A multi-objective optimization for green supply chain network design

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Abstract

In this paper, we study a supply chain network design problem with environmental concerns. We are interested in the environmental investments decisions in the design phase and propose a multi-objective optimization model that captures the trade-off between the total cost and the environment influence. We conduct a comprehensive set of numerical experiments. The results show that our model can be applied as an effective tool in the strategic planning for green supply chain. Meanwhile, the sensitivity analysis provides some interesting managerial insights for firms.

Research Highlights

► We study a supply chain network design problem with environmental considerations. ► We find that supply chain networks with larger capacities exhibits lower total cost and lower CO2 emission. ► Consideration of environmental emissions of supply chain network is more effective and necessary at a higher demand level.

Introduction

The operations in supply chain and logistics are part of today's most important economic activities as they remain to be vital tools for businesses to remain competitive. The ever growing volume of activity generated by both passenger and freight transportation not only benefits the growth and sustainability of international economy and globalization but also has its own consequences, particularly those pertaining to the environment. Transportation activities are significant sources of air pollution and greenhouse gas emissions, with the former known to have harmful effects on human health and the latter, responsible for global warming. These issues have raised concerns on reducing the amount of emissions worldwide. In this respect, many countries, including both developed countries and developing countries, have set strict targets on reducing their carbon emissions in the near future. For example, China, in its 11th five year developing plan, sets a clear objective to “reduce the carbon emission by 10%.” The central government is studying and ready to publish regulatory policies for protecting environments, which are expected to play positive effects on resolving current environment problems. Billions of dollars are spent each year by government and private enterprise on the environmental pollution control.

Some leading companies are now proactively implementing “green” initiatives. For example, the largest furniture manufacturer, IEKA, built a train transportation network with an emphasis on the “greenness” of train operations. HP, IBM, and GE are all taking “green” as an important merit in their enterprise's value system in order to maintain good public images. They are designing greener products by adopting new energy saving technology. Besides product design, they are also thinking of enhancing their supply chain management capability to release environmental concerns. For example, the global procurement center of IBM, located in Shenzhen, China, adds “CO2 Emission, Solid Waste Produced” and other environment related indicators in the logistics management KPIs. We are motivated to study a “green” supply chain network design problem where an initial investment on environmental protection equipment or techniques should be determined in the design phase. This investment can influence the environmental indicators in the operations phase. Therefore, a trade-off exists between the initial investment and its long-term benefit to environment. With such a concern, the decisions on facility location and capacity allocation have to be integrated with the decision on environmental investment.

There is a large amount of literature on supply chain management concerned with environmental issues through the emerging concept “green supply chain management” (GrSCM). According to the most recent comprehensive review on GrSCM by Srivastava [34], two types of “greenness” are considered by researchers: green design for products [18] and green operations. Our research falls in the second category which is mainly composed of green manufacturing and remanufacturing [32], reverse logistics and network design [10], [38], and waste management [4], [5]. Among them, the most relevant work is the reverse logistics network design problem which focuses on setting up some special facilities (i.e., recovery center) to enable the recycling initiatives [10] or optimizing the network configurations in a close-loop network [31]. However, our research has a different perspective on the “greenness.” More specifically, we are interested in the environmental investment decision making in the network design phase and taking precautions against environmental pollution.

Another relevant research is the classical supply chain network design problem which receives a lot of researchers' attentions. The network design problem is one of the most comprehensive strategic decision problems that needs to be optimized for long-term efficient operations of the whole supply chain. It determines a portfolio of configuration parameters including the number, location, capacity, and type of various facilities in the network. The problem covers a wide range of formulations ranged from linear deterministic models [20], [24], [28] to complex non-linear stochastic ones [30], [33]. In literature, there are different studies dealing with the design problem of supply networks and these studies have been surveyed by Vidal and Goetschalckx [36], Beamon [3], Erenguc et al. [9], and Pontrandolfo and Okogbaa [27]. Researchers have attempted to extend the classical model by incorporating various factors such as transportation modes [37,6], tax issue [18], risk management [1], [13], etc. However, we do not find any one that explicitly considers the environmental investment decision in the design phase. On the other hand, the supply chain network design problem is usually modeled as a single objective problem [20,30]. However, any “design” in nature is usually involving trade-offs among different incompatible objectives. Therefore, considering supply network design with multi-objective optimization is another influential trend worthy of study. Comparing that with single objective, it is more reasonable and more practical in terms of actual applications. As we know, multi-objective optimization is widely used in a variety of areas [14], [16], [19], [25], [29] and is also used to embed into a multitude of decision support system [8], [12], [35]. Recently, multi-objective optimization of supply chain network design has been considered by different researchers in literature. For example, a multi-objective programming model is proposed by Mincirardi et al. [23] to analyze solid waste management. Gabriel et al. [11] propose a model for simultaneously optimizing the operations of both integrated logistics and its corresponding used-product reverse logistics in a close-looped supply chain. Alçada-Almeida et al.[2] propose a multi-objective programming approach to identify the locations and capacities of hazardous material incineration facilities and balance the society, economic, and environmental impacts. However, their study was limited in a special situation. It cannot be extended to common scenarios. Another related study is conducted by Paksoy et al. [26], who considered the green impact on a close-looped supply chain network and tried to prevent more CO2 gas emissions and encourage the customers to use recyclable products via giving a small profit. They have presented different transportation choices between echelons according to CO2 emissions. They also considered recyclable ratio of raw material. However, it always needs to set up some special recycle facilities in a close-looped supply chain network, which limits its applications to a certain extent.

In this paper, we make the following contributions:

  • 1)

    We provide a multi-objective mixed-integer formulation for the supply chain network design problem. To our knowledge, it is the first model that considers the environmental investment decision in the supply network design phase. The multi-objective model explicitly considers the environmental issues by introducing a new category of decision variables: the environmental protection level (we will explain this concept later). This new type of variables links the decision of environmental investment in the planning phase as well as its environment influence in the operation phase.

  • 2)

    We apply a normalized normal constraint method, which is a posteriori articulation of preference method and can find a set of even distributed Pareto optimal solutions so that the result obtained can be easily applied to the decision support systems which the industry needs.

  • 3)

    We conduct a comprehensive set of numerical studies and characterize the Pareto solutions especially their sensitivities to various parameters. Consequently, we reach some useful managerial insights. For example, we find that, if we install more capacities in the network, not only the total cost but also the total environmental influence can be reduced.

The rest of the paper is organized as follows. In the next section, we detail our problem and present our general model. In Section 3, we optimize the given model by a linearization step and summarize the solving method. In Section 4, we conduct numerical experiments to characterize the optimal solutions and their sensitivities to various input parameters. Some interesting managerial insights are also introduced. Finally, conclusions are given in Section 5.

Section snippets

Problem definition and modeling

Consider a supply chain network, G = (N,A), where N is the set of nodes and A is the set of arcs. Here, N is composed by the set of suppliers, S, facilities, F, and customers, C, i.e., N = S  F  C. When given demand forecasting, we not only aim to choose the potential suppliers from the suppliers set and decide which facility to open and finally consider how to distribute the product but also consider the CO2 emission in each process of the whole network. Let us define:

    Parameters

    P

    the set of products

    dip

    the

Solving approach

In this section, we first introduce a modified model that transfers the GM as a linear program. Then, we introduce the solving approach.

First, due to the discrete and bounded property of zj, let us introduce a series of binary variables:zjl={1, if the environment protection level l is selected;0, if otherwise.

Note that the decision maker selects one and only one environmental protection level. Hence, we can reach the following property:

Property 1

We can rewrite zj=lLzjll, wherelLzjl=yj,jF

Proof

We consider

Computational experiments

In this section, in order to evaluate the model, we create two examples: a six-node problem and a mid-size network. By the first example, we want to portrait a real scenario for demonstrating the solutions. In the second example, we focus on the sensitivity analysis and its managerial insights. The problem is solved by the normalized normal constraint method and it is implemented by Microsoft Visual C++ 6.0, and each sub-problem is solved by ILOG CPLEX 9.0 solver subroutine. All the experiments

Conclusions

In this paper, we introduce a green supply chain network design model based on the classical facility location problem for the firm's strategic planning. The distinguishing feature of our model is its consideration of environmental element which includes environmental level of facility and environmental influence in the handling and transportation process. This model will have an important application in the regional or global supply chain network design with green consideration.

The model is a

Acknowledgements

This paper is supported by the National Natural Science Foundation of China (NSFC) under Project Nos. 70971142 and 70802063.

Fan Wang is a professor of operations and information management in Sun Yat-sen Business School, Sun Yat-sen University (China), and senior visiting professor in Grenoble de Management (France). His research interests include service operations management, E-service, and business analysis and optimization.

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    Fan Wang is a professor of operations and information management in Sun Yat-sen Business School, Sun Yat-sen University (China), and senior visiting professor in Grenoble de Management (France). His research interests include service operations management, E-service, and business analysis and optimization.

    Xiaofan Lai is currently a PhD student in The Hong Kong Polytechnic University. His research interests include operations management and optimization.

    Ning Shi is an associate professor in Sun Yat-sen Business School, Sun Yat-sen University. His primary research interests include supply chain and logistics management and financial engineering.

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