Using put option contracts in supply chains to manage demand and supply uncertainty
| DOI | https://doi.org/10.1108/IMDS-09-2017-0393 |
| Date | 13 August 2018 |
| Published date | 13 August 2018 |
| Pages | 1477-1497 |
| Author | Jiarong Luo,Xiaolin Zhang,Chong Wang |
| Subject Matter | Information & knowledge management,Information systems,Data management systems,Knowledge management,Knowledge sharing,Management science & operations,Supply chain management,Supply chain information systems,Logistics,Quality management/systems |
Using put option contracts in
supply chains to manage demand
and supply uncertainty
Jiarong Luo
Southwest University of Science and Technology, Mianyang, China
Xiaolin Zhang
Chengdu Sports University, Chengdu, China, and
Chong Wang
School of Management, Sichuan Agricultural University, Chengdu, China
Abstract
Purpose –The purpose of this paper is to value put option contracts in hedging the risks in a supply
chain consisting of a component supplier with random yield and a manufacturer facing stochastic demand for
end products.
Design/methodology/approach –This paper adopts stochastic inventory theory, game theory,
optimization theory and algorithm and MATLAB numerical simulation to investigate the manufacturer’s
ordering and the supplier’s production strategies, and to study the coordination and optimization strategies in
the context of random yield and demand.
Findings –The authors find that put options can not only facilitate the manufacturer’s order but also the
supplier’s production, that is, the manufacturer and the supplier can effectively manage their involved risks
and earn more expected profits by adopting put options. Further, the authors find that the single put option
contract fails to coordinate such a supply chain. However, when combined with a protocol, it is able to
coordinate the supply chain.
Originality/value –This paper is the first effort to study the intersection of put option contracts and
random yield in the presence of a spot market. From a new perspective, the authors explore the supply chain
coordination. The authors propose a mechanism to coordinate the supply chain under put option contracts.
Keywords Supply chain management, Demand uncertainty, Put optioncontracts, Yield uncertainty
Paper type Research paper
Nomenclature
TRandom yield rate of the supplier, which is
characterized by cumulative distribution
function (CDF), probability density
function (PDF), Φ(t)andφ(t), respectively.
The mean of the random yield rate is
E(T)¼μ,TA½a;bð0paobp1Þ
DMarket demand for the end-product, which
is a random variable with CDF F(x)and
PDF f(x), and E(x)¼δ,D∈(0, ∞)
wUnit wholesale price ($)
oUnit option price of the put option ($)
e
p
Unit exercise price of put option ($)
QProduction quantity of the supplier
q0
pFirm order quantity of the manufacturer
q1
pOption order quantity of the
manufacturer, q1
poq0
p
P
s
Spot market price ($) for the component,
which is a random variable with PDF v
(p
s
) and CDF V(p
s
) and
EðpsÞ¼ps;PsA½A;B
cUnit productioncost of the component ($)
rUnit retail price of the end-product ($)
Industrial Management & Data
Systems
Vol. 118 No. 7, 2018
pp. 1477-1497
© Emerald PublishingLimited
0263-5577
DOI 10.1108/IMDS-09-2017-0393
Received 6 September 2017
Revised 18 November 2017
Accepted 4 January 2018
The current issue and full text archive of this journal is available on Emerald Insight at:
www.emeraldinsight.com/0263-5577.htm
The authors are grateful to the Editors and the reviewers for their insightful and constructive
comments. This research is partially supported by Youth Foundation for National Natural Science
Foundation of China (No. 71702156, No. 71602134), Humanities and Social Sciences of Ministry of
Education of China (No. 17YJC630098) and Center for Information Management and Service Studies of
Sichuan (No. SCXX2017YB13).
1477
Put option
contracts in
supply chains
1. Introduction
The real optionwas first designed to amplify fortuneor mitigate loss in the capital investment
decision makingunder uncertainty (Lander and Pinches,1998). Over the last 40 years, the real
option has drawn constant attention from scholars in economic field. Different theoretical
types of real options have been developed in the early literature, including growth options
(Myers, 1977), options to abandon (Bonini, 1977), options to defer (Tourinho, 1979) and scale
options (Trigeorgis and Mason, 1987), etc. Meanwhile, various option-type decision-making
frameworks have been developed to model and value these real options and derive optimal
investment strategies, such as continuous-time models (Black and Scholes, 1973), finite-
difference schemes (Brennan and Schwartz, 1978), and trinomial models (Kamrad (1995) and
binomialmodels (Lander and Pinches, 1998). Landerand Pinches (1998) stated that mosttypes
of the early models are complex and require substantial mathematical techniques to solve,
which are often violated in the application of real options. Later studies endeavor to propose
more practical frameworks/models and solutions, for example, the papers of Cassimon et al.
(2011), Zhang et al. (2014), Nigro et al. (2014) and Cassimon et al. (2016). Due to its success in
investmentmarket, many flexibility contracts derivated fromthe real option have been widely
applied by practitioners and scholars to manage supply chain risks in the last two decades
(Barnes-Sc huster et al., 2002; Nagali et al., 2008; Chen and Shen, 2012).
Essentially, the real option is a right: by pre-paying a fee, the buyer (manufacturer) gets
the right (not the obligation) to reorder items from the seller (supplier) at a predetermined
price or the right to return unsold goods to the seller (supplier) at a predetermined salvage
value. The former is known as call option contract and the latter put option contract
(Burnetas and Ritchken, 2005; Liu et al., 2013). Both option contracts are frequently adopted
in practice, e.g., to hedge their risks, Hewlett-Packard Company (Nagali et al., 2008) and
China Telecom Corporation Limited (Chen et al., 2014) adopt call option contracts while
Enron (Chen and Parlar, 2007) adopts put option contracts. In the academic circle, issues
concerning supply chain management with real option contracts have been extensively
studied, but the majority of these works focus on the call option contract and a few studies
concern about the put option contract (see Nosoohi and Nookabadi, 2016 for a complete
review). Furthermore, to the best of our knowledge, there is no research on the application of
put option contracts in supply chains in the presence of supply uncertainty so far. Our study
accordingly stands on the intersection of put option contracts and supply uncertainty.
Supply uncertainties are not new; they even have existed as long as supply chains
(Snyder et al., 2016). In many industries, the problem of unexpected supply disruption (result
from man-made or natural disasters such as fires, earthquakes and terrorist attacks, etc.)
and yield uncertainty (also known as random yield, due to weather, environment and other
unpredictable factors in complicated production) are regarded as the main causes of supply
uncertainties (Singhal et al., 2011). In general, disruptions may cause entire or a significant
fraction of production loss, but it occurs very infrequently (rare events). In contrast, random
yield may cause certain loss of some fraction of production, but it occurs frequently in
production and assembly, which will influence the daily production plan. Some industries
even suffer from random yield nearly in every batch, e.g. semiconductor, chemicals,
agriculture and pharmaceuticals (Kulkarni, 2006; Deo and Corbett, 2009). On the other hand,
in literatures, stochastically proportional yield model is commonly adopted to depict yield
uncertainty (Yano and Lee, 1995; Grosfeld-Nir and Gerchak, 2004). Under this context, if the
yield is a Bernoulli random variable, disruptions can be viewed as a special case of yield
uncertainty (Snyder et al., 2016). Hence, we focus on the random yield in this paper. To some
extent, we can conclude that our result also makes sense in the case of the disruption.
Motivated by semiconductor industry, this paper considers a one-period two-echelon supply
chain composed of one component-supplier and one end-product manufacturer. The production
of the supplier is subject to yield uncertainty and the market demand for the end-product is
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