CHAPTER 3 – Research Methodology
This chapter will describe in detail the methodology to realize the basic constructs of an approach to dynamic environmental LCA by evaluating structural economic sequences. In this chapter is an introduction and discussion of the application of environmental LCA in a Sequential Interindustry Model (SIM) context. This includes a general discussion of assumptions and limitations of the model; an introduction to the SIM model and a mathematical presentation; coupling the SIM model to a life-cycle perspective; and the inclusion of environmental parameters to complete the model.
Section 3.1 – The General Model
The model proposed in this research generates a simulation of emissions to the environment based on scenarios of economic activity. This is accomplished by creating a projection in time of a sequence of production activities and consumption activities based on present and future consumer demand activities. This sequence of production and consumption or use activities is then the foundation for estimating resources consumed and emissions generated. This is accomplished through a series of conversion factors as shown in Figure 3-1. Economic activity in monetary terms is converted to physical quantities (in tons, liters, MWh etc.) through deflators. Physical quantities that represent economic activity are then related directly to resources used. Emissions generated are based on the utilization of these physical quantities via specific techniques of commodity production. Ultimately, consumption of resources and emissions released to the environment are related to detrimental impacts to the environment.
Figure 3-1. Conversion factors relating economic activity to environmental impact.
This last step is beyond the scope of the model presented for the following reason. In order to calculate actual impacts one must consider the complex causality chain between industrial activities analyzed and the associated environmental impacts. The calculation of actual impacts due to specific industrial activities is highly complex. Actual impacts may involve the analysis of cause and effects relationships, the incorporation of fate and exposure information, and distinctions of preexisting background elements and spatial differentiation (Jager and Visser 1994). In acknowledgment of the sophistication necessary to calculate and claim such potential impacts, the model presented is limited to describing temporal characteristics of emissions generated due to production and consumption activities.
The focus of this research will greatly expand the LCI component of an LCA study that will lead to greater insights for decision-making. Traditionally, LCIs have been static representations of emissions data due to the life-cycle of a product, process or activity. A static LCI is an accounting exercise conducted within life-cycle perspective loosely bounded by an interval of time. In many cases temporal aspects are ignored. The expansion of the LCI for this research is two-fold. First, the LCI will include the time-related parameters to describe the sequences relevant to the LCA study. This will enable the LCI to capture elements of change that would otherwise be assumed in steady-state or assumed to change discretely, ignoring any potentially important transient characteristics. Second, the inherent nature of the SIM used to develop a LCI will capture the complex web of activities that represent both the direct and indirect activities of environmental concern. The essence of SIM, as with all Leontief based economic models, is the ability to capture interdependencies. By using SIM, the LCI will ultimately document the sequential distribution in time of total quantities, both direct and indirect, of resources used and emissions released to the environment.
Section 3.2 – Introduction to Sequential Interindustry Modeling (SIM)
SIM is based on the Leontief static model where production is augmented by the specifics of production chronology (Romanoff and Levine 1981). In SIM, sequences are important. SIM considers the time consuming nature of the production process and the corresponding timing of industry input. For example, SIM has been used to model time associated with the production schedule of an industry and transportation delay representing the time goods are in transit between suppler and demander (Levine and Romanoff,89). In general, the emphasis of SIM is on “modeling interindustrial and intertemporal production in order to examine transient processes associated by final demand” (Romanoff and Levine 1986, 74).
SIM is part of a recent revival in the interest of dynamic interindustry models first conceived in the mid-20th century. Contemporaries of SIM include: Mules (1983), ten Raa (1986a) and ten Raa (1986b), Cole (1988), and Sonis and Hewings (1998) (Romanoff and Levine 1991). The general philosophy of SIM originates in part from modern Austrian economic theory (an association to wit interindustry analysis was rebuffed by Leontief himself)[4] (Durand and Romanoff 1986) (Dorfman et al. 1958). The basic element of Austrian economics is the analysis of processes extended over time that are transformed into a stream of output that are also extended over time (Hicks 1985). SIM embodies earlier economic program management work found in Wood and Geisler (1951) and Wood (1965). In essence, SIM unravels the ‘whirlpools’ of interindustry relationships, providing an empirical approach to investigate transient behavior of finite economic activities.
In the basic model of SIM (Core SIM), production is not simultaneous as in the static Leontief model, but occurs over a sequence of time intervals. In SIM, sequences of input and output flows of materials are captured by distinguishing intervals of interindustry production activities. The duration in time of the intervals for interindustry production activities “need not be identical for all industries,” and “alternative modes of industry behavior are recognized, providing the means for gaining insights into the ‘black boxes’ of production” (Romanoff 1984, 354).
Within core SIM, two production modes are defined - anticipatory production and responsive production. In anticipatory production, production occurs based on knowledge or estimates of future orders. In responsive production, production occurs in response to known orders. For responsive production, this includes both the case where after an order is placed, goods are produced to fill that order, and the case where after an order is placed, goods are shipped from inventory and production follows the order to replenish the inventory. In general, the responsive model represents a system where production occurs in response to demand. This is in contrast to an anticipatory model where production occurs based on estimates of future demand (Romanoff and Levine 1981).
Enhancements made to Core SIM have resulted in a “Modified SIM”. Modified SIM is enhanced with “features adding realism to the portrayal of production” (Romanoff and Levine 1984, 354). Features of Modified SIM include:
1. The further refinement in the treatment of the industry interval,
2. the consideration of capacity limitations,
3. the handling of information on changes in future orders and on the structure of production,
4. the use of alternative inventory management policies, and,
5. the description of transient process and technical change in a time-varying model
(Romanoff and Levine 1984, 1986, 1990b, 1991).
Within SIM, there are two views of the dynamics of production: a temporal view and a cross-sectional view. In the temporal view, production is associated with “the timing of input applications and with the duration of each of the industry’s direct production schedules, each planned for a different date of product completion” (Romanoff and Levine 1991, 263). Here, a transition of production occurs from an originating steady-state of production technology to a new (or final) state of production technology. In the cross-sectional view, one “observes at a specific time, t, different ‘slices’ of progressively ‘forward moving’ ” production technologies. In this view, each ‘slice’ represents production for a “time series of final output.” Thus, the “hybrid generalized inverse … reflects the mix of techniques that contribute directly and indirectly to a time series of final output” (Romanoff and Levine 1991, 264). [5]
A further analogy of the comparison between a cross-sectional view and a temporal view can be made to the Eulerian reference system and the Lagrangian reference system methods of water quality modeling. The Eulerian reference frame is utilized when an observer stays at a point on a riverbank and observes and quantifies water quality as the river flows past. This is analogous to the cross-sectional perspective where economic activity is observed for slice of time. The Lagrangian reference is used when an observer follows the flow in a river with a boat traveling at the average velocity of the flow. The Lagrangian perspective is similar to the temporal view, where one follows the flows of a commodity from initial production to final demand. The Eulerian perspective is well suited for understanding the total mass-balance of a system, that is at a single point in time one can quantify all of the inputs and outputs of the river system. The strength of the Lagrangian perspective lies in the ability to understand cause-and-effect relationships (McCutcheon 1989). The corresponding strengths of each perspective are similar to their economic counterparts. In the cross-sectional view we observe all of the inputs and output of the economic system – similar to a mass balance observation. In the temporal view, the analysis determines the linkages to satisfy a final demand parameter of interest.
A Mathematical Description of SIM
A mathematical description of SIM derived from Romanoff and Levine (1990b) and Romanoff and Levine (1991) is as follows. We begin with the simple example of baking bread to develop the mathematical description.
As shown in Figure 3‑2, the production of baking bread requires four separate processes: proofing the yeast, mixing the dough, letting the dough rise, and the final step, baking the bread. In this example we assume that each process requires one interval to complete, with the exception of letting the dough rise. The time required for dough to rise requires is two intervals. Within each interval, multiple inputs arrive at the beginning and output is completed at the end of the interval. This assumes just-in-time production practices obviating the need for inventory.
Figure 3–2. Sequence of production for baking bread.
The processes are distinguished by the interval in which they are applied relative to the output of the finished product, a loaf of bread. This distinction is referred to as the application period as shown in Figure 3-3. For example the application period of mixing the dough four intervals prior to output, hence it has an application time of four intervals. Some input may have multiple application periods, as in the case of sugar. Sugar is used to proof the yeast and is also used as a sweetener added at the time of mixing the dough. In the real world, the baking of bread may be done in batches (production sequences can also done continuously). Several loaves of bread are made within one batch, and multiple batches can be done shifted in phase.
Figure 3–3. Multiple batches of bread making.
Also depicted in this figure is the concept that each batch of bread is defined by the time of the start of production t, to the end of production, s. The pass-through time for one batch of bread production is indicated by hj, where in this example, j is the bread making industry. This pass-through time is determined by the longest application period, hij, which indicates the time input is received by a supplying industry to the time of product completion. In this example the input required for the process of proofing the yeast has the longest application period, and therefore determines the pass-through time. For processes that last more than one interval, multiple intervals can be used. In this example, multiple intervals were used to describe the process for letting the dough rise.
The production sequences of Figure 3-3 represent anticipatory production. Assuming access to future perfect information, a final demand stimulus, Y(t) at interval t = 5, results in the completion of the final step of baking bread for s = 5. Also, from this cross-sectional perspective the “unfinished goods” or goods that are in process and yet to be accounted for at the time of output are observed. This intermediate phase of production within interval t = 5, includes production to meet final demand and intermediate production to meet future anticipated final demand. The cross-sectional view depicted by Figure 3–3 represents the direct production of baking bread. The indirect activities necessary to produce the ingredients that are input to bread making production sequences are not present.
In order to fully describe total production, the production of activities required to produce the input to bread-making are also to be considered. Figure 3-4 illustrates a simple example for the processes to produce yeast for baking bread; culturing the yeast and packaging it. In contrast to the five time intervals required for bread production, yeast production requires a pass-through time of two intervals.
Figure 3–4. Yeast production.
The production of yeast associated with the production of bread making is then illustrated by superimposing the two production sequences as shown in Figure 3–5.
Figure 3–5. The superposition of yeast production and bread making
production.
In Figure 3–5, the output production to meet final demand of bread at interval t = 5 is accomplished by the last production process of baking bread initiated at interval t = 1. Yeast production of interval t = (-1) is produced to meet the input of bread production initiated at interval t = 1. Thus from this figure, in order for the pass-through time for the production of bread to be five intervals, quantities of yeast necessary for production must be available precisely at t = 1, the first interval of production. Pre-planning, in the form of an existing inventory of yeast, or the production of yeast two intervals prior to the production of bread making is necessary to avoid any delays in production of bread.
From the cross-sectional perspective, the production activities within this interval include not only this final process of bread making, baking the bread, but also the intermediate processes for future demand, both for bread making and yeast production. A true total cross-sectional output production figure would include the activities necessary to produce the input of sugar, salt, flour and wood.
In the examples illustrated thus far, it is assumed that the processes do not change with time – they are time-invariant. Interesting issues arise when introducing the dynamics of technological change and changes in final demand or more commonly known as consumer preferences. For example, in the production of baking bread we assume a technological innovation has been applied to mutate and produce yeast that create more gases per unit of time, hence leading to a faster rising dough. The new yeast cultures reduce bread rising time in half, shortening the pass-through time to four intervals. This technological change replaces the existing method of making bread starting at interval four as shown in Figure 3–6.
Figure 3–6. Technological change of bread production.
Observing the production
chronologies depicted in Figure 3-6 from the cross-sectional view of t = 5, two techniques to produce the
same product are present. The older,
double-interval rise time technique is initiated at intervals one and two. The
new single interval rise time technique is applied at interval four. The timing
of the change to the new bread making technology has several
ramifications. Of note, despite the
change to the new technology, all future demands were still met. Also, the abrupt transition to the new
technology does not require yeast input at interval three. Such transitions of technological change can
create disruptions leading to economic hardship or unnecessary wastes of
resources.
A more realistic representation of technological change is the presence of a distribution of multiple technologies in place at the same time. The life span of an applied technique can vary dramatically based not only superior physical factors, but also factors of the real cost of capital. The real cost of capital involves an amalgamation of the real interest rate (the nominal rate minus the rate of inflation), the physical depreciation rate, the depreciation rate for tax purposes, the tax rate, investment tax credits, trends in equipment costs, and trends in the price of the product produced (Almon et al. 1974). Figure 3-7 illustrates the coexistence of the two technologies to produce bread. In this example, application of the old technology and the new technology coexist within several time intervals.
Figure 3–7.
Transitional technological change.
A detailed mathematical representation of the SIM is presented below:
Model Parameters:
General Indices
i – index referring to the supplying industry, represented by the rows of the system model,
j – index referring to the receiving, (i.e. producing) industry, represented by the columns of the system model,
n – the number of i supplying industries,
m – the number of j receiving industries,
Temporal Indices
t – time interval of input application,
s – time interval of output or product completion,
p – time period representing the sum of all time intervals,
hij – application time of an input from industry i used by industry j, referenced from the initial application interval, t, to product completion s,
hj – production pass-through time, that is, the production period of industry j, equivalent to the longest application period, hij,
General Parameters
xi(t) – total production by industry i within a defined interval of time, t,
xj(s) – output by industry j within a defined interval of time, s,
xij(t,s) – interindustry transfer from industry i to industry j with input applications at interval t and production output at interval s.
aij(t,s) – technical coefficient describing the ratio of input required by industry j from industry i at time interval t to produce output by industry j at time interval s.
yi(t) – final demand for production by industry i within a defined interval of time, t.
wi(t) – intermediate output produced by industry i within a defined interval of time, t.
Process
Production Technique Parameters:
mtip – production technique applied at t by input industry i, where p = 1 … lp, where lp is the numeration of possible production techniques of industry i,
Other
notation
b[×] – function representing total requirements within a defined interval t equivalent to a cross-sectional view of the total requirements described by the Leontief Inverse, [(I – A)-1] of the direct requirements matrix of the static model.
B[×] – (Capital of b) function representing total requirements over a defined period r, representing the sum of all output described by each interval t over the period of study. This function is equivalent to the total requirements described by the Leontief Inverse of the direct requirements of the static model distributed over time.
In the Leontief static model, all input are accounted for within the same interval of time as output. In contrast to the Leontief model, in SIM there may be several input distributed over a period of study delineated by several time periods to produce a final product. Thus, to handle the multiples of input over multiples of time intervals, the interindustry transfer of products from industry i to industry j is defined as xij, and is described by two temporal parameters:
(3-1)
The output by industry j, is defined as xj, and is described by one temporal parameter:
(3-2)
As shown in Figure 3-8, there is an industry j output at time interval s, that requires input at time interval s – 1, and time interval s – 2.
Figure 3-8.
Sequence of Input and Output.
Further, one can reference future output by the same conventions as shown in Figure 3–8 as depicted by Figure 3-9:
Figure 3-9. Shifted
sequence of Input and Output.
In this example, there is an industry j output at time interval s + 1. This output requires input at time intervals s, s – 1, and s – 2.
The technical coefficient representing the ratio of the total input necessary to produce a given output is:
, for 
. (3-3)
and, it follows that interindustry requirements can be described by:
. (3-4)
All intermediate input at interval t, are:
(3-5)
Substituting, (3-4) into (3-5) yields:
(3-6)
The total output within an interval is intermediate production and final demand as shown in equation (3-7).
(3-7)
And, total output from industry i at interval t is:
(3-8)
and it follows from (3–6) and (3–8):
(3-9)
The model presented thus far represents core SIM. SIM represents a family of models that include several variations. Enhancements made to the SIM allow for a more precise representation of real-world scenarios. Enhanced SIM includes a combined anticipatory and responsive production model, incorporation of inventory management capabilities, transportation delay effects, capacity limitation, closer examination of the time interval, the nuances of input pricing and output prices and technological change in a time-varying system (Romanoff and Levine 1991).
In general, the model presented in this research will assume that all production sequences are anticipatory, as predominately industrial activity anticipates future sales. Also, for this implementation the price of input from industry i is fixed. That is, a base year will determine the price of a commodity that will not vary through out the duration of a simulation. This is in acknowledgement of the complex factors that may dramatically affect a change in price. Such factors of change include relationships of supply and demand, changes in perceived utility (the whims of consumers), and any unforeseen events, catastrophic or otherwise (political conflicts or extraordinary changes in application of technology such as the proliferation of the use of the internet.
This model will also consider transportation delays as negligible, that is, the time that it takes to transfer a product from one industry to another will be contained within the interval of production. Transportation delays do exist in real world applications, however, their exclusion is justified based on the emphasis of the model on the entire life-cycle of a long-use product, such as the life-cycle of the automobile.
To incorporate the effects of technological change, the SIM model presented introduces the concept of production techniques m, numerated discretely by p. This production technique parameter represents the production technique applied at time t for input industry i, where p = 1 … lp, where lp is the number of possible production techniques for industry i.[6] The technique represented by each mtip describes the temporal parameters in the form of the application times, or hij's.
Equation (3-3) then becomes:
, for 
. (3-10)
And equation (3-6) becomes:
(3-11)
And, from equation (3-9), total output from industry i at interval t is:
(3-12)
Thus, the system is solved by:
(3-13)
where b [ × ] is a vector function equivalent to the Leontief Inverse calculation of total requirements where A(×) and Y(×) represent the appropriate manipulation of these matrices to arrive at the solution of cross-sectional total requirements.
Section 3.3 – Life-cycle SIM
The traditional emphasis of SIM has been historically on production. However, the examination of activities pertinent to environmental LCA involves not only production activities, but also those activities associated with the consumption of a commodity and its respective end-of-life disposition. The emphasis does not shift, but expands to include the entire life-cycle of a commodity. Thus, a schema for handling environmental LCA study phenomena using the constructs of production based SIM is presented. This augmented version of SIM will include the respective commodity consumption activities distributed in time.
Consider an example of the production sequence of an automobile. In Figure 3-10 production is sequenced in eight quarterly intervals over a period of two years. The eight intervals consist of material extraction, which requires two intervals, followed by two periods of material processing, one interval of fabrication of parts, followed by assembly, packaging and delivery and the final sale to the consumer. In the SIM schema, production sequences overlap, that is, activities accounted for in Q3 2000, include not only the sale of model year 2000 automobiles but also the packaging of automobiles to be sold in Q4 2000.
Figure 3-10. Production sequences of
the automobile.
In order to truly assess the environmental impacts of the automobile we must consider its entire life-cycle. The life-cycle of the automobile is expanded and depicted in Figure 3-11 (Graedel and Allenby 1998, 79) and (Keoleain et al. 1997, Fig. 2.2). As shown, the life-cycle of the automobile is separated into six life-cycle stages of the automobile:
· Raw material extraction,
· Material processing,
· Manufacturing,
· Product Delivery,
· Customer use, and,
· End of Life disposition.
The activities of each of these life-cycle stages involve several distributed activities of input and output as depicted in Figure 3-12. From this schema one can observe several differences from the traditional static LCA model and an economic production model. First and foremost is the obvious change in the perspective of production relative to the entire life-cycle. Temporally represented by SIM, the life-cycle of the automobile is predominately characterized by its use phase. This is in contrast to the traditional static LCA which emphasizes the intricacies of production. Second, in contrast to traditional I‑O modeling, there are multiple input distributed over a commodity's entire life-cycle – not just within the interval of production, but also within the intervals of use and end-of-life. Third, there are multiple output distributed over the entire life-cycle of a commodity – multiple output within production as well as multiple output beyond production.
