Optimal carbon reduction level and ordering quantity under financial constraints

• DOI: http://doi.org/10.1111/itor.12606
• Author: Kaiying Cao,Yi He,Bing Xu,Qingyun Xu
• Date: 01 September 2020
• Published date: 01 September 2020

Intl. Trans. in Op. Res. 27 (2020) 2270–2293

DOI: 10.1111/itor.12606

INTERNATIONAL

TRANSACTIONS

IN OPERATIONAL

RESEARCH

Optimal carbon reduction level and ordering quantity

under financial constraints

Kaiying Caoa, Bing Xub,YiHe

b,∗and Qingyun Xub

aSchool of Management & TourismResearch Institute, Nanchang University, 999 Xuefu Avenue,

Nanchang, Jiangxi 330031, PR China

bSchool of Management, Nanchang University,999 Xuefu Avenue, Nanchang, Jiangxi 330331, PR China

E-mail: kycao@ncu.edu.cn [Cao]; xubing99@ncu.edu.cn [B. Xu]; heyi@ncu.edu.cn[He];

xuqingyun94@126.com [Q. Xu]

Received 10 June2018; received in revised form 3 September 2018; accepted 7 October 2018

Abstract

Carbon tax policy is widely adopted by many countries to curb carbon emissions. In the context of carbon

tax policy, firms have more incentive to improve carbon reduction levels by reducing their carbon tax costs.

However, firms need to bear carbon reduction costs that may cause shortage of capital. Thus, firms may face

problems of financial constraints, which may demotivate firms to produce greener products. To address the

decision-making challenges of firms in the contexts of carbon tax policy and financial constraints, weconsider

a supply chain with a manufacturer who producesgreen products and a retailer who sells these products. Our

study develops five models to investigate the two firms’ optimal wholesale price, carbon reduction level and

ordering quantity, accordingto the manufacturer and retailer with or without financial constraints. Our goal

in this study is to explore how carbon tax policy and banks’ interest rates affect the profits of the two firms,

supply chain and consumer surplus. Certain managerial insights are obtained as follows. We demonstrate

that carbon tax policy and banks’ interest rates demotivate the manufacturer to produce greener products

and demotivate the retailer to order more products. If the interest rate to the manufacturer (retailer) is

relatively low, then the manufacturer with financial constraint benefits (harms) the consumers compared

with the retailer with financial constraint. Importantly, our analysis suggests that carbon tax policy harms

the firms but benefits consumers, and the government in some conditions should reduce unit carbon tax.

Keywords:supply chain finance; carbon tax policy; reduction level; financial constraint

1. Introduction

Environmental pollutions, such as global warming, sea level rising, and soil erosion, are caused by

carbon emissions, which have attracted increasingly great attention from all circles of the society.

∗Corresponding author.

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

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K. Cao et al. / Intl. Trans. in Op. Res. 27 (2020) 2270–2293 2271

To curb carbon emissions, many countries have enacted many policies, such as carbon tax and

cap-and-trade policies (Drake et al., 2016; Tao et al., 2018). Among these carbon policies, carbon

tax policy is widely adopted by many countries, such as Finland, Norway, Sweden, Denmark, the

Netherlands, Germany, United Kingdom, and Australia (Gale et al., 2013). Firms under carbon

tax policy need to improve their carbon reduction levels to curb carbon emissions. However, carbon

reduction costs are a huge burden for them. In this context, certain firms may face problems, such

as financial constraints, which may limit them in cutting carbon emissions.

In practice, there is a typical supply chain with manufacturers and retailers, where manufac-

turers produce products and the retailers order products from these manufacturers and then sell

them. Carbon tax policy affects the product wholesale prices and carbon reduction levels of man-

ufacturers, which may indirectly affect the ordering quantities of retailers. If firms are faced with

financial constraints, then they may loan money from banks that charge them the loan interest

(Kouvelis and Zhao, 2018). These additional costs incurred by loaning may affect firms’ opti-

mal decisions. If facing financial constraints, manufacturers may consider bank loans to address

these constraints. The banks’ interest rates to the manufacturers may affect the manufacturers’

optimal product wholesale prices and carbon reduction levels directly, and optimal ordering quan-

tities of the retailers indirectly. Moreover, if the retailers are faced with financial constraints, then

they may loan money from banks. The banks’ interest rates to the retailers may affect the op-

timal ordering quantities directly, and the product wholesale prices and carbon reduction levels

indirectly. The abovementioned findings raise questions as follows. How do carbon tax policy

and banks’ interest rates affect the manufacturers’ and retailers’ optimal decisions? Do carbon

tax policy and banks’ interest rates benefit the manufacturers, retailer, whole supply chain, and

consumers?

To answer these questions, our studyconsiders a supply chain with a manufacturer and a retailer.

The government enacts carbon tax policy in which the government taxes the manufacturer per

unit carbon emission. In the course of the process, the manufacturer and retailer may encounter

financial constraints. Four scenarios are formulated on the basis of the manufacturer and retailer

with or without financial constraints, namely, the two firms without financial constraints (NN),

the retailer with financial constraint (NY), the manufacturer with financial constraint (YN), and

the two firms with financial constraints (YY). Moreover, under NY we consider two cases: the

retailer loans from a bank (NYB) and the manufacturer offers trade credit to the retailer (NYT).

We develop five models based on these scenarios, investigate optimal product wholesale price,

carbon reduction level, and ordering quantity under the four models, and explore the impacts of

carbon tax policy and banks’ interest rates on optimal solutions, profits, and consumer surplus.

Note that this study considers the stochastic demand function and obtains interesting results and

managerial insights.Our paper is among the first to investigate supplychain finance under carbon tax

policy. Moreover, in practice,our results provide managerial insights for manufacturersand retailers

with and without financial constraints to determine optimal carbon reduction level and ordering

quantity.

The remainder of the paper is organized as follows. Section 2 presents the review of the literature.

Section 3 describes the research problems and introduces the demand function and firms’ cost

structures. Section 4 proposes the four theoretical models. Section 5 provides the analysis and

results. Lastly, Section 6 concludes with the main results and insights. Appendices A–G present all

the proofs.

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2018 The Authors.

International Transactionsin Operational Research C

2018 International Federation of OperationalResearch Societies