsvendor; emergency purchase; conditional value at risk (CVaR)

1. Introduction

With the rapid development of the economy and the improvement of people’s living standards, the

demand of customers tends in the direction of personalization and diversification, which results in

high uncertainty in market demand. Furthermore, in practice, the product usually has a long lead

time and a short selling season. Therefore, considering the long lead time and high uncertainty

in customer demand, it is very difficult to match between supply and demand, which brings great

challenge to supply chain management. In order to manage the demand risk, it is believed that a

well-designed mechanism can alleviate the impact of the demand uncertainty on the supply chain

performance (Cheng et al., 2003; Wang et al., 2014; Niu et al., 2016a). Therefore, option contract

have been proposed to provide the retailer with flexibility to respond to unanticipated demand.

Under option contract, the retailer gains the right (not the obligation) to engage in the transaction,

∗Corresponding author.

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2018 The Authors.

International Transactionsin Operational Research C

2018 International Federation ofOperational Research Societies

Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main St, Malden, MA02148,

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3080 X. Yuan et al. / Intl. Trans.in Op. Res. 27 (2020) 3079–3103

while the supplier assumes the corresponding obligation to fulfill the transaction.It can enhance the

supply chain efficiency as well as benefit both the retailer and supplier (Gomez-Padilla and Mishina,

2009; Chen and Shen, 2012). In fact, option contracts have been widely used in the supply chain

management, in practice, such as fashion apparel (Eppen and Iyer, 1997) and electronics (Carbone,

2001). It is employed to reduce risk and cost, such as Enron (Zellner et al., 2001) and Hewlett

Packard (HP) (Nagali et al., 2008). In this paper, we assume the retailer orders pureoption from the

supplier and the supplier adopts the make-to-order policy, which suggests that the supplier bears

the inventory risk and is compensated by additional revenue from option fee.

In the existing supply chain models,managers are mostly assumed to be risk-neutral and they aim

to maximize their expected profit. However, in the past few decades, the business environment has

become more and more complex, characterized by high uncertainty and rapidchange. Supply chains

are more vulnerable to uncertainties caused by many potential external sources of disruption, for

example, natural disasters, industrial actions, terrorist attacks, and so forth (Wu et al., 2010). After

the recent financial crisis and the economic downturn in Europe and North America, managers are

more concerned about risk management or loss minimization for their firms (Choi, 2016). They are

willing to sacrifice a portion of expected profit to avoid largelosses. Therefore,the assumption of risk

neutrality does not alwayshold in practice. For example,Schweitzer and Cachon (2000) conduct two

experiments to investigate newsvendor decisions across different profit conditions. They show that

the inventory manager is risk-averse even for high-profit products. Yang et al. (2016) showed that

risk sensitivity is very important for both the projectmanager and contractor by using the principal-

agent theory. The newsvendor problem with risk-related objectives under different criteria has been

examined, such as the mean-variance (MV) (Chiu and Choi, 2016), expected utility (EU) function

(Keren and Pliskin, 2006; Li and Li, 2016), value atrisk (VaR), and conditional value at risk (CVaR)

(Wu et al., 2013; Sharma and Mehra, 2017). Meanwhile, from the viewpoint of behavioral theory,

the leader, such as a large supplier, is risk-neutral because it can diversify its risk by serving a

number of retailers. While the follower, a small retailer, is risk-averse because its security of doing

business and income are related to the principal (Wiseman and Gomez-Mejia, 1998). For example,

most industrial supply chains dominated by a largesupplier (e.g., in the personal computer industry

such as HP, in fashion apparel such as Ralph Lauren) have many distributors who act as retailers

selling directly to customers. In fact, this assumption is popular in existing literature (Gan et al.,

2005; Adida and DeMiguel, 2011). Motivated by this, we propose a Stackelberg game between

a risk-averse retailer and a risk-neutral supplier. The supplier, acting as a leader, determines the

option price to maximize his expected profit, and the retailer determines her order quantities with

CVaR decision criteria.

In the existing literatures, many papers assume the retailer has only one chance to order the

product from the supplier. If there is unmet demand, she has to bear the shortage loss for the

insufficient order. However, in practice, retailers can immediately replenish stock from a secondary

supplier (Yan et al., 2003) or market (Lee and Whang, 2002; Li et al., 2017). Due to fluctuations

in currency exchange rates, and shortages or excessive inventories at the supplier, the emergency

purchase price may be high or low. If it is sufficiently high, the retailer will not choose to replenish

the inventory. Otherwise, the retailer orders additional products to avoid the shortage cost. In this

paper, we assume the retailer has a chance to replenish her inventory through an emergency order

and explore the effect of the emergency purchase price on the optimal decisions. The results show

that when the emergency purchase price is low, the risk-averse retailer’s optimal order quantity is

C

2018 The Authors.

International Transactionsin Operational Research C

2018 International Federation ofOperational Research Societies