Fuzzy input–output model for optimizing eco-industrial supply chains under water footprint constraints
Introduction
The impact of human activities on the environment is now a global concern, and in particular, climate change is perceived to be the most significant problem facing the world today. It is expected to affect global freshwater resources as precipitation patterns change, glaciers melt and sea levels rise. These effects will further intensify water stress experienced from continued population growth, economic development and industrial pollution (Rockstrom et al., 2009). It has been suggested that water may be the limiting resource for some economic activities. Although the industrial sector takes up only an average 22% of the water being used globally, water usage intensity is significant to all businesses whose sustainability will depend on its availability, cost and quality (WBCSD, 2006). Furthermore, industries utilize raw materials derived from agriculture, which utilizes 70% of the global water consumption. This is particularly true in producing biofuels, which have gained popularity due to both energy security and climate change issues. It has been argued that large-scale production of biofuels may be constrained by the availability of agricultural land (Ponton, 2009, Nonhebel, 2005) and water resources (Gerbens-Leenes et al., 2009, Tan et al., 2009a, Tan et al., 2009c, Yang et al., 2009, Harto et al., in press). The link between industrial and agricultural activity indicates that the total water intensity (or water footprint) of an organization or region is not only limited to the operational water directly utilized in processing the final product, but also includes the water utilized in all processes involved in the product supply chain. Accounting for the direct and indirect water use in industrial systems leads to transboundary concerns of virtual water trade vis-à-vis local water availability. For industries, the increasing value of freshwater resources can be viewed as an opportunity for creating new businesses which will provide solutions towards improving the sustainability of industrial water utilization (WBCSD, 2006).
Recent trends in waste management and environmental protection have focused on the development of cleaner production strategies which promote reduction in the generation of waste by reducing the consumption of resources. One approach is industrial ecology (IE), which adopts mechanisms found in natural ecosystems and applies them to industrial systems (Frosch and Gallopoulos, 1989). In particular, industrial symbiosis (IS) where waste materials of one industry are utilized as inputs for another industry can lead to synergies which yield greater benefits than can be achieved by companies acting independently. According to Chertow (2007) the exchange of common utilities such as energy and water often becomes a precursor to the emergence of full blown IS, which may eventually include exchanges of highly specific raw materials. Process systems engineering approaches have recently been developed to aid in the design of IS schemes. For example, Spriggs et al. (2004) and Foo (2008) used pinch analysis for identifying targets for establishing water exchange networks, while Liao et al. (2007) and Lovelady and El-Halwagi (2009) used mathematical programming for designing water exchange networks between different plants in an eco-industrial park (EIP). Chew et al. (2008) utilized the concept of a centralized hub topology for collecting and redistributing water, while Lovelady et al. (2009) used a modified property-based approach for designing EIP networks. Furthermore, as the establishment of these networks requires the cooperation of the participating plants, game theoretic approaches have been used to incorporate the potentially conflicting interests of the participants in designing the network. Kim and Lee (2007) utilized the concept of benefit sharing for designing Pareto optimal networks, and Lou et al. (2004) used emergy-based game theoretic analysis for assessing economic and environmental sustainability strategies under data uncertainty. Chew et al., 2009, Chew et al., in press used game theory approach to assess payoffs based on different water network designs. More recently, Aviso et al., 2010a, Aviso et al., in press b, Aviso et al., 2010b used fuzzy optimization to integrate goals set by the participants in designing the network, and took into account the role of the EIP authority in facilitating the emergence of IS through economic incentives or disincentives.
Fuzzy sets have been used in decision-making to account for uncertainties and inconsistencies in goals, objectives and constraints (Bellman and Zadeh, 1970). Its use in optimizing the design of IS schemes has the advantage of representing and integrating the multiple objectives arising from the presence of multiple decision-makers into a single parameter within the model. Fuzzy sets have also been used for other environmental applications, such as the evaluation of the sustainability of production processes (Tseng et al., 2008, Tseng et al., 2009a, Tseng et al., 2009b), the development of a municipal solid waste management model (Tseng and Lin, 2009) and the selection of sustainable industrial areas (Fernández and Ruiz, 2009) where evaluation criteria were characterized with uncertainty. Recent applications of fuzzy concepts in life cycle based optimization models have also been reported (Tan, 2008, Tan et al., 2008, Tan et al., 2009c).
However, most current studies on the design of water exchange networks have thus far not considered water consumed by a company along its supply chain. In order to assess the actual water intensity of products and processes, the concepts of virtual (Allan, 1998, Chapagain and Orr, 2009) and water footprint (Hoekstra and Hung, 2002, Chapagain and Hoekstra, 2004) have been introduced. These were initially utilized to analyze the water footprint and virtual water trade of nations due to the consumption of agricultural based products (Chapagain et al., 2006, Chapagain and Hoekstra, 2007, Velazquez, 2007) and have been recently extended to the product brand level (Ridoutt et al., 2009, Ridoutt and Pfister, 2010). The relationship of the water footprint to life cycle assessment and similar concepts has been discussed by De Benedetto and Klemes (2009). The concept of water footprint is utilized to assess water intensity at various levels of economic activity depending on the scope and goal of the study being undertaken. The main building blocks are the processes being accounted for either throughout a supply chain or as bounded by the region of interest. The total water footprint is defined as the associated amount of freshwater used to produce the goods and services consumed by a defined group, such as a business entity or a country (Hoekstra and Hung, 2002, Chapagain and Hoekstra, 2007, Chapagain and Hoekstra, 2008). At the enterprise-level, the business water footprint will consist of the total amount of freshwater used (directly and indirectly) to run the business unit; it consists of operational water directly used by the plants, and the indirect water embedded in the raw materials utilized by the plant in the form of virtual water (Gerbens-Leenes and Hoekstra, 2008). The business water footprint is the total amount of water utilized in the supply chain of a business unit in order to support its activities and can be considered as a consumption-based indicator for water use. On the other hand, the water footprint may also be defined to account for the water intensity associated with all the activities within a specified geographical region (Hoekstra et al., 2009) and thus reflects a production-based indicator of water use.
The total water footprint consists of three components, namely, green water, blue water and gray water. Green water pertains to the amount of rainwater evaporated or rainwater incorporated in the product during the production process and is typically applicable to agricultural products. It accounts for the rainwater required to grow a crop and its resulting product yield (Hoekstra et al., 2009). These values are typically derived from models such as the CROPWAT (FAO, 2009). Blue water is the amount of surface and ground water evaporated or incorporated into the product due to the production process or service and is equivalent to the amount of surface or ground water utilized which does not return to the environment. If water is taken up in a process and returned to the environment in liquid form, the net consumption is zero, and all that is required is a footprint index that takes into account the degradation of water quality. This gray water footprint component refers to “the volume of water required to dilute pollutants to such an extent that concentrations are reduced to agreed maximum acceptable levels” (Hoekstra and Chapagain, 2007). It is simply a quantitative index of the extent of harm the pollution in the wastewater stream will contribute, and does not necessarily imply deliberate dilution of wastewater from plant operations. A greater value of gray water indicates that the pollution load of the wastewater stream is high. Furthermore, it takes into consideration the assimilative capacity of the receiving body of water. The overall water footprint is simply the sum of these components. In the production of cotton textile for example, growing the crop requires water. This water requirement will consist of green and blue water footprints. Suppose, for example, that 2000 tons of rainwater (green water) and 5000 tons of irrigation water (blue water) are required to grow a ton of cotton. Furthermore, in order to process the cotton crop into textile, 1000 tons of water is taken up from the environment, and returned as wastewater that meets legislated effluent standards; hence, the associated gray water is 1000 tons. The total water footprint for the production of 1 ton of cotton textile is thus 8000 (2000 + 5000 + 1000) tons.
This paper focuses on developing a model for optimizing the supply chain in the presence of multiple stakeholders/decision-makers and water footprint constraints. The paper is organized as follows. Sections 2 and 3 provide a brief description of the overall nature of the problem being addressed in this paper. Section 4 then discusses the development of the generic model for optimization based on input–output analysis. Two cases are then presented in the succeeding sections to demonstrate the applicability of modified variants of the general model. The first case study accounts water intensity based on the consumer’s perspective and takes into consideration processes which are related vertically via the product supply chain. It optimizes the supply chain network in consideration of water footprint limits set by multiple consumers in the presence of product/process alternatives. The second case study on the other hand utilizes the water footprint concept from a producer’s perspective and accounts for water intensity related to activities contained within a region. It optimizes the exchange network between producers and consumers by satisfying product demands in the presence of resource constraints identified by multiple producers. Finally, conclusions and possible extensions to the problem are presented in the last section.
Section snippets
Generic input–output model
The relationship which exists between the production of goods and exchange of materials between economic sectors within a region can be represented by an input–output model (Leontief, 1936, Leontief, 1951). This basic model has been extended to integrate environmental burdens associated with the consumption of materials in single- and multi-regional trade. It has been utilized as well to assess production flows and evaluate environmental burdens along supply chains (Albino et al., 2002, Albino
Problem statement
The total water footprint of a business unit, an industrial plant or an entire geographic region pertains to the total water consumed in order to sustain its activities. This includes the water used for operations and the water used for the production of raw materials required by the plant. Since raw materials may be acquired from another country or region, environmental burdens may occur in a different location from where the final product is consumed. The general system being considered has NK
Mathematical model
The production of goods has associated water footprint. However, products are traded between different regions and environmental consequences associated to a region’s activities may impact the local environment of another (e.g., through virtual water import or export). For example, regions where water is scarce will benefit from importing water-intensive goods from places where water is abundant. The total water footprint of any Region k may be defined based on a consumer’s or producer’s
Case study 1
The first case study demonstrates the optimization of the water intensity of industrial activities when considering the product supply chain from a consumer-based perspective. The model is used to identify the optimal network for material exchange between regions having similar industries but with different technological specifications while simultaneously satisfying the demand for products of each region and under water footprint constraints. This case considers the tile manufacturing industry
Case study 2
The second case study is focused on the production of biofuels whose popularity has grown due to climate change and the increase in the price of conventional fossil fuels. Ecological footprints for bioenergy systems have been estimated to be about one order of magnitude lower than those of corresponding fossil fuels (Stoeglehner and Narodoslawsky, 2009). Other secondary benefits that have been cited include increased energy security for oil-importing countries, as well as job creation and
Conclusion
A multi-regional fuzzy input–output model has been developed to optimize production and trade under consumption- or production-based water footprint constraints. The approach makes use of scale-invariant technological coefficients and max–min aggregation to yield a linear programming model for which a global optimum may be easily determined. Two case studies have been used to demonstrate the capability of the model in identifying the optimal network of material/product exchange between
Acknowledgment
The authors are grateful for financial support through the Graduate Fellowship Program of De La Salle University.
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