Multi-period dual-sourcing replenishment problem with option contracts and a spot market

Date14 May 2018
Published date14 May 2018
AuthorNana Wan,Xu Chen
Multi-period dual-sourcing
replenishment problem with
option contracts and a spot market
Nana Wan
School of Economics and Management,
Southwest University of Science and Technology, Mianyang, China, and
Xu Chen
School of Management and Economics,
University of Electronic Science and Technology of China, Chengdu, China
Purpose The spot market has been gradually recognized as an important alternative purchasing source.
To maintain a flexible replenishment strategy, call, put and bidirectional option contracts, as a risk hedging,
are in combined usage with the spot market, respectively. The purpose of this paper is to analyze a
finite-horizon replenishment problem with option contracts in the context of a spot market.
Design/methodology/approach Based on stochastic dynamic programming, the firms optimal
replenishment policy with either call, put or bidirectional option contracts is always shown to be order-up-to
type, characterized by an upper threshold and a lower one. The corresponding policy parameters in different
cases are calculated through an approximate algorithm. This research highlights the effectiveness of option
contracts on the firms operational strategies and overall profitability.
Findings This study reveals that the firm is better off with option contracts than without them. When the
price parameters are the same for different option contracts, bidirectional option contracts are the best choice
among these flexible contracts; otherwise, unilateral option contracts might be either better or worse than
bidirectional ones. In addition, if low inventory costs and high spot price volatility are confronted, the firm
prefers to call option contracts rather than put ones; otherwise, there exists an opposite conclusion.
Originality/value In addition to highlight the advantage of option contracts over wholesale price
contracts, this paper provides interesting observations with respect to the effect of different option contracts
on the firm. Many significant insights derived from this research do not only contribute to the providers
feasible design of the supply contracts, but also contribute to the users rational operational strategies for
higher profitability.
Keywords Spot market, Stochastic dynamic programming, Dual-sourcing replenishment,
Multi-period inventory, Option contracts
Paper type Research paper
1. Introduction
Replenishment/procurement managementhas always been recognized as a critical element of
one firms core competitiveness, and it has been at thecore of the firms operational planning
cycles. With the rapid upgrading of technology and the increasing intensification of market
competition,customer expectationshave been gradually heightened, whichleads to a growing
trend in their demand toward diversity an d individuation (Chen and Wang, 2015). Obviously,
consumer demand has become increasingly difficult to predict than ever before. This
mismatchbetween supply and demandinduces the firm to sufferfrom the loss associated with
over- and under-purchasing,which in turn exerts an increasing pressure onits replenishment
schedule. In many practical settings, thereexists a common phenomenon that the life span of
goods is often divided into multiple successive periods. Apparently, the decision makers are
often challenged with series of relevant optimal solutions over times, which is especially true
even for perishable products (Chen and Xiao, 2011; Cheaitou et al., 2014; Chung et al., 2015).
The multi-periodic structure makes the decision-making process more sophisticated. In the
recent research, the multi-period replenishment problem has become a hot topic.
Industrial Management & Data
Vol. 118 No. 4, 2018
pp. 782-805
© Emerald PublishingLimited
DOI 10.1108/IMDS-07-2017-0291
Received 3 July 2017
Revised 14 September 2017
Accepted 10 October 2017
The current issue and full text archive of this journal is available on Emerald Insight at:
With the rapid development of electronic commerce, the contract market is not the sole
source to acquire the desired goods. The spot market is gradually treated as another
important alternative source. Traditional commodities such as grains, livestock, oil, copper,
aluminum, chemicals, plastics, etc., are often traded on the spot markets (Seifert et al., 2004;
Xing et al., 2012; Wu et al., 2014). Recently, the spot markets are successfully developed for
many high-tech industries like semiconductors, memory chips, etc. (Fu et al., 2010; Ma et al.,
2013; Luo and Chen, 2017). The advantage of the spot market purchasing is that the
firm can obtain the goods at negligible lead time and avoid exposure to the demand risk
(Lee et al., 2014). Nonetheless, its shortcoming is that the firm has to face the spot price
uncertainty (Shi et al., 2016; Kong et al., 2017). Facing such a big challenge, a combined
usage of these two procurement sources can help the firm avoid over-reliance on the spot
market and obtain a high purchasing flexibility. Under such a situation, an appropriate
contract type should be selected and used as a risk hedging.
In recent years, a spectrum of risk-sharing contracts such as revenue-sharing
contracts, buy back contracts, etc., are designed to help the firm better accommodate the
fluctuating market environment. Among these different contracts, option contracts,
originated in financial derivations, are considered as the most suitable contract format to
be used together with the spot market. With this type of flexible contracts, the firm is
provided with the right to buy or sell a certain amount of goods up to the negotiated
quantity after both stochastic demand and random spot price have been observed.
Obviously, the usage of option contracts is conducive to reaping the advantages of the
alternative sources and balance the two-source procurement risks. Recently, more
companies such as Land Rover, Hewlett-Packard, etc., have started to conduct a
transaction through this portfolio purchasing mechanism (Fu et al., 2012; Fu, 2015).
This portfolio procurement approach, initiated in year 2000, helps Hewlett-Packard save
more than $425 million (Chen and Shen, 2012).
In general, there exist a variety of option contract types. One of the most prevalent types
is unilateral option contracts, which comprise call and put option contracts. The firm, as the
option buyer, pays a unit purchase price upfront for reserving (returning) one unit of good at
a certain future time, and after the two-source uncertainties have been resolved, the firm
could increase buying (cancel ordering) by sending payment (claiming compensation)
to (from) the option writer at a unit pre-negotiated exercise price if necessary. Apparently,
call ( put) option contracts enable the firm to equip with a capacity of adjusting its initial
order only upward (downward). As an extension of unilateral ones, bidirectional option
contracts allow the firm to adjust its initial order in two different directions. So far, whether
concerning a spot market or not, the problem relating to the selection of an appropriate
option contract format in a multi-period setting has remained unaddressed.
This study is very important in that it analyzes a finite-horizon replenishment problem
with various types of option contracts in the context of a spot market. As pointed out in
Section 2, quite a number of papers consider the portfolio replenishment strategy under
the single-period situation. However, some recent literature relating to the multi-period
combined procurement problem mainly focuses on call option contracts that cannot be
deemed as real ones, while ignores other option contract types. To fulfill this gap,
we individually integrate call, put and bidirectional option contracts into the multi-period
replenishment models with a spot market. The following questions will be addressed in
our study:
RQ1. With a spot market, what policy does the firms replenishment follow, either
without or with option contracts?
RQ2. With a spot market, how to develop an approximate algorithm to evaluate the
policy parameters, either without or with option contracts?
contracts and a
spot market

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