Optimal inventory control policy and supply chain coordination problem with carbon footprint constraints

• Published date: 01 November 2018
• Author: Tijun Fan,Kin Keung Lai,Feng Tao
• Date: 01 November 2018
• DOI: http://doi.org/10.1111/itor.12271

Intl. Trans. in Op. Res. 25 (2018) 1831–1853

DOI: 10.1111/itor.12271

INTERNATIONAL

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IN OPERATIONAL

RESEARCH

Optimal inventory control policy and supply chain

coordination problem with carbon footprint constraints

Feng Tao a, Tijun Fanaand Kin Keung Laib

aDepartment of Management, Science and Engineering, East China University of Science and Technology,

Shanghai, P.R. China

bDepartment of Management Sciences, City University of Hong Kong,Hong Kong

E-mail: ftao@ecust.edu.cn [Tao]; tjfan@ecust.edu.cn[Fan]; mskklai@cityu.edu.hk [Lai]

Received 7 March 2015; receivedin revised form 11 November 2015; accepted 17 January 2016

Abstract

Carbon footprint constraints exertpressure on supply chains to reexamine decisions. In this paper, we consider

carbon transfer cost and carbon holding cost in a supply chain. A multiperiod dynamic programming model

with carbon footprint constraints is presented to investigate the impact of carbon transfer cost and carbon

holding cost on inventory controlpolicy as well as the supply chain coordination problem. A two-controllimit

inventory control policy is proved to be optimal and a contract with wholesale price,subsidy, and fixed setup

cost is verified analytically to coordinate the supply chain. Finally, a numerical study is conducted to reveal

managerial insights. We find that when the supply chain is coordinated, the chain’s profit is more sensitive

to carbon transfer cost while inventory level is more sensitive to carbon holding cost. Additionally, because

of the complexity of the coordinated contract, when it is not easy to coordinate the supply chain, it is better

to keep the values of wholesale price, subsidy, and fixed setup cost below the corresponding values for the

coordinated supply chain.

Keywords:carbon footprint; supply chain coordination; inventory control; dynamic programming

1. Introduction

Global climate change is becoming one of greatest threats to humans, which is largely contributed

by carbon emissions resulting from human activities. In order to reduce carbon emissions, many

countries have enacted legislation or designed mechanisms (Hua et al., 2011; Islegen and Reichel-

stein, 2011; Barker and Davey, 2014), such as carbon label, carbon footprint, carbon tax, exchange

policy and so on. Among these mechanisms, carbon footprint is one of the veryimportant measures

to be implemented.

According to Carbon Trust, UK (2012), carbon footprint “measures the total greenhouse gas

emissions caused directly and indirectly by a person, organization, event or product.” As supply

chain entities are paying more attention to carbon footprints (Shaw et al., 2013), there is a strong

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International Transactionsin Operational Research C

2016 International Federation of OperationalResearch Societies

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1832 F. Taoet al. / Intl. Trans. in Op. Res. 25 (2018) 1831–1853

appeal to optimize inventory control policy and supply chain coordination problem with carbon

footprint constraints.A spectrum of environmental regulations has been continuallyimplemented at

various stages of the supply chain, such as production, distribution, use, and disposal of products.

The Stern report shows that transportation accounts for 14% of total greenhouse gas emissions

(Stern, 2006). Up to 2020, over 80% of the companies providing road freight transport operations

are likely to be affected by climate change (Piecyk and McKinnon, 2010). Carriers can opti-

mize distribution covered network to minimize distance covered and energy consumption, and the

drivers can reduce energy consumption by optimizing the routing (Rizet et al., 2012). On the other

hand, retailers and logistics are emitting significant amounts of carbon at their end, such as the

energy or fuel used for holding inventories (Singh et al., 2015).

Motivated byprior research and carbon footprint constraints on the supply chain, we formulate a

multiperiod dynamic programming model to investigate the impact of carbon footprint constraints

on inventory management and further to analyze the supply chain coordination scheme over a

finite planning horizon. The inventory control policies are characterized analytically and a contract

with parameters including wholesale price, inventory subsidy, and fixed setup cost is determined to

coordinate the carbon footprint of the supply chain.

Our research pertains to the literature on inventory management of the carbon footprint of the

supply chain, which has been widely discussed recently (Choi and Sethi, 2010; Sarkis et al., 2011;

Bouchery et al., 2012; Arikan and Jammernegg, 2014). Chen et al. (2013) consider the impact of

carbon emission constraints on the economic order quantity (EOQ) model and conclude that carbon

emissions can be reduced through operational adjustments without increasing costs significantly.

Jaber et al. (2013) formulate a two-echelon supply chain and examine the effectiveness of different

legislation. Song and Leng (2012) investigatethe stochastic inventory management with newsvendor

settings. They consider a mandatory carbon emission capacity, carbon emission tax, and cap-and-

trade system. Rosiˇ

c and Jammernegg (2013) consider the impact of carbon emission regulations,

carbon tax, and cap-and-trade systems on the second order in a dual sourcing newsvendor model.

The research on channel coordination has attracted considerable attention in the past decade

(Cachon, 2003), which is another stream of literature related to this paper. Kouvelis et al. (2006)

commented that coordinationand contracts are particularly important in a competitive environment

in which the entire supply chain is competing for customers. Individual players coordinate the

supply chain using various contracts for better management of supplier–buyer relationship and

risk management. The contracts specify the parameters, including quantity, price,time, and quality

such that the retailer places orders and the supplier fulfills the orders (Arshinder et al., 2008).

Boyaci (2005) explores the impact of channel inefficiency on ordering decisions and develops

contract schemes to coordinate the supply chain. Palsule-Desai (2013) develops and analyzes a

game theoretical model for revenue-dependent revenue-sharing contracts in which the sharing

among supply chain players depends on the quantum of revenue generated.

The work most related to this paper is Hua et al. (2011), in which they formulate an EOQ model

to investigate how firms manage their carbon footprint in inventory management under the carbon

emission trading system. The impact of carbon trade, carbon emission rights price, and carbon cap

on the optimal order quantity is analyzed and examined in a numerical study. In their paper, the

demand is deterministic such that there is no leftover inventory in each ordering period. However,

retailers may need to periodically determine the inventory level in each decision period and leftover

inventory is in evitable in daily decisions when the demand is stochastic. Generally, the inventory

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2016 The Authors.

International Transactionsin Operational Research C

2016 International Federation of OperationalResearch Societies