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A Classroom Simulation to Teach Economic Input−Output Life Cycle Assessment


Address correspondence to:
Troy Hawkins
Industrial Ecology Program
Norwegian University of Science and
Realfagsbygget E1-137, Høgskoleringen 5
NO-7014 Trondheim, Norway


Life cycle assessment (LCA) methods and tools are increasingly being taught in university courses. Students are learning the concepts and applications of process-based LCA, input−output-based LCA, and hybrid methods. Here, we describe a classroom simulation to introduce students to an economic input−output life cycle assessment (EIO-LCA) method. The simulation uses a simplified four-industry economy with eight transactions among the industries. Production functions for the transactions and waste generation amounts are provided for each industry. Students represent an industry and receive and issue purchase orders for materials to simulate the actual purchases of materials within the economy. Students then compare the simulation to mathematical representations of the model. Finally, students view an online EIO-LCA tool (http://www.eiolca.net) and use the tool to compare different products. The simulation has been used successfully with a wide range of students to facilitate conceptual understanding of one EIO-LCA method.


The field of life cycle assessment (LCA) has experienced a shift in recent years from an analysis method used by academic researchers to an important practice for decision makers in business and policy. As businesses demand environmental responsibility from suppliers and as policy makers evaluate more complex scenarios, firms hiring for positions that previously had no relation to environmental issues now want staff who are able to competently address social and environmental issues related to their role within the organization. Thus, demand for workers trained in LCA methods is increasing. Employees are expected to have a range of experience with process-based methods (Baumann et al. 2006), input−output (IO) methods (Hendrickson et al. 1998; Joshi 2000; Albino et al. 2003; Hendrickson et al. 2006; Peters and Hertwich 2006), hybrid approaches (Suh et al. 2004; Udo de Haes et al. 2004; Hawkins et al. 2007), commercial software packages (NIST 2007; PE International 2008; Pré Consultants 2008), and various data sources (NREL 2008; Swiss Center for LCI 2009). Many universities now offer courses in LCA and environmental analysis to train students in these methods and tools.

One IO-based LCA approach that has become part of a number of graduate-level LCA curricula is the economic IO LCA (EIO-LCA) tool developed at Carnegie Mellon University (Hendrickson et al. 1998; Hendrickson et al. 2006). The EIO-LCA tool is based on Wassily Leontief's (1970) IO method for environmental analysis. The approach uses transactions between industry sectors, along with environmental emissions data (e.g., sulfur dioxide, particulate matter, carbon dioxide) and natural resource consumption data (e.g., coal, natural gas, petroleum products), to determine the environmental impacts throughout supply chains within the economy.

The EIO-LCA tool, based on national IO tables and a variety of environmental, energy, and material data sources, has been widely used and extended by LCA researchers and practitioners for analyzing consumer products (MacLean and Lave 1998; Williams 2004), infrastructure (Horvath and Hendrickson 1998; Ochoa et al. 2002), emerging technologies (Lloyd et al. 2005), industry sector impacts (Matthews and Hendrickson 2002; Marriott and Matthews 2005; Sharrard et al. 2007), and the international impacts of U.S. household consumption (Weber and Matthews 2007). The EIO-LCA method is available as an Internet tool (http://www.eiolca.net) with a simple user interface to provide wide access to the method. Currently, the Internet tool includes models of EIO-LCA for the United States (1992 and 1997), Canada, Germany, and Spain as well as models based on producer and purchaser prices and custom-designed sectors.

The availability and simplicity of the online tool led to its use with students in undergraduate classes as well as in an educational outreach program for high school students. Through these experiences, our team at Carnegie Mellon University discovered the importance of having a working understanding of the method for appropriately interpreting the user interface and results of the tool. In response to the need to teach students the EIO-LCA method, we created a simulation exercise to be done in a classroom setting to provide students with a hands-on representation of the method and its results. The simulation uses a simplified economic model consisting of only four industry sectors, with only eight transactions between them. Students simulate the transactions between the industries, then determine the amount of two environmental emissions from the transactions. The simulation replicates the mathematical steps of the EIO-LCA method and the results of the online tool.

Our primary purpose in this article is to provide a description of the classroom activity we have developed so that it can be easily used by others in their own teaching. Our secondary purpose is to discuss what we have learned through the development and implementation of this activity to provide a basis for the creation and improvement of activities intended to convey concepts of industrial ecology in a way that is accessible to a general audience. In this article, we describe the simplified model and simulation exercise for use in a classroom setting, discuss outcomes we have observed working with students, and reflect on our experience with the simulation exercise.

The goal of the simulation activity is to illustrate how environmental impacts occur along the entire supply chain of a product, represent the complexity of the relationships between industries, and demonstrate how industry transactions can be used to estimate environmental impacts. After performing the simulation and the related activities, students should be able to

  • • describe the environmental impacts of a product in terms of its supply chain and economic circularity,
  • • explain how industry purchases can be used to estimate the economic activity and environmental impacts associated with a product,
  • • discuss advantages and limitations of the EIO-LCA method, and
  • • describe how the model results can help decision makers target efforts to reduce environmental impact.

The simulation emphasizes the potential complexity within the supply chain or, more appropriately, supply web of a product; the circularity of transactions among suppliers; and how matrix-based methods can be used to account for all inputs into a product or process. In this way, the simulation demonstrates how difficulties in accounting for boundary conditions can be overcome with an IO LCA approach.

Design of the EIO-LCA Simulation Exercise

The basis of the simulation is a hypothetical economy made up of four industries: a soft drink producer, a water treatment facility, a can manufacturer, and an aluminum manufacturer, as shown in Figure 1. The soft drink producer packages its soft drinks only in 12-ounce cans. The can manufacturer makes empty aluminum cans. The aluminum manufacturer makes aluminum. The water treatment facility produces clean, drinkable water. The arrows in the figures represent the transactions between industries. For example, the soft drink producer requires water from the water treatment facility and empty cans from the can manufacturer. Each of these eight arrows indicates that one industry purchases materials from another.

Figure 1.

Four-industry, eight-transaction model economy for the simulation. Note that soda is another term for soft drink.

In an attempt to mimic actual production requirements, we assigned realistic physical units to the transfers between industries when feasible. A summary of these transfers can be found in Table 1. The soft drink producer consumes 1 gallon (128 ounces) of water to produce ten 12-ounce cans of soft drink, and it needs ten empty cans to produce ten 12-ounce cans of soft drink. The can manufacturer requires 1 pound of aluminum sheet to produce 32 empty cans (Can Manufacturer's Institute 2007). The aluminum manufacturer needs 1.58 gallons of water to produce a pound of aluminum (IAI 2003). We used gallons and pounds in an attempt to keep the exercise as simple as possible for U.S. high school students, for whom these measures are most familiar. In another context, we would suggest converting to SI 1 or other locally familiar units.

Table 1.  Direct requirements matrix for the four-industry simulation
IndustrySoft drink producerCan manufacturerAluminum manufacturerWater treatment facility
  1. Note: Al = aluminum.

Soft drink producer0005 cans of soft drink
10,000 gallons water
Can manufacturer1 empty can
1 can of soft drink
01 empty can
2 pounds Al
Aluminum manufacturer01 pound Al
32 empty cans
05 pounds Al
1,000 gallons water
Water treatment facility1 gallon water
10 cans of soft drink
5 gallons water
1,000 empty cans
1.58 gallons water
1 pound Al

In certain cases, the actual transactions between industries are unknown or result in very small values (thus ending the simulation too quickly). To provide interesting numerical results in the simulation, we have taken some liberties in inventing transactions. Therefore, the can manufacturer requires 5 gallons of water for every 1,000 cans produced (this value is more than the actual amount). The aluminum manufacturer purchases scrap and low-quality cans from the can manufacturer—the equivalent of one can's worth of recycled scrap material goes into two “new” pounds of aluminum. The actual amount of recycled material in a pound of aluminum varies widely and originates from a number of sources in addition to postconsumer aluminum cans. Finally, although the values for the water treatment facility are artificial, we have found that, with some justification, they are acceptable to students. First, the water treatment facility purchases soft drinks for its workers—five cans for every 10,000 gallons of water produced. Clearly, the workers are tired of seeing water all day and want something else to drink. Next, the water treatment facility purchases 5 pounds of aluminum for every 1,000 gallons water produced for the replacement of pipes that wear out in the course of normal use. As shown in Table 1, each industry's use of the others’ products is presented in the form of a direct requirements matrix used in IO models.

We also designate environmental impacts for the facilities in terms of wastewater and mixed solid wastes, as shown in Table 2. These figures represent waste generated within a given industry in production of the single product in that industry. Again, we used actual data when they were available or created realistic data on the basis of production requirements.

Table 2.  Waste production per unit output for the four-industry simulation
IndustryWastewaterMixed solid waste
  1. Note: Al = aluminum.

Soft drink producer8 ounces/10 cans1 pound/100 cans
Can manufacturer5 gallons/1,000 empty cansNone
Aluminum manufacturer1.58 gallons/pound Al2.7 pound/pound Al
Water treatment facilityNone1 pound/1,000 gallons water

The premise of the simulation is to have a group of four students work together, each representing a single industry. During the simulation, an industry receives a request from another industry for its product. This request requires the industry to request materials from other industries in its own supply chain. To represent this ongoing series of requests through the supply chain, we created “purchase orders” for each industry to complete and present to other industries (see Figure 2). These purchase orders allow students to monitor incoming requests and determine the amount of goods they, in turn, need to purchase. Students are also given a log sheet (see Figure 3) for their industry to record both incoming purchase orders and outgoing requests for raw materials.

Figure 2.

Purchase order for the simulation. Students complete purchase orders for materials needed and give them to the representative of the appropriate industry.

Figure 3.

Log sheet for the simulation. Students record information from purchase orders received on the left, then calculate the materials needed to fulfill those purchase orders on the right. Then they write purchase orders for those materials. Note that there are no horizontal lines in the portion the students fill out, because different industries will record more or fewer purchase orders as a result of each purchase order received.

The purchase orders and log sheet require students to perform the necessary calculations for determining the flow of materials through the supply chain. Students then use results from the transactions to calculate the amount of wastewater and mixed solid waste generated at each facility. After the simulation, students participate in a discussion of the results, analyzing the circularity of the supply chain and identifying the overall impact on the environment. We then present the simulation in mathematical terms—first algebraically, then in matrix form. Finally, we present the online version of the EIO-LCA tool, selecting an example analysis to run and discussing the results.

Using the Simulation in a Classroom Setting

In this section, we describe the inclusion of the simulation in a classroom setting. We have divided the activity into three parts: (1) calculation and discussion of production and waste totals, (2) comparison of simulation logs with mathematical equivalents, and (3) use of the Web-based EIO-LCA tool. Instructors can use either all three parts or parts 1 and 3 together, depending on the background of the students. For each part, we list required materials and an approximate time in boxes 1, 2, and 3. The Supplementary Material available on the Web includes copies of the student worksheets and spreadsheets listed in the materials required.

In class, we divide the students into groups of four and present them with the four-industry model. During this part of the activity, groups are asked to focus their attention on the industry transactions sheet (see Figure 1; see also W2 in the Supplementary Material on the Web). We present the students a text describing the eight interindustry transactions and ask each group to add the numerical ratios to the industry transactions sheet (W2). We then discuss the transactions and the accompanying units, emphasizing that the units of the denominator are the units for the purchasing industry (e.g., cans of soft drink for the soft drink producer, empty cans for the can manufacturer). Next, we ask students to respond to simple transaction requests. For example, knowing that the soft drink producer requires 1 gallon water for 10 cans of soft drink, we ask for the amount of water the producer must purchase directly to produce 100 cans of soft drink (answer: 10 gallons); knowing that the water treatment facility requires 5 cans of soda for every 10,000 gallons of water delivered, we ask for the number of cans of soft drink purchased for 25,000 gallons of water delivered (answer: 12.5 cans of soft drink).

Box 1. Part A: Calculation and Discussion of Production and Waste Totals
Materials Required:
 • Calculator (1 per student)
 • Pencil (1 per student)
 • Industry Transactions Sheet, W1 (1 per group)
 • Log Example Sheet, W2 (1 per group)
 • Log Sheet, W3 (1 per student)
 • Purchase Order Organizer, W4 (1 per student)
 • Purchase Orders, W6 (approximately 15 per student)
 • Final Total Sheet, W5 (1 per group)
Approximate Time Required:
 • Activity introduction and completing Industry Transaction Sheet—10 minutes
 • Initial round of simulation—5 minutes
 • Group simulation—10 minutes
 • Calculating total production and environmental impacts—10 minutes
 • Discussion—10–15 minutes
It is helpful to have one or more assistants who have performed the simulation themselves to observe and guide the individual groups.

Next, we introduce the purchase orders (W6), the purchase order organizer (W4), and the log (W3). Students exchange purchase orders to represent requests for materials. Each participant places his or her purchase order organizer (W4) toward the center of the group so that others can place their requests in the form of purchase orders on the “received” side of the purchase order organizer belonging to the participant representing the industry they are purchasing from. An industry selects a purchase order, records the request for materials on the left side of the log sheet (W3), uses the production ratios calculated earlier and recorded on the industry transactions sheet (W1) to calculate the amounts of materials that must be purchased to fulfill the purchase order, issue the appropriate purchase orders, and moves the original purchase order to the “completed” side of the organizer (W4). We have found it is best to demonstrate this process once in painstaking detail to avoid confusion later in the simulation.

We begin the actual simulation by presenting the soft drink producer with a purchase order from an outside industry, the soft drink distributor, for 1 million cans of soft drink. Participants are then asked to log the resulting purchase order requests and issue purchase orders for necessary supplies. For younger students, it may be necessary to have them perform the first set of transactions as a group to ensure that each student sees how the initial purchase order for the 1 million cans of soda results in an entry on the log sheet for the soft drink producer and two purchase orders issued—one for water, and one for empty cans. For university-level students, we ask them to perform calculations only for the first two tiers of transactions: soft drink producer to water treatment facility and can manufacturer (Tier 1), then water treatment facility to soft drink producer and aluminum manufacturer (Tier 2), and then can manufacturer to aluminum manufacturer and water treatment facility (Tier 2). We then pause to orally check results to verify that students are following the simulation correctly.

Students then continue the simulation, receiving and logging purchase orders given to their industry, then determining materials needed and issuing purchase orders for those materials. All purchase order requests should be logged and calculations for materials completed by the student representing the appropriate industry. We ask students to stop issuing purchase orders when the amount of material that would be requested becomes less than one unit. The supply chain ends at that point. The students perform calculations and issue purchase orders until all requests are less than one unit or a time limit has been reached. A completed log sheet for the soft drink producer is shown in Figure 4. Note that purchase orders are received only from the water treatment facility, whereas purchase orders are issued to both the water treatment facility and the can manufacturer. The order in which the purchase orders are recorded and written is not important, although it can be interesting to see the transactions proceed in tiers.

Figure 4.

Completed log sheet for the soft drink producer. Purchase orders are received from the soft drink distributor initially, then only from the water treatment facility (water). Purchase orders are issued to the can manufacturer (Can Mfr) and the water treatment facility.

Once students complete the exchange of purchase orders, each student (or industry) determines his or her total production. This is the sum of amounts on purchase orders received that has been recorded on the left side of the log sheet. Students transfer this value to the final totals sheet, where they use the information on solid waste and wastewater created per unit of product to calculate the total waste generated at each facility. The completed final totals sheet is shown in Table 3. Figure 5 shows the environmental implications of the supply chain economic activity associated with the production of the million cans of soft drink. After reviewing the students' completed final totals we have found it helpful to use Figure 5 to display the results visually to help students visualize the relative scale of impacts and to provide an example of how data should be displayed simply and clearly.

Table 3.  Completed final totals sheet for the simulation
IndustryAmount producedWastewater per unitTotal wastewaterSolid waste per unitTotal solid waste
  1. Note: Results are given beyond reasonable significant digits so that students can check whether their results match. Al = aluminum; lb = pound.

Soft drink producer1,000,078 cans8 ounces per 10 cans6,250 gallons1 lb per 100 cans10,001 lbs
Can manufacturer1,016,339 empty cans5 gallons per 1,000 empty cans5,082 gallons  
Aluminum manufacturer32,525 lbs Al1.58 gallon per lb Al51,389 gallons2.7 lbs per lb Al87,816 lbs
Water treatment facility156,475 gallons  1 lb per 1,000 gallons water156 lbs
Total for all  62,721 gallons 97,974 lbs
Figure 5.

Volume of wastewater (gallons) and amount of solid waste (pounds) generated by the various industries in the simulation. The fraction that occurs at the soft drink (soda) producer, the industry that received the initial request, is only a small amount of the total wastes generated.

The discussion at this point focuses the students on two key points:

  • • The waste generated from the production of 1 million cans of soft drink (if calculated from the known ratio) vastly underestimates the total waste generated. When the entire supply chain is considered, other industries provide the largest contribution to the wastes.
  • • The total amount of production from the soft drink producer is more than the original 1 million cans of soft drink. When one considers the entire supply chain, the total amount of production includes the million cans of soft drink plus the demand for soft drink by the water treatment facility. It also includes production of empty cans, aluminum, and water for the other industries in the economy.

We discuss the implications of the totals. For example, if the soft drink producer wants to minimize wastewater generated from production, it should focus on reducing its aluminum consumption rather than on the wastewater generated in its own facility. It could do so by using less aluminum per can or a larger can. Using a larger can, however, raises issues related to the functional unit desired. Once the can is opened, the soft drink will not last long. Instructors can highlight many points in the discussion, including direct versus indirect production and impacts, the potential effect of including more industries and transactions in the model, other environmental impacts that might be added to the model, and impacts related to transportation of goods between facilities. To prepare students to interpret results of the EIO-LCA tool later, it is helpful to discuss how industry sectors are defined. In this example, each industry produces a single product; however, in reality, an industry sector could produce both distinct products and similar products with a range of characteristics. For example, the computer industry produces both laptops and desktops (distinct products) as well as laptops with varying features and capabilities (similar products with different characteristics). To stimulate critical and creative thinking, it can also be interesting to discuss shortcomings of the model and ways to improve its estimates of environmental impact. A simple example is increasing the number of sectors. This discussion could include deciding which sectors would be the most important additions to the model. Another interesting topic for discussion is the additional information and analysis needed for decisions makers. The simulation provides information on the wastes generated at the facilities (environmental inventory) but does not provide any information about the impact of those wastes on environmental systems (environmental midpoints) or the implications of those impacts for environmental and human health (environmental endpoints).

Box 2. Part B: Comparing Simulation Logs With Mathematical Equivalents
Materials Required:
 • Mathematical Equivalent Spreadsheet
Approximate Time Required:
 • Algebraic equivalents—5–10 minutes
 • Matrix formulation—10–20 minutes
 • Discussion of EIO-LCA method—10–15 minutes

The next part of the exercise involves relating the series of calculations performed during the simulation to their mathematical equivalents, both algebraically and in matrix form. This is not essential to interpreting model results or using the online tool. Depending on the level of the students and the instructor's goals, this portion of the activity can be omitted or can be modified to meet individual needs.

We instruct students to examine their log sheets to see how the results they calculated can be formed into general equations. Algebraically, the amount of goods requested in the first tier can be expressed as follows, where Y is the initial demand of goods (in our case, 1 million cans of soft drink):


Equations (1) and (2) provide the amounts on the first purchase orders issued to the can manufacturer and the water treatment facility. This, in turn, results in the following equations for the can manufacturer,


and the water treatment facility,

Cans soft drink


Equations (3) and (4) represent the second-tier purchases by the can manufacturer, whereas equations (5) and (6) represent the second-tier purchases by the water treatment facility. Students quickly see that the simulation could be extended to additional industries and transactions, as long as the production ratios were known. They also see that the calculations could continue indefinitely, as each round results in more materials that need to be produced. The size of transactions quickly approaches zero, however.

Students with knowledge of linear algebra techniques can reformulate the algebraic equations in matrix form. Note that for all vectors and matrices, the industries are in the order of soft drink producer, can manufacturer, aluminum manufacturer, and water treatment facility. We display the following vectors and matrices using a spreadsheet on which we reveal each item one by one.

First, we create the final demand vector indicating the initial request of 1 million cans of soft drink from the soft drink producer and no products from the other industries.


Final demand is equal to the first-tier production (R1) by the soft drink producer. We point out that this vector is the same as the first-round purchase orders, on which the soft drink producer records 1 million and the others nothing. Next, we ask students to create the direct requirements matrix, A, with the production ratios for the transactions between industries. The value in the first row, fourth column, for example, represents the five cans of soft drink (row) for every 10,000 gallons of water (column).


Multiplying this A matrix by the Y vector is equivalent to the calculation the soft drink producer uses to determine how many empty cans and how many gallons of water to purchase. Similarly, the values in the resulting vector correspond to the second-round purchase orders, where the can manufacturer records 1 million, the water treatment facility records 100,000, and the soft drink producer and aluminum manufacturer effectively record zero.


We continue in this fashion, calculating the AA matrix, multiplying it by Y, and showing the results; calculating the AAA matrix, multiplying it by Y, and showing the results; and so on. Each time, we pause to examine the result vector Ri and find the corresponding values on the student's log sheets. Last, we sum the elements of each result vector, R, to determine the total production of each of the four industries, as shown below. We indicate that these values should correspond to the sum of production from the purchase orders students received.


 After viewing the matrix formulation, students see how much easier it is to determine the production of the industries using this method. They also note that the model could easily be extended to include more industries and additional transactions. We then show the matrix forms of the environmental impact vectors and include them in the matrix method:


where F represents a matrix with the environmental impact per unit of output for each industry across the diagonal and b represents the total environmental impact.

As a final extension of the model, we demonstrate how the matrix model defined above in physical units can easily be transferred into other units, such as dollars, which are typically used in IO-LCA models. We designate dollar values for each product in the model and create an equivalent direct requirements matrix in dollar units. We repeat the matrix manipulations using dollar values to show that the results are equivalent. Likewise, we define the environmental impact vectors per dollar and calculate the resulting environmental impact vectors.

Finally, we use the matrix model to demonstrate the equivalency of the infinite series I+A+AA+AAA+… and the Leontief inverse, (I - A)−1. A full discussion of Leontief's (1970) model and the results of the EIO-LCA method calculated with the Leontief inverse is a final step.

Box 3. Part C: Use of the Web-Based EIO-LCA Tool
Materials Required:
 • Computer with Internet access
Approximate Time Required:
 • Demonstrating user input—5 minutes
 • Discussing and evaluating results—10–20 minutes

The final part of the activity is to demonstrate the EIO-LCA method using the tool available online (http://www.eiolca.net). We select the U.S. 1997 Industry Benchmark model as the economy of interest. We proceed step by step through the interface, selecting an industry sector for analysis and reading the description, entering a final demand value, and selecting desired impacts to view. For consistency with the simulation activity, it is useful to analyze the supply chain impacts associated with soft drink and ice manufacturing (312110). The demand for 1 million cans of soft drink is modeled simply as demand for $500,000 of output from that sector; this assumes that the price to produce a can of soft drink is approximately $0.50. The model performs the necessary calculations and displays the results.

Note that the EIO-LCA model is based on producer prices, which are defined as the cost to produce a product. These differ from purchaser's prices, with which we are more familiar, as they assign the costs of trade and transportation to specific sectors rather than including them in the cost of the product itself (Eurostat 2008). Fifty cents is the estimated price paid by the soft drink producer to make a can of soft drink. If we use the average margins provided by the U.S. Bureau of Economic Analysis to estimate costs of transportation (approximately $0.05), wholesalers (approximately $0.075), and retail margins (approximately $0.20), we are assuming that the purchase price is roughly $0.80 per can.

When working with students, we present economic results first, discussing the resulting list of sectors that contribute to the supply chain of an industry and differentiating between direct and indirect suppliers. Next, we show results for various environmental impacts, noting that sectors with the highest impacts are not necessarily the same as those with the greatest economic input. We emphasize the need to examine the full supply chain of an industry to determine where the largest impacts are generated and thus where to target changes. For example, in terms of global warming potential (GWP) and greenhouse gas (GHG) emissions, most industry sectors have lower direct emissions than those from the power generation and supply sector. Therefore, an industry that wishes to reduce its carbon footprint should focus on changing to nonfossil-based sources and reducing its use of electricity.

As a final activity or homework assignment, students are directed to use the EIO-LCA tool to compare different industries’ impacts along various categories. In some cases, students use EIO-LCA to analyze various products and present their results to the group. With high school students, we have most often used an activity in which each group analyzes impacts from sectors producing different types of beverage containers, such as plastic bottles, aluminum cans, steel cans, or tetrapaks. We then compare results across the different types. Other assignments include giving students results of the EIO-LCA tool to assess how well these results represent a given product. For example, we might give students results from a $1 million demand from Sector 31181A: bread and bakery products, except frozen, manufacturing and results from a $1 million demand from Sector 311830: tortilla manufacturing and have them discuss the advantages and disadvantages of using the EIO-LCA results.


We have used variations of the simulation described with high school students, 1st-year and 2nd-year nonengineering undergraduates, junior and senior engineering undergraduates, and graduate students. Lessons range from very basic to semiadvanced. For novice students, the activity demonstrates the importance of converting between units, a simple skill we have found students could benefit from practicing. During Part B, when we show the mathematical solution in the spreadsheet, students check their own results to find the corresponding values on the completed model. A lesson from this task is that it is easy to make a mistake when working by hand, even with this very small, four-industry and eight-transaction scenario. Yet, knowing the capabilities of computers, students recognize how easy it would be to extend the model to include many more industries and seemingly endless transactions.

Connecting this practical activity of estimating environmental impacts, which appeals to a wide range of students, to linear equations and matrix algebra engages students in a way many math lessons struggle to do. Of course, the level of the discussion of the derivation and meaning of the matrix algebra must be catered to the level of the students. For younger students, our experience in using the simulation has shown that displaying the mathematical formulas of the calculations lends credibility to the results of the model and demonstrates the usefulness of higher level mathematical techniques to which they will be exposed later. For more advanced students, the discussion provides an opportunity to practice matrix algebra. For university-level students, the derivation of the method and comparison of the Leontief inverse and Taylor expansion results provides a final connection between the concrete example given by the simulation and the mathematics behind the EIO-LCA method.

From an LCA perspective, the activity demonstrates the importance of defining boundaries for an analysis. Students recognize not only how the entire supply chain can be addressed in an LCA but how important it is to include a broad supply chain. Graduate students have a much better understanding of how the model works, having seen the series of linear algebra transformations, the Leontief equivalency, and the extension to environmental impacts. Likewise, students see the how industry transactions, even if based on economic data, can be used to estimate environmental impacts.

Although we have not conducted a formal study of how well the simulation aids learning objectives related to LCA or IO-LCA specifically, the impetus behind the creation of the simulation was that simply presenting the online tool and discussing model results was causing many misconceptions and incomplete understanding. In this situation, the online tool was a “black box” where students entered a sector and a dollar value and used the results. Despite our efforts to explain, without a concrete example, building understanding of how the model works was a slow process. As a result, students repeatedly asked similar questions about the model and often misinterpreted the results.

Similarly, showing an example spreadsheet with completed matrix calculations is not sufficient. For students in high school and some nonengineering students, the spreadsheet model alone does not adequately explain the relationship between transactions among industries and the resulting environmental impacts. The simulation provides a clear connection between requests for products and purchases of materials, on the one hand, and the matrix model, on the other. We have found that after physically performing the transactions, many more students are able to comprehend the supply chain complexities, calculate values, and explain how these transactions lead to impacts.

In connection with an appropriate curriculum, this activity can be used effectively to increase students’ interest in and understanding of the environmental impacts of products while also achieving a number of other educational outcomes related to the practical application of mathematical techniques to a real-world problem. An understanding of the impacts of production along supply chains is important to making informed decisions in a number of areas, from consumer decisions of what products to purchase to political issues of which environmental policies to develop. Increasingly, companies and their employees are pressured to address environmental issues for which the traditional curriculum has not prepared them. As a result, new educational activities are required that foster a deeper understanding of the environmental impacts of products. The activity described in this article also promotes interest in engineering from an early age by demonstrating the usefulness of engineering techniques for answering questions of interest to a wide range of people. One particular problem in educational systems is promoting the participation of women in engineering education. Environmental LCA is one area of engineering that we have found has interested many women in pursuing an engineering education.

Simulation Development and Lessons Learned

From a development and instructor perspective, we have learned the importance of iteration in developing such exercises. The initial simulation we designed involved four students only, whereas the remainder of the class observed. The four students walked around the room “buying” goods from the other industries by exchanging money. The nonparticipating students, however, were not engaged in the activity and did not follow the calculations as well. Designing a scenario and economy with the desired number of tiers and with transactions neatly divided in dollar amounts was difficult. A second iteration involved having multiple groups within the classroom perform the same calculations (as described above), but with each student communicating requests verbally and using only the log sheet. This resulted in miscommunications, as classroom noise and multiple requests for materials to a single industry made it difficult for individual students to capture all requests for materials. The addition of the purchase orders for tracking requests made a significant improvement in helping students follow transaction paths to their end. The newest addition is the purchase order tracking sheet for students to organize incoming purchase orders and completed purchase orders; this sheet has helped ensure that each purchase order is counted only once.

Students are generally open to the simulation design and the assumptions of the four-industry model. Of course, certain features of the simulation must be explained. For example, some students have questioned the purchase of can manufacturing scrap by the aluminum manufacturer, asking, “Why does the can manufacturer make cans to be scrap?” We have explained that the transaction is not for good-quality empty cans but instead for scrap materials—poor-quality cans and pieces of metal that remain after can production. We emphasize that the scrap is the equivalent amount of metal as that in an empty can. This is so-called “new” scrap material resulting from the can manufacturing process; it is sold back to the aluminum manufacturer and results in a small income stream for the can manufacturer. This type of transaction is not uncommon. Obviously, this source of income must be much lower than the income from sales of finished cans for the can manufacturer to receive a profit. This example, however, demonstrates how this simple exercise can also lead to a much deeper discussion.

Another issue that can be brought out in discussion is determining which industry is truly “responsible” for the environmental wastes generated. As the final totals (see table 3 and figure 5) indicate, most of the wastewater and solid waste are generated by the aluminum manufacturer. We inquire of the students whether the soft drink producer is responsible for this waste, because the production was necessary to complete the production of the cans of soft drink. This discussion is useful and can be directed to cause students to consider the assumptions that go into creating engineering models used for decision making. In the case of LCA, allocation and responsibility are common themes for discussion (Baumann et al. 2006; Peters and Hertwich 2006; Lenzen et al. 2007).

Before introducing the simulation in class, we recommend that students have some initial exposure to life cycle thinking in general and, to some extent, process-based LCA and the boundary issues related to LCA (Hendrickson et al. 1998; ISO 1998; Lenzen 2001; Lenzen and Treloar 2003; Suh et al. 2004). For novice students, we have a life cycle thinking exercise in which they create unstructured diagrams of the materials and energy needed to make a simple, one-material product (e.g., aluminum beverage can or plastic beverage bottle). One could also introduce process-based LCA case studies.

During the initial stages of the simulation in the classroom, proceed slowly, and verify that students understand the activity and are doing the calculations correctly. Having correct answers on a log sheet aids students in connecting the pen-and-paper portion of the activity to the values shown on the spreadsheet. Individual group leaders are helpful, especially with high school students, to provide immediate assistance to groups with questions or confusion. In our program, graduate students have assisted in this role. We suggest the group leaders familiarize themselves with the simulation beforehand—doing the calculations, writing purchase orders, and recording amounts as the students are expected to do.


To teach students about the EIO-LCA methodology, we developed an in-class simulation in which students represent industries and mimic the transactions along the supply chain of canned soft drink production. The four-industry, eight-transaction model reduces the complexity of the model into a form that allows students to perform calculations representing purchases of materials, and the results are easily compared to an equivalent spreadsheet model. The spreadsheet model demonstrates how the method can easily be scaled up to the size of a large-scale economy, such as those national models currently available in the EIO-LCA online tool. The simulation has been used in a variety of settings, with high school through graduate-level students. The resulting three-part activity aids students in understanding the structure of the EIO-LCA approach and emphasizes the link between industry transactions and environmental impacts.


  • 1

    The conversions between the units used here and their SI equivalents are as follows: 1 gallon (gal) = 128 fluid ounces (oz) = 3.78 Liters; 1 pound (lb) = 0.454 kilograms.

About the Authors

Troy R. Hawkins is currently a researcher in the Industrial Ecology Program at the Norwegian University of Science and Technology in Trondheim, Norway. He was a PhD candidate at Carnegie Mellon University at the time the simulation was developed. Deanna H. Matthews is a research engineer with the Green Design Institute in the Department of Civil and Environmental Engineering at Carnegie Mellon University in Pittsburgh, Pennsylvania, USA.