Capital-constrained bi-objective newsvendor model with risk-averse preference and bankruptcy threshold

Date22 October 2019
Pages406-424
DOIhttps://doi.org/10.1108/IMDS-03-2019-0200
Published date22 October 2019
AuthorChen Yang,Desheng Wu,Weiguo Fang
Subject MatterInformation & knowledge management
Capital-constrained bi-objective
newsvendor model with
risk-averse preference and
bankruptcy threshold
Chen Yang
School of Economics and Management, Beihang University, Beijing, China
Desheng Wu
School of Economics and Management,
University of Chinese Academy of Sciences, Beijing, China, and
Weiguo Fang
School of Economics and Management, Beihang University, Beijing, China and
Key Laboratory of Complex System Analysis, Management and Decision,
Ministry of Education, Beihang University, Beijing, China
Abstract
Purpose The purposeof this paper is to investigate the majorfactors influencing retailersoptimal ordering
strategy in a supplychain consisting of one supplier and oneretailer, where the retailer is newsvendor-like and
capital-constrained, and further explore the issue of supply chain coordination.
Design/methodology/approach Based on bi-objective programming which is modeled under the
mean-variance framework, the retailers optimal ordering strategy is derived. Furthermore, through comparative
analysis between decentralized system and centralized system along with a numerical simulation, this study
examines the theoretical conclusions about supply chain coordination.
Findings This study shows that a po or retailer with a high Expected T erminal Wealth Target Threshol d
(ETWTT) would ignore ba nkruptcy risk and order more, wher eas a rich retailer is relatively con servative.
It also reveals that in some cases, the optimal order quantity and performanceof decentralized system could
be both improved. Howeve r, the centralized system can always get more p rofit than the decentralized one.
Originality/value This study uses a bankruptcy threshold to describe retailers bankruptcy risk, and
considers retailers wealth status to formulate the model as an innovative bi-objective programming. The type
of retailer as rich or poor in terms of his wealth status and asset structure is distinguished. Moreover,
the impacts of retailers type and ETWTT on ordering strategy are examined.
Keywords Risk aversion, Supply chain coordination, Bankruptcy threshold, Bi-objective programming,
Capital constraint
Paper type Research paper
1. Introduction
Working capital plays an important role in supply chain management. In the capital-constrained
newsvendor problem, at the beginning of sales season, money is not enough to satisfy capital
need, which has an adverse effect on retailers reputation and profitability. In order to seize
market share and build reputation, the retailer would borrow from a bank or a supplier to meet
capital need.
In the field of supply chain financing, the capital-constrained newsvendor problem with
risk-neutral assumption has been studied in depth. However, the risk-neutral assumption seems
inadequate because a supply chain is very complex in some situations. Note that in practice,
there are many examples that decision-maker does not always only persist in maximizing
expected profit. Other than the classical capital-constrained newsvendor problem, retailers have
different collaterals to help them to defend against bankruptcy risk. In reality, the collaterals
could influence retailers decision-making. However, the existing literature ignored this issue.
Industrial Management & Data
Systems
Vol. 120 No. 2, 2020
pp. 406-424
© Emerald PublishingLimited
0263-5577
DOI 10.1108/IMDS-03-2019-0200
Received 31 March 2019
Revised 13 June 2019
27 August 2019
Accepted 7 September 2019
The current issue and full text archive of this journal is available on Emerald Insight at:
www.emeraldinsight.com/0263-5577.htm
406
IMDS
120,2
Inspired by previous studies but different from the classical newsvendor model, this
study considers the situation of a retailer-dominated supply chain, where the retailer decides
his optimal order quantity from his own perspective, and then the supplier produces and
delivers items according to the retailers order. In our assumption, the market demand is
uncertain, retailer undertakes the inventory risk and may go bankrupt. To measure
retailers bankruptcy risk, we introduce the bankruptcy threshold as Kouvelis and Zhao
(2012) defined. This paper focuses on the retailers ordering decision-making. We
distinguish the type of retailer as rich or poor based on his wealth status (initial capital and
collaterals) and asset structure (the ratio of initial capital and collaterals to total wealth). We
investigate the capital-constrained newsvendor model with risk-aversion preference and
bankruptcy threshold in the context of bi-objective programming which is modeled under
the mean-variance framework.
In the past years, one of the key findings about supply chain coordination is that, the
retailers optimal order quantity in decentralized system is no more than that in centralized
system. This paper examines whether this widely accepted result is still validated when the
retailers type,risk preference and Expected TerminalWealth Target Threshold (abbreviated
as ETWTT) are taken into consideration. Our findings are quite different from the common
sense believed in existing literature on supply chain coordination. We demonstrate that in
some cases,for a poor retailer with a higherexpected profit target threshold,his optimal order
quantity in a decentralized system would reach or even exceed that in a centralized system.
We also point out a centralized system can always get more profit than a decentralized one,
despite how many the optimal order quantity in decentralized system is.
The main innovations of our work are in the following four aspects. First, we incorporate
the bankruptcy threshold in our proposed model, and capture the balance of retailers two
objectives under mean-variance framework. Second, we characterize a retailer in terms of
his wealth status and asset structure, and discriminate a retailer as poor or rich. We examine
the impact of retailers type and ETWTT on his ordering strategy, and demonstrate that in
certain situation, the poor retailer would venture to order more, while a rich retailer is
relatively conservative. Then, a feasible region about ETWTT is given, and the theorem
that can be used as the guidance of ordering decision is also derived. Our work sheds light
on how to help retailer make correct decision when bankruptcy risk exists. Last, based on
the proposed model, we use a numerical simulation to reveal that the optimal order quantity
in decentralized system may equal to or even exceed that in centralized one, while the
expected profit may not. Note that not only should the decentralized systems optimal order
quantity equal to centralized one, but also should the expected profit, in this case the supply
chain can be thought coordinated. This means it is inadequate to use the order quantity as
the sole indicator to judge the channel coordination.
The rest of this paper is organized as follows. In Section 2, we review the related
literature. The basic model underlying our study is constructed in Section 3. Then, based on
the model, we derive the retailers optimal ordering strategy in a decentralized supply chain
system and related properties in Section 4. We further explore the supply chain coordination
problem in Section 5. In order to show and verify our findings, a numerical simulation is
conducted in Section 6. At last, in Section 7, we give conclusions.
2. Literature review
Our work is related to three realms of literature, involving capital-constrained newsvendor
problem, decision-making methods and supply chain coordination.
Xu and Birge (2004) first considered the capital-constrained issue within a simple
newsvendor model. They illustrated that financial constraint would affect retailers operational
decisions, and analyzed the interaction between them. Buzacott and Zhang (2004) first jointed
asset-based financing into operational decisions and demonstrated the importance of this joint.
407
Bi-objective
newsvendor
model

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