Low carbon chance constrained supply chain network design problem: a Benders decomposition based approach
Introduction
Rapid industrialization, increase of logistics services, modernization of human lives, ever growing population, depletion of greeneries have broadly resulted into increasing the temperature of the earth, which can be called as global warming (Du, Hu, & Wang, 2015). The harmful effects of global warming are being faced by the mankind in terms of various kinds of natural calamities like flood, drought, cyclone, unnatural monsoon, unusual heat, unusual cold, and melting of ice at unusual rate (Dore, 2005). Global warming is a complex problem and certainly, numerous factors are responsible for it. However, most of the studies across the world have unanimously accepted the over emissions of green house gases in the environment as one of the key reasons behind rapid increase of earth’s temperature (Pachauri & Reisinger, 2008). The international communities are assembled on periodic basis and are engaged in negotiation to develop legally binding international laws for carbon footprint reduction (Du et al., 2015, Duan et al., 2014). Several negotiations at global level have resulted into various carbon reduction policies such as carbon emissions tax, inflexible cap, and cap and trade which are gradually being adopted by various economies across the world (Benjaafar, Yanzhi, & Daskin, 2013). As a result, a purely economic oriented approach of conducting business is now facing wide criticism across the world.
Over the period of time, eminent scholars have emphasized on sustainability and its incorporation in corporate strategy to improve the competitiveness of supply chain (Gunasekaran et al., 2015, Hart, 1997, Lash and Wellington, 2007, Packard and Reinhardt, 2000, Porter and Kramer, 2006, Subramanian and Gunasekaran, 2015). Most of them suggested that environmental sustainability should be viewed as an opportunity rather than a risk. Recently, many firms have realized that sustainability is a bottom-line requirement, which cannot be ignored further. The concept of sustainable supply chain is not new. The readers can refer the following review papers for developing an overall idea about various issues related to sustainable or green supply chain (Ahi and Searcy, 2013, Brandenburg et al., 2014, Fahimnia et al., 2015, Seuring and Müller, 2008, Srivastava, 2007).
The concept of low carbon supply chain has recently been established, and received wide attentions across the business communities within very short span of time (Hongjuan & Jing, 2011). According to Alyson Slater, “whatever sector or business you’re in, disclosure is increasingly expected, and failure to disclose can put you at a strategic disadvantage”, Global Reporting Initiative (Bortz, 2007).
Numerous researchers have suggested different ways to manage emissions of a supply chain such as supplier selection (Govindan, Rajendran, Sarkis, & Murugesan, 2015), carbon constrained lot sizing (Purohit, Shankar, Dey, & Choudhary, 2016), supply chain network optimization (Choudhary et al., 2015, Govindan et al., 2015, Zhang et al., 2014), and application of game theory in the context of sustainability (Hafezalkotob, 2015, Ren et al., 2015). Supply chain network design is one of many options to reduce the emissions. Over the period of time, firms have realized the importance of restructuring their supply chain networks to become more sustainable. This realization was observed in a survey, conducted by Aberdeen Group over 300 firms, located in various parts of the world. It was observed that 50% of the surveyed firms wished to redesign their supply chains for becoming more sustainable than earlier (Chaabane et al., 2011, Chaabane et al., 2012, Viswanathan et al., 2008). According to Wu and Dunn (1995) transportation is the largest source of emissions in the logistics system. Therefore, proper optimisation of the supply chain may decrease the emissions of a supply chain. Choudhary et al. (2015) have given significant stress on the development of strategic supply chain network that should serve cost and emissions reductions simultaneously.
Traditionally, supply chain network design problems were mostly analyzed from the perspective of fixed and variable costs without taking carbon footprint factor into account (Elhedhli & Merrick, 2012). However, this trend has been changing rapidly. Environmentally conscious supply chain planning intends to build optimization models where economic aspects such as profit maximization and cost minimization are integrated with environmental goal such as carbon footprint reduction (Sundarakani et al., 2010, Varsei et al., 2014). Over a short span of time, a significant amount of studies have been conducted over sustainable supply chain network design. Despite all the studies, there is a huge potential for developing quantitative models addressing the sustainability issues (Gunasekaran & Spalanzani, 2012).
Interestingly, most of the studies were conducted taking consideration of deterministic environment. As of now, very few studies have been conducted addressing stochastic issues for sustainable supply chain network design (Alhaj et al., 2016, Govindan et al., 2015, Rezaee et al., 2015). Alhaj et al. (2016) study especially considered demand as a stochastic variable and ignored stochastic properties of other variables such as supplier’s capacity, plant’s capacity, and warehouse’s capacity. Their study did not consider the fixed emissions factor for supply chain network design. In the same line, Govindan, Jafarian et al. (2015) and Rezaee et al. (2015) did not consider the fixed emissions for sustainable supply chain network design. We believe that fixed emissions are an integral part for carbon focused supply chain network design. In addition, applications of decomposition techniques (for example: Benders, Lagrangian and Dantzig-Wolfe decompositions) to handle the stochastic sustainable network design problems were sparsely reported in the scientific journals (Rezaee et al., 2015). Most of the time uncertainty issues for green supply chain were managed by applying fuzzy programming techniques (Pishvaee and Razmi, 2012, Pishvaee et al., 2012, Pishvaee et al., 2014, Talaei et al., 2016).
Apart from these, the impacts of probabilities on the flow of materials across the supply chain network have not been adequately studied in the context of sustainable supply chain network design problem. As per our knowledge a combined Benders and chance constrained programming based approach to handle sustainable supply chain network design problems has been inadequately addressed in literature. Most of the time stochastic sustainable supply chain network models were developed considering various scenarios of probabilities (Alhaj et al., 2016, Govindan et al., 2015). This study addresses all the above discussed research gaps of the existing literature.
The aim of this paper is to develop a sustainable supply chain network design model considering the uncertainties of suppliers’ capacities, uncertainties of plants’ capacities, uncertainties of warehouses’ capacities and uncertainties of customers’ demands. The study also applies Benders based solution methodology to solve the proposed problem.
Few contributions of this paper are as follows. This paper applies the chance constrained programming to handle uncertainties of various variables in sustainable supply chain network design problem. A Benders based solution methodology is proposed to handle the proposed model. This paper also conducted various sensitivity analyses considering different probability levels of different factors. The analyses may be helpful for managers to manage the carbon footprint as well as cost in the competitive world. The remainder of the paper is organized as follows. Section 2 discusses the relevant literature related to sustainable supply chain network design, stochastic supply chain network design, and network design using Benders decomposition. Section 3 presents the proposed model and the proposed methodology. Section 4 addresses the illustrative example. And lastly, Section 5 reports the conclusion of the paper.
Section snippets
Literature review
Supply chain network design is an ever green research topic. As of now, a significant amount of studies have been conducted addressing various aspects of the business. For more details about the existing literature related to supply chain network design, readers may refer the following review papers: Vidal and Goetschalckx, 1997, Meixell and Gargeya, 2005, Melo et al., 2009, Klibi et al., 2010, Farahani et al., 2012. Carbon constrained supply chain network design is relatively new concept as
Model development
In this section, a chance constrained mixed integer programming model is proposed for a single product supply chain with four echelons: suppliers, plants, warehouses and customers. In this model, procurement of the material is conducted from a pool of potential suppliers. The potential suppliers can be identified based on different criteria such as quality, cost, environmental performance and delivery performance. This study considers environmental impacts of logistics as well as environmental
An illustrative example
The effectiveness of the proposed model is illustrated through a hypothetical case of a supply chain. The considered supply chain consists of a set of suppliers, plants, warehouses and customers. In this study, required data to illustrate the model are generated randomly. Table 1 shows the data related to the capacities of the suppliers, standard deviations of supplying capacities, variable costs from suppliers to plants and variable emissions from suppliers to plants, respectively. Variable
Conclusion
Carbon footprint reduction has become a critical factor for conducting business. This study intends to address carbon emissions factors in a supply chain network design problem. Contributing to existing green supply chain literature, this study has modeled the stochastic behaviors of various factors by applying chance constrained programming. The chance constrained based problem has been subsequently converted into a deterministic formulation. The modified model has been solved by using Benders
Acknowledgements
The authors sincerely acknowledge the valuable comments of the anonymous referees and support of the editor, which have helped to improve the quality of this paper.
References (72)
- et al.
Green supply chains with carbon trading and environmental sourcing: Formulation and life cycle assessment
Applied Mathematical Modelling
(2012) - et al.
A carbon-sensitive two-echelon-inventory supply chain model with stochastic demand
Resources, Conservation and Recycling
(2016) - et al.
A multiobjective chance constrained programming model for supplier selection under uncertainty
Transportation Research Part B: Methodological
(2011) - et al.
An integrated approach for sustainable supply chain planning
Computers & Operations Research
(2015) - et al.
Quantitative models for sustainable supply chain management: Developments and directions
European Journal of Operational Research
(2014) Benders decomposition applied to multi-commodity, multi-mode distribution planning
Expert Systems with Applications
(2009)- et al.
Design of sustainable supply chains under the emission trading scheme
International Journal of Production Economics
(2012) - et al.
A carbon market sensitive optimization model for integrated forward–reverse logistics
International Journal of Production Economics
(2015) A survey on benders decomposition applied to fixed-charge network design problems
Computers and Operations Research
(2005)- et al.
How will the emissions trading scheme save cost for achieving China’s 2020 carbon intensity reduction target?
Applied Energy
(2014)
Climate change and changes in global precipitation patterns: What do we know?
Environment International
Optimal carbon taxes in carbon-constrained China: A logistic-induced energy economic hybrid model
Energy
Green supply chain network design to reduce carbon emissions
Transportation Research Part D
Sustainable supply chain network design: An optimization-oriented review
Omega
Green supply chain management: A review and bibliometric analysis
International Journal of Production Economics
Covering problems in facility location: A review
Computers & Industrial Engineering
Bi-objective integrating sustainable order allocation and sustainable supply chain network strategic design with stochastic demand using a novel robust hybrid multi-objective metaheuristic
Computers & Operations Research
Multi criteria decision making approaches for green supplier evaluation and selection: A literature review
Journal of Cleaner Production
Sustainability of manufacturing and services: Investigations for research and applications
International Journal of Production Economics
Green supply chain collaboration and incentives: Current trends and future directions
Transportation Research Part E: Logistics and Transportation Review
Competition of two green and regular supply chains under environmental protection and revenue seeking policies of government
Computers & Industrial Engineering
The strategies of advancing the cooperation satisfaction among enterprises based on low carbon supply chain management
Energy Procedia
Multi-objective green supply chain optimization with a new hybrid memetic algorithm using the Taguchi method
Scientia Iranica
The impact of carbon policies on supply chain design and logistics of a major retailer
Journal of Cleaner Production
Hybrid robust and stochastic optimization for closed-loop supply chain network design using accelerated Benders decomposition
European Journal of Operational Research
Benders’ decomposition for concurrent redesign of forward and closed-loop supply chain network with demand and return uncertainties
Transportation Research Part E: Logistics and Transportation Review
The design of robust value-creating supply chain networks: A critical review
European Journal of Operational Research
Design and planning for green global supply chains under periodic review replenishment policies
Transportation Research Part E
Global supply chain design: A literature review and critique
Transportation Research Part E
Facility location and supply chain management – A review
European Journal of Operational Research
A high performance neural network model for solving chance constrained optimization problems
Neurocomputing
Accelerating Benders stochastic decomposition for the optimization under uncertainty of the petroleum product supply chain
Computers & Operations Research
Environmental supply chain network design using multi-objective fuzzy mathematical programming
Applied Mathematical Modelling
An accelerated Benders decomposition algorithm for sustainable supply chain network design under uncertainty: A case study of medical needle and syringe supply chain
Transportation Research Part E
Credibility-based fuzzy mathematical programming model for green logistics design under uncertainty
Computers & Industrial Engineering
Non-stationary stochastic inventory lot-sizing with emission and service level constraints in a carbon cap-and-trade system
Journal of Cleaner Production
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