Low carbon chance constrained supply chain network design problem: a Benders decomposition based approach

https://doi.org/10.1016/j.cie.2016.06.011Get rights and content

Highlights

  • A chance constrained programming based sustainable supply chain network design model has been proposed.

  • Benders based solution methodology has been proposed.

  • Carbon emissions & Cap and trade issue have been addressed.

  • Performance of the algorithm has been compared with existing solver lpsolve.

  • Various scenarios have been developed by changing various model parameters.

Abstract

This paper proposes a chance constrained based green supply chain network design model addressing carbon emissions and carbon trading issues. The model determines the optimal flow of materials as well as emissions across the supply chain network. The basic model has been further extended into two models addressing different carbon emission issues. This study has contributed to the body of existing green supply chain literature through addressing uncertainties of suppliers’ capacities, plants’ capacities, warehouses’ capacities and demand for sustainable supply chain network design problem. This study applies Benders decomposition algorithm to handle chance constrained sustainable supply chain network design problem. The proposed models are illustrated with suitable examples and results are carefully analyzed and discussed. The results demonstrated that the flow of materials across the supply chain network varies with the change of the probability as well as carbon credit price. The number of openings of the plants is also influenced with the change of carbon credit price. Similarly, variable cost and variable emissions have been found increased and decreased, respectively with the increase of carbon credit price for the base model. The model is also equipped with dissimilar carbon prices for handling cap and trade scenario. This paper may help managers to deal uncertainties as well as managing emissions of a supply chain network.

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.

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