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The Wuppertal Institute developed, in the early 1990s, an input-oriented lifecycle-wide resource accounting method, the “Material Input per Service-Unit” concept (MIPS), today also referred to as “Material Footprint”. The official handbook applicable to products, services, and processes describes a MS Excel-based sequential approach for calculating MIPS. Today’s computing power, available to every researcher, and access to software and databases dedicated to lifecycle analysis make calculating MIPS using matrix inversion possible. This also opens up possibilities for enhancing MIPS-models programmatically: parameterizing the foreground and background systems, batch modeling for producing time series, and computational algorithms enhancing interpretation. The article provides (1) an overview of the methods and tools used for calculating MIPS from its origins to today, and (2) demonstrates some of the programmatically enhanced capabilities offered to MIPS-practitioners.

The Wuppertal Institute (WI) developed, in the early 1990s, an input-oriented life cycle-wide resource accounting method, the “Material Input Per Service-unit” concept (MIPS) [

A MIPS value is a proxy for the environmental impact caused by the whole life cycle of a product relative to the service it provides. A MIPS value is the sum (in mass unit) of all resources (“material” in the MIPS concept) extracted from nature along the life cycle of one service-unit of the studied product. Material inputs are classified in biotic raw material, abiotic raw material, water, air, and earth movement in agriculture and silviculture.

Material input indicators represent the “cumulative primary materials demand” (by analogy to cumulative primary energy demand) and as such are “generic environmental pressure indicators” [

Over the years, the WI prepared so-called material intensity (MIT) factors for many materials, energy and transport services and made them publicly available through its website [

The MIPS concept is largely comparable to the input-side of a LCI in traditional LCA. Therefore, using LCA databases seems a promising way to streamline the calculation of MIT factors and MIPS values. There are, however, also noticeable differences between MIPS and ISO LCA. First, a MIPS-abiotic value is not simply the sum of the categories “resource, in ground” of a traditional LCI. A MIPS-abiotic value includes the total used and unused resource extraction. For example, an LCI would account for some metal input, while a MIPS would include the extracted ore (run-of-mine,

This paper proposes to adopt modern inventory problem solving techniques to streamline the production of MIT factors and more complex MIPS. MIPS and LCA practitioners, alike, will find concrete options for calculating (abiotic) material input indicators using well established LCA software and databases. It allows MIPS and LCA analysts to extend their customary material input indicators and LCA potential impact indicators, respectively, with complementary indicators, while using a unified set of tools.

Historically MIPS was developed as a sequential inventory method comparable to the early days of LCI. All inputs from nature at each step of the process chain of the modelled product are inventoried and summed up in five categories (biotic raw material, abiotic raw material, water, air, and earth movement). The main advantage of the sequential approach is that it is in principle simple and does not require complex or costly software tools.

After the MIPS concept had matured in the 1990s, a handbook was released in the early 2000s, together with a spreadsheet calculation tool and first MIT data [

A MIPS study starts by defining a product system (cradle-to-product boundaries) delivering a particular service, which includes the use and end-of-life phases of said product (cradle-to-grave boundaries). The next steps consist in representing the process chain, compiling data, and expressing total material input (MI) per mass unit of product (material intensity MIT) and/or per unit of service (MIPS).

For doing so, the MIPS spreadsheet calculation tool [

All inputs listed in the compilation sheet are then entered in the calculation sheet scaled for one mass unit (or another physical unit, e.g., energy) of the modeled product. Natural inputs such as metals, unused extraction, biomass,

For a cradle-to-grave approach, additional processes and material inputs involved in the use and end-of-life phases have to be drawn up on the compilation sheet. MIPS values expressed in mass of moved nature by unit of performed service are then calculated using the calculation sheet as described above.

The spreadsheet calculation tool is targeted at an audience without access to dedicated software. Some of the MIT values on MIPS-online, however, were generated at the WI using specific features of the LCA software GaBi [

GaBi has an aggregation function that automatically adds up (without characterization factors) the elementary flows of an LCI into predefined categories. We, therefore, define new categories of elementary flows in GaBi following the classification and hierarchization used in the MIPS spreadsheet calculation tool. We create for instance a category “abiotic raw materials” consisting of the sub-categories “minerals”, “energy carrier”, “unused extraction”, and “soil excavation”. GaBi will automatically add up all elementary flows marked “minerals” together and present the result along with the detailed LCI. GaBi will, similarly, deliver an aggregated result for “abiotic materials”. MIPS values can therefore be read directly from the LCI result page in GaBi.

For this method to work, however, the relevant elementary flows must occur in the product system model and be labeled properly. The ecoinvent database or the built-in GaBi database provides no unused extraction flows, for instance. Such flows must be entered by hand along the modeled process chain, wherever they might occur. The associated cost is a limitation of this method.

Manually inputting material flows such as “unused extraction” has, however, advantages over using a rigid characterization method that would automatically associate a given unused extraction to a given elementary flow. Regional and other differences can be accounted for at the level of the extraction process and associated elementary flows.

An inventory problem (LCI or MI inventory) can be written as a system of linear equations. First described in [^{−1} ⋅

If the matrix A respects certain conditions, such as being mono-functional (each process column produces only one output flow, which is achieved by allocation procedure) and normalized (the elements in each column are normalized for one unit of output of the corresponding process), Suh and Heijungs [

Replacing Equation (2) in Equation (1), it appears that each ^{k}^{th}

In LCA studies, Equation (1) gives the LCI (vector

MIPS was purposely not developed as a LCI characterization method, while LCA databases were developed with midpoint and endpoint interpretation in mind. We show here, however, that MIPS calculations and today’s LCA databases can be seamlessly integrated using custom characterization methods. We use the ecoinvent database version 2.2 [

First, we define five midpoint categories after the five MI categories in the MIPS concept. Note that those are not “impact categories” in the usual LCIA sense. Second, we establish characterization factors (MIT factors) to convert LCI results into the five MI categories. Third, the new MI characterization method can be imported into the software of your choice and used together with ecoinvent 2.2.

We detail below how the second step is or can be implemented. In the rest of the article, we focus on abiotic materials.

An ecoinvent-based LCI lists abiotic materials extracted from nature as “elementary flows” in the category “resource, in ground”. These elementary flows do not account, however, for all material flows required in a MIPS calculation: used and unused extractions are missing.

We propose to generate characterization factors that would convert ecoinvent’s elementary flows of the category “resource, in ground” into material input flows including used and unused extraction.

MIPS and LCA terminologies for material flows in the case of metal mining, after [

Description of the material | Common terminology | MFA/MIPS terminology | Ecoinvent LCI terminology |
---|---|---|---|

Material removed to get access to reserve, |
Overburden, interburden | Unused extraction | N.A. |

The metal containing material | Run of mine, gross ore, crude ore | Used extraction | N.A. |

The pure metal | Net ore or metal content | Metal component of used extraction | Elementary flow |

Construction of selected MI abiotic characterization factors for the “midpoint impact category” MI abiotic.

Elementary flows in ecoinvent 2.2 | Allocation factor [%] | Allocated used extraction [kg/kg elementary flow] | Unused extraction coeff. [kg/kg used extraction] | MI abiotic factor [kg/kg elementary flow] | ||
---|---|---|---|---|---|---|

Case | Unit | |||||

A | Granite, in ground | [kg] | 100 | 1.00 | 0.01^{*} (world average) |
1.01 = 1.00 × (1 + 0.01) |

B | Nickel, 1.98% in silicates, 1.04% in crude ore, in ground | [kg] | 100 | 96.15 = 1/0.0104 | 0.60^{**} (world average) |
153.75 = 96.15 × (1 + 0.60) |

C | Silver, Ag 4.6E−5%, Au 1.3E−4%, in ore, in ground | [kg] | 0.26 = 4.6E−5/(4.6E−5 + 1.3E−4) | 568,181.82 = 0.26*1/4.6E−7 | 1.25 (Peru) | 1,278,409.09 = 568,181.82 × (1 + 1.25) |

C | Copper, Cu 0.38%, Au 9.7E−4%, Ag 9.7E−4%, Zn 0.63%, Pb 0.014%, in ore, in ground | [kg] | 0.37 = 0.38/(0.38 + 2 × 9.7E−4 + 0.63 + 0.014) | 97.47 = 0.37 × 1/0.0038 | 2^{***} (Sweden) |
292.41 = 97.47 × (1 + 2) |

D | Cadmium, 0.30% in sulfide, Cd 0.18%, Pb, Zn, Ag, In, in ground | [kg] | 0 (Cd is always a by-product) | 1.00 (by-product’s own mass) | N.A. | 1.00 (by-product’s own mass) |

Notes: ^{*} [^{**} [^{***} Personal communication of U.S. Bureau of Mines to Dr. H. Schütz in the context of [

The column “unused extraction coefficient” in

Materials corresponding to case A in

Cases B, C, and D below deal with materials (mostly metals) for which net and gross ore (see

Materials belonging to case B are metals mined alone. Used extraction (gross ore) can be estimated directly as the inverse of metal concentration in ore, about which ecoinvent provides information in the description of the elementary flows (e.g. 1.04% nickel concentration in crude ore). The unused extraction coefficient then applies to the calculated used extraction. The MI abiotic characterization factor is the sum of used and unused extraction associated with one kilogram of elementary flow.

We are in presence of “coupled production” [

The MIPS handbook defines by-products as “products which are also marketable, but for which the process in not mainly operated, perhaps because the market price is too low, or because they accumulate as surplus” [

In the MIPS concept, biotic material inputs from nature cover plant biomass from cultivation and biomass from uncultivated areas (plants, animals, _{2} binding from the atmosphere [_{2} from the atmosphere (

Wood is considered elementary flows in ecoinvent (see

The approaches delineated above are not pursued in this article. Further efforts are needed for integrating ecoinvent data and MI biotic calculation.

Elementary flows in ecoinvent related to biotic raw material extraction.

Elementary flows in ecoinvent 2.2 | Unit |
---|---|

Wood, hard, standing | [m^{3}] |

Wood, primary forest, standing | [m^{3}] |

Wood, soft, standing | [m^{3}] |

Wood, unspecified, standing | [m^{3}] |

Carbon dioxide, in air | [kg] |

Any LCI generated with ecoinvent 2.2 contains nine elementary flows related to water extracted from nature and either stored or used. A ReCiPe midpoint impact category uses water depletion potential (WDP) characterization factors on five of them to build a freshwater depletion indicator. Since the ReCiPe method focuses on potential freshwater water shortages it is restricted to elementary flows where freshwater “is lost from an area” rather than “consumed, but also released very close to the point of consumption” [

Comparison of characterization factors for ReCiPe midpoint impact category freshwater depletion and MI water category.

Elementary flows in ecoinvent 2.2 | Unit | Water depletion, GLO (H) [m^{3}/m^{3}] |
MIT water factor [kg/m^{3}] |
---|---|---|---|

Volume occupied, reservoir | [m^{3}] |
0 | 0 |

Water, cooling, unspecified natural origin | [m^{3}] |
0 | 1000 |

Water, lake | [m^{3}] |
1 | 1000 |

Water, river | [m^{3}] |
1 | 1000 |

Water, salt, ocean | [m^{3}] |
0 | 1025 |

Water, salt, sole | [m^{3}] |
0 | 1007–1200 |

Water, turbine use, unspecified natural origin | [m^{3}] |
0 | 0 |

Water, unspecified natural origin | [m^{3}] |
1 | 1000 |

Water, well, in ground | [m^{3}] |
1 | 1000 |

The moved soil category is defined as mechanical earth movement or erosion [

Air inputs in the MIPS concept encompass combustion, and chemical and physical transformation processes [_{2} emissions into air inputs, using the stoichiometry of the combustion equation and an average composition of air. This approach, however, would not be suitable for calcination processes (e.g., cement production, calcinated lime) and for chemical processes that use air as an input (e.g., formaldehyde production by catalytic oxidation of methanol with atmospheric oxygen). We leave these aspects for future developments.

A beta version of the MIT abiotic characterization factors in EcoSpold format is available from Supplementary Material S3. It should be noted that this is a beta release, fit for testing but not for production as bugs may remain. Future versions will be made available through the WI website.

The EcoSpoldImpact xml file can be imported into the LCA software of your choice after you have imported the ecoinvent database and, optionally, other impact assessment methods. This approach has been tested with the software openLCA [

For those, like the authors, who prefer importing the ecoinvent database into numerical computation software (we use Scilab [

Technology matrix (A) of processes × processes;

Intervention matrix (B) of elementary flows × processes;

Characterization matrix (C) of impact categories × elementary flows.

Importing the beta MIT abiotic characterization factors requires the following steps:

Add an empty row to the characterization matrix C;

Fill this new row with the MIT abiotic characterization factors in the columns corresponding to the elementary flows of the category “Resource, in ground”.

What follows in

Calculating MIPS using large LCA databases, as demonstrated in the previous sections, can both simplify the modeling exercise and complexify the modeled process chains. Analytical tools are needed to assess the contributions of the thousands processes interrelated in feedback loops to the life cycle impact of a product system. Structural path analysis and accumulative structural path analysis are such methods [

Bourgault’s algorithm provides detailed useful information but stops at the process level. The elementary flows activated by a given process are not further disaggregated. In the case of MI abiotic it can become critical to know which of the abiotic raw materials extracted from nature by a given process contribute most to this process’ MI abiotic category.

The following list presents Bourgault’s algorithm augmented with our own algorithm (steps 7 to 9). The disaggregation now goes all the way down to the elementary flows, subject to the user-defined threshold:

Pre-calculation: direct ^{−1} MI abiotic for one unit of each process in the technology matrix A (“total” means life cycle-wide here);

Build a final demand vector (f) to model the product system;

Use the results of step 1 to calculate the reference total MI abiotic associated with the product system defined in step 2: ^{−1} ∙

Choose a disaggregation criterion (e.g., 5%), contribution threshold to MI abiotic under which processes are not further disaggregated;

For each element in the final demand vector (or in the vectors built in step 10 after the first round), store relevant information (e.g., process name, parent process name, disaggregation path length,

Divide each of the

Divide each of the

If the

Divide the MI abiotic results from each of the elementary flows obtained in step 8 by the reference calculated in step 3. Store the result. The resulting relative contributions to total MI abiotic of the product system can be compared to the disaggregation criterion but, whatever the ratio, no further disaggregation is possible because we have already reached the elementary flow level;

All processes that have been tested in steps 5 to 9, and not flagged in step 6, are to be disaggregated one level deeper down the process chain. A vector is created for each of these now “parent processes”, gathering the flows from their “children processes”. The flows are scaled according to the corresponding coefficient of the technology matrix A and the demand of the parent process. Take these vectors and go back to step 5;

We have implemented this extended algorithm in Scilab with ecoinvent 2.2 and show an application in

LCA and MIPS usually are static, meaning that the matrices A, B, and C and the vector f have point value coefficients (although vintages should be documented) without further possibility to let them vary over time. Dynamic LCA (DLCA) and dynamic MIPS (DMIPS) are approaches where Equation (3) becomes:
^{−1}(

Existing DLCA studies have used LCA software and large LCA databases (e.g., Umberto and IFEU database in [

We propose here a simple algorithm that LCA and MIPS analysts using numerical calculation software (e.g., Scilab) can easily implement, in particular with large LCA databases (e.g., ecoinvent, expanded or not with own process models). As prerequisite, we assume that the following matrices have been imported into the numerical calculation software of choice:

Technology matrix A and corresponding matrix of meta-data A_meta containing at least a list of the processes in matrix A with a unique ID and their position in matrix A (

Intervention matrix B and corresponding matrix of meta-data B_meta containing at least a list of the elementary flows in matrix B with a unique ID and their row number in matrix B;

Characterization matrix C and corresponding matrix of meta-data C_meta containing at least a list of the impact categories in matrix C with a unique ID and their row number in matrix C.

The algorithm then consists of the following steps:

Preparation:

In the numerical calculation software, replicate the matrices A, B, and C, and vector f to cover each time step of the time series and rename the replicates accordingly (e.g., A_2020 for matrix

Write a routine to automatically export spreadsheets as separate text files. Although numerical calculation software have read/write functions for usual spreadsheet programs such as Microsoft Excel, compatibility issues may arise. Using dedicated read/write functions for text files helps avoiding such issues;

For dynamic technology and intervention matrices

Create a spreadsheet for each process that should be dynamic. The first row after the headers should contain at least the unique ID of this output process. Each subsequent row corresponds to an intermediary input or elementary flow that should be modified in matrix A or B, respectively. Flows that do not vary need not be listed. Each row should contain a code identifying the type of flow, the flow unique ID, and time series of the quantities needed for one unit of output process;

Save the spreadsheets as text files (see step 2);

Read each text file into the numerical calculation software. Start by matching the unique ID of the output process with the meta-data in matrix A_meta, which gives its column number (_{j}

Then read each subsequent row. If it refers to an intermediary input, match its unique ID with the meta-data in matrix A_meta. If it refers to an elementary flow, match its unique ID with the meta-data in matrix B_meta. In both cases it also gives the row number (_{i}_{i}_{j}

For a dynamic characterization matrix

Create a spreadsheet for each characterization method that should be dynamic. The first row after the headers should contain at least the unique ID of the impact category. Each subsequent row corresponds to an elementary flow whose characterization factor should be modified in matrix C. Factors that do not vary need not be listed. Each row should contain the flow unique ID and time series of the characterization factor;

Save the spreadsheets as text files (see step 2);

Read each text file into the numerical calculation software. Start by matching the unique ID of the characterization method with the meta-data in matrix C_meta, which gives its row number (_{i}

Then read each subsequent row. Match each unique ID with the meta-data in matrix B_meta. It gives the column number (_{j}_{i}_{j}

For a dynamic functional unit vector

Create a spreadsheet for the functional unit vector. The first row after the headers should contain a code that identifies it as a functional unit vector. Subsequent rows should contain the unique ID of each process making up the functional unit with time series of the quantities needed for one functional unit;

Save the spreadsheet as text file (see step 2);

Read the text file into the numerical calculation software;

Match each row’s unique ID with the meta-data in matrix A_meta. It gives the row number (_{i}_{i}

Calculation:

Compute Equation (4) for each time step of the time series, save and export the results.

We have implemented this algorithm for a dynamic technology matrix

Life cycle assessment evolved from a process-based approach to hybrid LCA, which is now considered state-of-the-art [

In tiered analysis IO-based LCI or LCIA results are simply added to process-based LCI or LCIA results. The part of the model using input-ouput typically corresponds to inputs (such as services) in the upstream process-chain that are not explicitly modeled in the process-based approach.

IO-based hybrid analysis is a tiered analysis where the use and end-of-life phases of the product system are modeled process-based, while the entire upstream process-chain is modeled with a disaggregated input-output table. Industries in the original input-ouput table are disaggregated iteratively and so are the environmental extensions, until the production phase of the product system can be modeled accurately and comprehensively.

Integrated hybrid analysis builds an expanded technology matrix in four blocks, with the process-based technology matrix A in the top left corner and the input-ouput table in the bottom right corner. Equation (1) becomes Equation (5) [

Each of these approaches can be used to produce hybrid MIPS. It requires, however, to use input-ouput tables with environmental extensions that include both used and unused material extraction, or to generate such extensions.

In

What follows offers simple but eloquent example applications of how the algorithms described in

When testing MIPS calculation with ecoinvent and MI abiotic characterization factors, we needed a procedure to locate potential sources of error. When an ecoinvent-based MIPS result looked suspicious compared to existing MIPS data, we ran a structural path analysis to identify the processes and elementary flows contributing most the MIPS result. We then had valuable information on possible sources for the discrepancy: difference in the modeling of the process chain, problem with some of the MI abiotic characterization factors,

The situation described above occurred when calculating the MI abiotic of stainless steel using ecoinvent 2.2’s process “Chromium steel 18/8, at plant, RER”. A value of 107 kg abiotic material extracted per kg of produced stainless steel came out. The WI MIT table provides a value around 15 kg/kg for a comparable product. Part of the difference can be related to different shares of primary

We therefore ran the MI abiotic of ecoinvent’s “Chromium steel, 18/8, at plant, RER” through a structural path analysis as described in

After looking into ecoinvent’s documentation [

Structural path analysis for MI abiotic of stainless steel calculated with ecoinvent 2.2 (% of MI abiotic of “chromium steel 18/8, at plant, RER”).

With the ecoinvent matrices (technology A, intervention B, characterization C) imported into Scilab and matrix C expanded with MI abiotic characterization factors, one can easily calculate MI abiotic values for all ecoinvent 2.2 processes. It takes no more than a few minutes to invert matrix A with the computing power about any researcher has access to today.

The MI abiotic results obtained are abiotic MIT values because they are expressed in kg per unit of product (“process” in ecoinvent terminology) expressed in kg or kWh,

The MIPS online MIT values have in most cases out-of-date energy systems in the background. The German electricity mix, however, has been updated to 2008. Its MIT value is close to that of the corresponding ecoinvent process (vintage 2005).

The MIPS online table has over ten abiotic MIT values (not shown on

The abiotic MIT values for metals depicted in

This heterogeneity is not surprising considering all the parameters that can influence the final MIT abiotic. Such parameters include metal concentration in ore, which in turn influences the processing technologies that differ regarding energy intensity, recovery yields,

Comparison between MIT values from MIPS online and values calculated with our MI characterization method applied to ecoinvent 2.2 (MIT values in kg/kg, except for electricity in kg/kWh; logarithmic scale).

This first evaluation of abiotic MIT values calculated with a custom midpoint characterization method shows very promising results. We did not expect perfect matches between MIPS online and ecoinvent-based values but at least values within a reasonable range from one another, accounting for differences in background systems, regional specifications,

We present here a simple application of dynamic MIPS. The underlying equation is the following simplification of Equation (4):
^{−1}(

We build instances of the dynamic technology matrix

(

We present here a simple application of tiered hybrid MIPS analysis. We extend a process-based wind power plant model with an environmentally extended input-output model. The general equation is as follows:

The term ^{−1}

The term

Our overall functional unit is “one wind power plant 800 kW, Europe”. The process-based functional unit vector f pulls two processes from ecoinvent 2.2: “wind power plant 800 kW, fixed parts, RER, unit” and “wind power plant 800 kW, moving parts, RER, unit”. This ecoinvent model covers the processing, transport, and disposal of the materials required for the fixed (tower and base) and moving (rotor, nacelle, electric parts) components of the wind turbine, the energy requirements for the installation itself, and the connection to the grid [

The input-output-based tier represents about 3% of the modeled total abiotic material requirement for an 800 kW wind turbine (

Breakdown of land-based wind turbine cost by [

Components of installed capital costs | NREL cost modeling [$/kW] | included in ecoinvent model | included in IOA model + WIOD industry |
---|---|---|---|

Direct capital cost | |||

Turbine | 1212 | yes | no |

Foundations | 57 | yes | no |

Electrical interface and connections | 154 | yes | no |

Indirect capital costs | |||

Turbine transportation | 40 | yes | no |

Roads and civil work | 85 | no | yes—Construction |

Turbine assembly and installation | 59 | yes | no |

Engineering and permits | 24 | no | yes—Renting of M&Eq and Other Business Activities |

Soft costs | |||

Contingencies | 100 | no | no |

Market price adjustment | 362 | no | no |

Financing cost | 63 | no | yes—Financial Intermediation |

Tiered hybrid IOA-MIPS of an 800 kW wind turbine; the process-based part uses ecoinvent 2.2 with the MI abiotic characterization method; the input-output part uses WIOD tables and environmental extensions.

Abiotic MIT values can be calculated using ecoinvent 2.2 and abiotic characterization factors. The results we obtain are of the same order of magnitude than existing MIT results. Some of the discrepancies that still exist are the result of several inhomogeneities in the modeling: cut-off criteria, background systems, allocation procedures, year, and region of reference. In certain cases the reason can be pinpointed very precisely. For example, the ecoinvent iron/steel processes use lower grade ores compared to existing MIPS studies. This may stem from the fact that current LCA studies are often aimed at life cycle outputs (e.g., emissions) or, when looking into life cycle inputs, do not account for used and unused extraction. In the latter case, whether modeling, for example, life cycle iron use, or implementing the midpoint characterization method Abiotic Depletion Potential, only the existing “net ore” elementary flows are required. Since used and unused extraction quantities are closely linked to ore quality and mining techniques, extraction processes are usually more differentiated in MIPS studies.

A closer integration of MIPS concepts into LCA databases such as ecoinvent could help overcome this issue. New elementary flows labelled “used extraction” and “unused extraction” would be introduced. Some of the existing ecoinvent extraction processes could be duplicated and modeled with different used and unused extractions (and possibly other changes regarding e.g., energy intensity) to represent the extraction of different types of ores. The MI abiotic characterization method would then simply add up the used and unused extraction elementary flows, leaving out the traditional “net ore” elementary flows, thus avoiding double counting.

Future-oriented MIPS analyses can be tackled with dynamic MIPS. Forecasts of technological change in the foreground and background systems are used to alter the technology matrix A and intervention matrix B. To keep the added complexity manageable, processes both contributing significantly to the MIPS results and expected to vary substantially over time should be focused on [

Hybrid MIPS analyses can be conducted today and represent the same improvement over regular MIPS as hybrid LCA over regular LCA: limit truncation errors [

This article has attempted to provide a complete picture of historical MIPS calculation methods and extend it with modern inventory problem solving techniques based on matrix inversion. The matrix formulation is a powerful one. It allows one to rather simply use whole LCA databases and implement algorithms for in-depth result analysis, dynamic modeling, and hybridization with IOA. We have demonstrated how a custom midpoint characterization method can be applied to the ecoinvent database for calculating abiotic MIT and MIPS.

We conclude that it is viable to use ecoinvent data combined with abiotic MI characterization factors and that this approach can be extended to other MI categories. We advocate a closer integration of the MIPS concept in LCA databases such as ecoinvent, which would benefit both ISO LCA and MIPS analysts. New elementary flows would cover “used extraction” and “unused extraction”. Extracting processes modeled in the technology matrix would be more differentiated (e.g., regarding ore types). We also conclude that MIPS calculations based on matrix inversion opens up a new range of applications towards dynamic and hybrid studies, which places MIPS at a similar level of development as its well-established LCA counterpart.

The authors thank and acknowledge Helmut Schütz (Wuppertal Institute) for compiling and providing the data on unused extraction necessary for generating the MI abiotic characterization factors.

The authors declare no conflict of interest.