Inﬂuence of Different Allocation Methods for Recycling and Dynamic Inventory on CO 2 Savings and Payback Times of Light-Weighted Vehicles Computed under Product- and Fleet-Based Analyses: A Case of Internal Combustion Engine Vehicles

: Light weighting by material substitution is a key to reducing GHG emissions during vehicle operation. The GHG beneﬁts are a salient factor in selecting lightweight materials for vehicles. Although the literature has performed lightweight material selections using GHG beneﬁts under product- and ﬂeet-based life-cycle inventory (LCI) analyses, recycling effects have therein been accounted for by arbitrarily selecting allocation methods for recycling, as the consensus on their selection is absent. Furthermore, studies have mistreated the temporal variations of the LCI parameters (the dynamic inventory (DI)), though that could be an important factor affecting the overall LCI results when allocation methods for recycling are in place. Therefore, to investigate their inﬂuence on greenhouse gas (GHG) beneﬁt evaluations, an LCI case study was conducted, centered on aluminum- and magnesium-substituted internal combustion engine vehicles (ICEVs) at the product- and ﬂeet- levels. “CO 2 savings” and the “CO 2 payback time”, as well as four allocation methods for recycling, were considered to represent the GHG beneﬁts and address the recycling effects, respectively. The dynamic inventory was based on the world average electricity grid mix change. The results indicate that changing the conditions of the DI and the allocation methods for recycling could alter the better performing material under ﬂeet-based analyses. Therefore, we ascertained that the choice of the allocation method for recycling and conducting ﬂeet-scale dynamic LCI analyses in the presence of the DI is pivotal for material selections.


Introduction
The transportation sector is an important industrial sector in any economy that deals with the movement of people and products [1]. It includes air freight and logistics, airlines, and marine, road, rail, and transportation infrastructure [2]. Despite its importance to society, the transportation sector has become one of the major sources of global greenhouse gas (GHG) emissions caused by the burning of fossil fuels [3,4]. For instance, in 2020, about 16% of the global GHG emissions were from the transportation sector [5]. More than two-thirds of transportation-related emissions are derived from automobiles [5,6]. Hence, stringent fuel consumption regulations have been imposed to ensure sustainable road transportation by regulating these emissions [7,8].
time, and this means that the timing of, for instance, production, is not the same as that of the end-of-life or recycling. Moreover, in terms of a fleet-based analysis, the timing of, for example, the recycling for each unit, may vary as per lifetime.
So far, the cut-off approach and the end-of-life recycling method have been deployed by previous product-and fleet-based LCI analyses in search of the GHG and energy benefits of lightweight materials (see Table 1). For instance, by deploying the cut-off approach under conventional product-based LCI analysis, Suzuki et al. [24] attempted estimating the energy savings associated with replacing the steel of a conventional steel-intensive car with carbon-fiber-reinforced plastics. Moon et al. [25] and Hakamada et al. [26] followed a similar approach in their analyses of the energy and GHG savings observable in aluminumand magnesium-substituted vehicles. Several studies along the same line are Tharumarajah and Koltun [27], Tharumarajah and Koltun [28], and Kelly et al. [29]. Deploying the cutoff approach under a fleet-based dynamic LCI analysis, Du et al. [30] assessed the GHG and energy savings of introducing aluminum-intensive vehicles to the current Chinese vehicle fleet. In the presence of the end-of-life recycling method, Ribeiro et al. [31], Bertrum et al. [32], Puri et al. [33], Das [34], Baroth et al. [35], and Dhingra and Das [36], conducted conventional product-based LCI analyses to learn the life-cycle GHG and energy benefits bound to high-strength steel and aluminum fenders, aluminum body parts, aluminum and fiber door skins, steel, carbon-fiber-reinforced plastic -based floor panels, plastic fenders, and aluminum-and magnesium-substituted automotive engines, respectively. Similar natured studies, such as Mayyas et al. [37] and Dubreuil et al. [38], are also evident. Several dynamic natured LCI studies deploy the end-of-life recycling method; for instance, both the energy and CO 2 payback times of aluminum vs steel and ultralight steel car bodies-inwhite have been estimated using product-and fleet-based LCI analyses by Das [39]. Under the same conditions, Das [40] and Kim [10] estimated the energy payback time associated with a magnesium automotive liftgate inner, and the GHG savings and payback times of high-strength steel and aluminum-substituted cars, respectively. In an attempt to evaluate the CO 2 payback time of aluminum-over steel-intensive fleets, Field et al. [41] deployed two product fleet growth models (i.e., exponential and logistic) under the presence of both abinitio, i.e., the fleets of both conventional and alternative vehicles grow at the same rate till a steady state is reached and displacement scenarios, i.e., consider that the alternative product fleet gradually replaces the conventional fleet that is already in use. Some other studies along the same line are Cáceres [42] and Stasinopoulos [43], which estimate the CO 2 payback times and the energy benefits of light-alloy-substituted vehicle fleets over steel-intensive vehicle fleets, respectively. Table 1. Recent research work on lightweight material selections and the placement of our study.

Author (Year) Allocation Method for Recycling Type of LCI Analysis Inclusion of DI (Yes/No) Content
Das [39] (2000) EOLR method Product-based Fleet-based No Energy and CO 2 payback times of aluminum vs. steel and ultralight steel car bodies-in-white.
Field et al. [41] (2000) EOLR method Product-based Fleet-based No CO 2 payback time of aluminumover steel-intensive fleets using novel product fleet-growth models.
Suzuki et al. [24] (2005) Cut-off approach Product-based No Energy savings associated with carbon-fiber-reinforced plastic-substituted vehicles.
Das [40] (2005) EOLR method Fleet-based No Energy savings and payback time associated with a magnesium automotive liftgate inner.
Moon et al. [25] (2006) Cut-off approach Product-based No Energy and GHG savings of an aluminum-substituted vehicle.
Hakamada et al. [26] (2007) Cut-off approach Product-based No CO 2 and energy benefits associated with magnesiumand aluminum-substituted vehicles. Although previous studies have performed material selections using GHG and energy benefits under diversified scenarios, their allocation methods for recycling have been selected arbitrarily, in situations where a consensus on selecting them is absent. Several previous studies have described the selection of allocation methods for recycling [23,44]. However, those have been confined to the market-and price-based approaches. Because of the regular fluctuations in material prices and their discontinued documentation, those approaches could not be applied to real situations. Furthermore, the dynamic inventory has been neglected by the above LCI studies (see Table 1). This is perhaps due to the uncertainty and complexity around deciding the temporal profiles of the LCI parameters [15,45,46]. Under these circumstances, investigating the influence of the allocation methods for recycling and dynamic inventory on the GHG benefits becomes indispensable for accurate lightweight material selections for greener automotive designs. However, to the best of our knowledge, previous LCI studies addressing such a research gap are absent. Therefore, to fill this gap, an LCI case study at both the product and fleet levels is performed herein on aluminum-and magnesium-substituted internal combustion engine vehicles (ICEVs).

Overview of the Method
This study deploys the "CO 2 savings" and the "CO 2 payback time" as indicators for the CO 2 benefits. A steel-intensive mid-sized ICEV manufactured in 2010 was considered as the baseline ICEV of the study. Furthermore, aluminum and magnesium were considered as the lightweight materials that substitute for the conventional steel in the above ICEV. The cut-off approach and three commonly used allocation methods for recycling, waste-mining, and 50:50, and end-of-life recycling methods were selected for the evaluation [23] (See Section 2.2 for more details).
Three different natured LCI analyses were conducted centering on the life cycles of steel-, aluminum-, and magnesium-intensive ICEVs (The basic life cycle of an ICEV is depicted in Figure 1) under the respective allocation methods for recycling, as stated above. Those were: (1) A single-ICEV static LCI analysis; (2) Single-ICEV dynamic analyses, with and without dynamic inventory; and (3) Fleet-scale dynamic analyses, with and without dynamic inventory. The average lifetime of an ICEV was set at 12.6 years, as per the lifetime distribution model used in the fleet-scale dynamic LCI analyses herein. ICEV. The cut-off approach and three commonly used allocation methods for recycling, waste-mining, and 50:50, and end-of-life recycling methods were selected for the evaluation [23] (See Section 2.2 for more details). Three different natured LCI analyses were conducted centering on the life cycles of steel-, aluminum-, and magnesium-intensive ICEVs (The basic life cycle of an ICEV is depicted in Figure 1) under the respective allocation methods for recycling, as stated above. Those were: (1) A single-ICEV static LCI analysis; (2) Single-ICEV dynamic analyses, with and without dynamic inventory; and (3) Fleet-scale dynamic analyses, with and without dynamic inventory. The average lifetime of an ICEV was set at 12.6 years, as per the lifetime distribution model used in the fleet-scale dynamic LCI analyses herein. In view of preserving the simplicity in the above LCI analyses, the processing scrap generated during the vehicle assembly was assumed to be internally recycled, and the CO2 burdens associated with the replacement of tires, fluids, and batteries during vehicle use were neglected. Furthermore, processes demarcated by a blue perforated line in Figure 1 were considered as a single conglomerate, representing the production phase of ICEVs.
Inventories of baseline, aluminum-, and magnesium-intensive ICEVs were calculated following the WorldAutoSteel Energy and GHG Model [47]. The required parameters (i.e., the parameters of the end-of-life recycling method, the fuel economy of the baseline ICEV, and the fuel reduction values for light-weighted ICEVs, required to calculate the use-phase emissions, emission factors, etc.) were established with reference to the literature found on the IDEA, version 2.2 [48], and the Ecoinvent, version 3.5 [49] LCI databases. The CO2 savings were computed by subtracting the life-cycle CO2 emissions of the baseline ICEV from those of the respective light-weighted ICEVs under each allocation method. The payback times of the single-ICEV dynamic and fleet-scale dynamic analyses were determined with reference to the cross-over points of the cumulative CO2 emissions of the baseline and the light-weighted ICEVs under the same (see Table S1 in Supplementary Materials for all parameters used in the study).

Allocation Approaches and Methods
Materials can be recycled multiple times in a series of product life cycles, generating recycling effects, i.e., burdens avoided, for instance, by consuming the secondary re- In view of preserving the simplicity in the above LCI analyses, the processing scrap generated during the vehicle assembly was assumed to be internally recycled, and the CO 2 burdens associated with the replacement of tires, fluids, and batteries during vehicle use were neglected. Furthermore, processes demarcated by a blue perforated line in Figure 1 were considered as a single conglomerate, representing the production phase of ICEVs.
Inventories of baseline, aluminum-, and magnesium-intensive ICEVs were calculated following the WorldAutoSteel Energy and GHG Model [47]. The required parameters (i.e., the parameters of the end-of-life recycling method, the fuel economy of the baseline ICEV, and the fuel reduction values for light-weighted ICEVs, required to calculate the use-phase emissions, emission factors, etc.) were established with reference to the literature found on the IDEA, version 2.2 [48], and the Ecoinvent, version 3.5 [49] LCI databases. The CO 2 savings were computed by subtracting the life-cycle CO 2 emissions of the baseline ICEV from those of the respective light-weighted ICEVs under each allocation method. The payback times of the single-ICEV dynamic and fleet-scale dynamic analyses were determined with reference to the cross-over points of the cumulative CO 2 emissions of the baseline and the light-weighted ICEVs under the same (see Table S1 in Supplementary Materials for all parameters used in the study).

Allocation Approaches and Methods
Materials can be recycled multiple times in a series of product life cycles, generating recycling effects, i.e., burdens avoided, for instance, by consuming the secondary resources from the previous life cycle in the current life cycle. To consider the recycling effects, expanding the system boundary to previous and subsequent product life cycles is necessary. Then, to calculate the LCI of the current life cycle, allocating the recycling effects between the previous, current, and subsequent product life cycles is required. Though this "allocation of recycling effects" is under much debate in the field of life-cycle assessment (LCA), several allocation approaches and methods have already been proposed in the literature [50]. Of them, the commonly used allocation approaches and methods were considered for this study.

The Cut-Off Approach
This approach only accounts for the environmental impacts that are directly related to the functional units of products [23]. In other words, this approach is constrained to the system boundary of the production system itself and tends to neglect the allocation of recycling effects derived from both consuming and recovering secondary resources on the input and output sides of the current life cycle, respectively. The formula for the cut-off approach is defined by Equation (1) [23]: where X LCI is the LCI (with recycling effects) of the material used for the current product; X pr is the LCI for primary material production; X re is the LCI for secondary material production; S is the fraction of secondary resources supplied for the material of interest; Y is the process yield; W is the LCI of the waste treatment of the material used for the current product; and R is the fraction of material recovered as secondary resources during the life cycle of the current product.

The Waste-Mining Method
If the market for a secondary resource has shrunk or disappeared, providing the secondary resource will not bring benefits [44,51]. In such cases, the increase in the secondary resource may lead to a decrease in the recovery from other products, and those resources may no longer be treated as resources [50]. Here, a credit created by recycling should be given to the consumption of secondary resources [23]. In this method, no environmental credit is given for recovering secondary resources, and it is modeled as if the end-of-life recycling rate is zero (100% waste disposal); the formula representing the waste-mining method is given in Equation (2) [23]: where W previous is the LCI for the waste treatment of the material used for the previous product.

The End-of-Life Recycling Method
In the end-of-life recycling method, the recycling effects incurred by recovering a secondary resource in the current life cycle is allocated to the current life cycle itself on the premise that this recovered secondary resource avoids the production of primary materials in the subsequent life cycle; however, the consumption of secondary resources in the current life cycle is not credited [23]. The equation for the end-of-life recycling method can be given as Equation (3): where X pr,next and X re,next are the LCIs for primary and secondary material production in the next life cycle.

The 50:50 Method
The 50:50 method shares the credits (generated by consuming and recovering secondary resources in the current life cycle) and the burdens incurred from recycling in the current life cycle with previous and subsequent life cycles; it can be defined as Equation (4). This method is based on the premise that the price elasticity of the supply and demand of the material of interest is equal [50]:

Material Inventory Calculations
The baseline ICEV herein weighed 1656 kg [47]. The yield ratios at vehicle assembly for steel-, aluminum-, and magnesium-related materials were assumed at 65% [26], while those for the rest of the materials were presumed to be 100%. Moreover, a 0% yield ratio was assumed at the material finishing stage for all materials. The weight of each material at the inventory of the ICEV was divided by the corresponding yield ratio to acquire its unfinished weight on the input side of the "material finishing".
Conventional steel, weighing 360 kg (i.e., 90% of flat carbon steel and 10% of long and special steel) could be replaced by lightweight materials [52], i.e., wrought aluminum and magnesium. Therefore, the amount required to replace the steel to be removed was calculated by multiplying the aforementioned weight by the material replacement coefficients of aluminum and magnesium. The reduced weight is deemed "primary weight savings". The savings acquired through the further reduction of materials at the suspension, structural components, transmission, etc., are called "secondary weight savings" [10]. Herein, the secondary weight savings were assumed to be 30% of the primary weight savings. Flat carbon and special steel and wrought and cast aluminum were assumed to have shares of 30, 20, 20, and 30% of the secondary weight savings, respectively. The "weight savings for each material", thus, could be calculated by adding its primary and secondary weight savings. Bills of the materials of the aluminum-and magnesium-intensive ICEVs were obtained; the final weights of them were recorded at 1485 and 1396 kg, respectively.

Use-Phase Inventory Calculations
Use-phase-bound CO 2 emissions for the baseline and light-weighted vehicles were calculated following Equations (5) and (6), respectively. The fuel economy, F C , and the fuel reduction values (FRVs) of those equations were determined with reference to Kim et al. [11]. Required emission factors (i.e., gasoline production and combustion) were extracted from the IDEA version 2.2 database [53]. The annual distance traveled was assumed to be 15,000 km and remained constant throughout the lifetime of the ICEVs.
where X use,baseline , F C , d, EF gp , and EF gc are the CO 2 emissions from the use phase, the fuel consumption of the standard ICEV, the running distance, and the CO 2 emission factors for gasoline production and combustion, respectively.
where X use,lightweighted , ∆M, and FRV are the CO 2 emissions from the use phase of the light-weighted ICEV, the weight change, and the fuel reduction value, respectively.

Development of Dynamic Inventory
In general, dynamic inventory refers to the temporal variations of the LCI parameters along the period of forecast. To avoid complicacy in preparing the dynamic inventory, the aforementioned variations herein were based on the fluctuations in the CO 2 intensity of the world average electricity grid mix along the forecast period. Parametric variations related to primary aluminum and magnesium (i.e., the Pidgeon process: 70%; the electrolytic process: 30%), plastic, secondary steel (i.e., the electric arc furnace process), and aluminum production were considered for the dynamic inventory. However, considering the lack of inventory data and the dependency on electricity, the rest of the parameters were assumed unchanged along the forecast period. The temporal variation of each LCI parameter was calculated by changing the CO 2 emissions derived from the electricity use per functional unit (within the "overall CO 2 emissions per functional unit"), according to the CO 2 intensity change in the subjected electricity grid mix.
The carbon dioxide intensities of the world average electricity grid mix were extracted from the International Energy Agency's historical and sustainable development scenario (SDS) data [54]. Because of the absence of CO 2 intensities beyond 2040 in the SDS, the existing CO 2 intensities were extrapolated up to 2060, assuming those will reach 0 kg CO 2 per kWh by 2050.

Single-ICEV Static LCI Analyses
The single-ICEV static LCI analysis herein estimates the life cycle CO 2 emissions of a single ICEV and assumes that the life-cycle model parameters remain constant over time; hence, it necessarily "compresses" all time-dependent emissions into a single value, and merely provides a snapshot of the life-cycle CO 2 emissions [14,15]. The single-ICEV static analyses herein are based on the parameters from the year 2010. The CO 2 savings were calculated by subtracting the CO 2 emissions of the baseline ICEV from those of the lightweight ICEVs for each allocation approach.

Single-ICEV Dynamic LCI Analyses
Similar to the single-ICEV static analysis, single-ICEV dynamic analyses belong to the conventional LCI category, as they are based on a single product [15]. In this type of analysis, life-cycle emissions are distributed across time; hence, they provide a more detailed overview of the temporal variations of emissions than its single-ICEV static counterpart. All of the life-cycle stages of the single-ICEV dynamic analyses without dynamic inventory were based in the year 2010, while the production, use, and end-of-life phases of those with dynamic inventory were based in the years, 2010 and 2023, respectively. Paybacks were achieved referring to point "0" of the cumulative CO 2 emission differences (i.e., the crossover points of the cumulative CO 2 emissions of the baseline and the respective light-weighted ICEVs) of each light-weighted ICEV under the respective allocation method. The time series change of the CO 2 savings is represented by the cumulative CO 2 emission difference curve belonging to each allocation method.

Fleet-Scale Dynamic LCI Analyses
Fleet analyses account for changes over time in the CO 2 emissions in a vehicle fleet using a fleet model that accounts for the dynamics of vehicle introduction and the scrappage rates in each year [14,43,55]. Since the objective here is to investigate the behavior of the payback times of ICEVs with new material types, the start of the analysis is a zero-car fleet that grows at a fixed rate annually during the forecast period, i.e., 50 years [40,41]. A single unit of vehicle is assumed to be produced each year for simplicity, as it could be any multiple of any sales figure. Furthermore, a flat annual growth rate of the ICEVs (i.e., one unit is produced and added to the "units in service" annually) was assumed to preserve the simplicity in the calculations. The fleet model was constructed following the lifetime distribution model for ICEVs in Daigo et al. [55]. The payback times for each light-weighted ICEV were acquired for each allocation method by referring to the point "0" of the cumulative CO 2 emission differences. The cumulative CO 2 emission difference curve represents the time-series change of the CO 2 savings for each allocation method. Figure 2 illustrates the life-cycle CO 2 emissions of baseline, aluminum-, and magnesiumintensive cars, acquired using the cut-off approach, and the waste-mining, end-of-life recycling, and 50:50 methods for single-car static analyses. As per Figure 2, the use-phase emissions dominated the overall emissions of baseline, aluminum-, and magnesiumintensive cars. Since the recovery rates assumed for flat carbon, long special steel, and wrought aluminum are larger than their recycled contents, avoided burdens from recovering secondary resources under the end-of-life recycling and 50:50 methods have become larger than those from consuming secondary resources under the cut-off approach and the waste-mining method in the case of aluminum-intensive ICEVs. As a result, CO 2 emissions recorded under the cut-off approach and the waste-mining method become larger than those under the end-of-life recycling and 50:50 methods for that ICEV. On the other hand, the magnesium's recycled content and end-of-life recycling rates were assumed to be 0% for this study. Hence, total avoided burdens from recovering secondary resources (under the end-of-life recycling and 50:50 methods) have become smaller than those from consuming secondary resources (under the cut-off approach and waste-mining method) for magnesium-intensive ICEVs; this has made CO 2 emissions under the end-of-life recycling and 50:50 methods larger than those computed under the cut-off approach and the waste-mining method. Furthermore, both light-weighted ICEVs have yielded CO 2 savings at each allocation method, indicating the possibility of CO 2 payback times. life recycling, and 50:50 methods for single-car static analyses. As per Figure 2, the usephase emissions dominated the overall emissions of baseline, aluminum-, and magnesium-intensive cars. Since the recovery rates assumed for flat carbon, long special steel, and wrought aluminum are larger than their recycled contents, avoided burdens from recovering secondary resources under the end-of-life recycling and 50:50 methods have become larger than those from consuming secondary resources under the cut-off approach and the waste-mining method in the case of aluminum-intensive ICEVs. As a result, CO2 emissions recorded under the cut-off approach and the waste-mining method become larger than those under the end-of-life recycling and 50:50 methods for that ICEV.

Results
On the other hand, the magnesium's recycled content and end-of-life recycling rates were assumed to be 0% for this study. Hence, total avoided burdens from recovering secondary resources (under the end-of-life recycling and 50:50 methods) have become smaller than those from consuming secondary resources (under the cut-off approach and waste-mining method) for magnesium-intensive ICEVs; this has made CO2 emissions under the end-oflife recycling and 50:50 methods larger than those computed under the cut-off approach and the waste-mining method. Furthermore, both light-weighted ICEVs have yielded CO2 savings at each allocation method, indicating the possibility of CO2 payback times.  Figure 3 depicts the CO2 savings and payback times of single-ICEV dynamic analyses for both aluminum-and magnesium-intensive ICEVs, with and without dynamic inventory. In all cases, the CO2 payback times appear during the use phase and tend to vary across the allocation methods, i.e., the shortest payback period is from end-of-life recycling, while the second shortest, and the longest, are from the 50:50 method, the cut-off approach, and the waste-mining method, respectively. The difference of the avoided burdens from consuming secondary resources at the baseline ICEV remain larger than those from the aluminum-and magnesium-intensive ICEVs. Zeroed recycled contents of wrought aluminum and magnesium are the main factors for the lowered avoided burdens. Hence, the emission offsets under the cut-off approach and the waste-mining method were more delayed than those under the 50:50 and end-of-life recycling methods for those vehicles.  Figure 3 depicts the CO 2 savings and payback times of single-ICEV dynamic analyses for both aluminum-and magnesium-intensive ICEVs, with and without dynamic inventory. In all cases, the CO 2 payback times appear during the use phase and tend to vary across the allocation methods, i.e., the shortest payback period is from end-of-life recycling, while the second shortest, and the longest, are from the 50:50 method, the cut-off approach, and the waste-mining method, respectively. The difference of the avoided burdens from consuming secondary resources at the baseline ICEV remain larger than those from the aluminumand magnesium-intensive ICEVs. Zeroed recycled contents of wrought aluminum and magnesium are the main factors for the lowered avoided burdens. Hence, the emission offsets under the cut-off approach and the waste-mining method were more delayed than those under the 50:50 and end-of-life recycling methods for those vehicles. Sustainability 2021, 13, x 10 of 17 According to Figure 3a,b, the CO2 savings for the magnesium-intensive ICEV under the cut-off approach and the waste-mining method have become larger than those for the aluminum-intensive ICEV under the same. Furthermore, the largest CO2 savings are visible in the cut-off approach and the waste-mining method for the magnesium-intensive ICEV. The influence of CO2 credits from the uplifted fuel economy and the zeroed avoided burdens from the recovery of secondary resources of magnesium in the end-of-life recycling and 50:50 methods are the roots of such trends. At this juncture, one who uses the cut-off approach or the waste-mining method may select magnesium over aluminum, while someone else who uses the end-of-life recycling or the 50:50 methods does vice versa. Therefore, material selection using CO2 savings can differ from that implemented using payback times under single-ICEV dynamic analyses.
However, according to Figure 3c,d, the inclusion of the dynamic inventory has altered neither the payback times nor the CO2 savings for both aluminum-and magnesiumintensive ICEVs for the following reasons: (1) Paybacks occurred during the use phase, the parameters of which remain unchanged; and (2) The changes that the dynamic inventory gives to the end-of-life phase of the respective ICEV are negligible. Figure 4 encapsulates the figures for the time-series changes of the CO2 savings and payback times under fleet-scale dynamic LCI analyses, in the presence and absence of dynamic inventory, for both aluminum-and magnesium-intensive fleets. In Figure 4a,b in which the dynamic inventory is not included, all payback times for both vehicles were delayed, unlike those indicated under single-ICEV dynamic LCI analyses. However, at all allocation methods, the aluminum-intensive ICEV tends to perform better than the magnesium-intensive ICEV, resembling the results of the corresponding single-ICEV dynamic analyses. In general, delays in payback times can occur because of the nature of the fleet model; in the fleet model, fresh units are introduced in the early years, allowing production-based CO2 emissions to dominate in the early stages. Since no CO2 emission credits can be expected from the production phase of the lightweight ICEVs (i.e., aluminum-and According to Figure 3a,b, the CO 2 savings for the magnesium-intensive ICEV under the cut-off approach and the waste-mining method have become larger than those for the aluminum-intensive ICEV under the same. Furthermore, the largest CO 2 savings are visible in the cut-off approach and the waste-mining method for the magnesium-intensive ICEV. The influence of CO 2 credits from the uplifted fuel economy and the zeroed avoided burdens from the recovery of secondary resources of magnesium in the end-of-life recycling and 50:50 methods are the roots of such trends. At this juncture, one who uses the cutoff approach or the waste-mining method may select magnesium over aluminum, while someone else who uses the end-of-life recycling or the 50:50 methods does vice versa. Therefore, material selection using CO 2 savings can differ from that implemented using payback times under single-ICEV dynamic analyses. However, according to Figure 3c,d, the inclusion of the dynamic inventory has altered neither the payback times nor the CO 2 savings for both aluminum-and magnesiumintensive ICEVs for the following reasons: (1) Paybacks occurred during the use phase, the parameters of which remain unchanged; and (2) The changes that the dynamic inventory gives to the end-of-life phase of the respective ICEV are negligible. Figure 4 encapsulates the figures for the time-series changes of the CO 2 savings and payback times under fleet-scale dynamic LCI analyses, in the presence and absence of dynamic inventory, for both aluminum-and magnesium-intensive fleets. In Figure 4a,b in which the dynamic inventory is not included, all payback times for both vehicles were delayed, unlike those indicated under single-ICEV dynamic LCI analyses. However, at all allocation methods, the aluminum-intensive ICEV tends to perform better than the magnesium-intensive ICEV, resembling the results of the corresponding single-ICEV dynamic analyses. In general, delays in payback times can occur because of the nature of the fleet model; in the fleet model, fresh units are introduced in the early years, allowing production-based CO 2 emissions to dominate in the early stages. Since no CO 2 emission credits can be expected from the production phase of the lightweight ICEVs (i.e., aluminum-and magnesium-intensive ICEVs), CO 2 emission gaps between the baseline and respective lightweight fleets tend to get larger during the early years.  The behavior of the payback times for the magnesium-intensive fleet is different from that of the aluminum-intensive fleet, where the curves converge before reaching the breakeven points; this has given the cut-off approach, and the waste-mining and EOLR methods the shortest and longest payback times, respectively. Convergence here reflects the weakened effect of the end-of-life phases of the end-of-life recycling and 50:50 methods, where the avoided burdens from recovering secondary resources of magnesium are zero. In this case, unlike the CO2 payback times observed in the single-ICEV dynamic analyses, those observed in the fleet-scale dynamic LCI analyses were influenced by the CO2 emissions associated with the EOL phase.
Carbon dioxide savings seem to depend on the "period of forecast" in fleet-scale dynamic LCI analyses. For instance, the CO2 savings computed in the cut-off and wastemining methods for both aluminum-and magnesium-intensive ICEVs are almost the same for the 50-year period of the forecast (see Figure 4a,b). Therefore, an intersection of them can be expected when a longer period of forecast than 50 years is considered; this means that the CO2 savings of magnesium-intensive ICEVs become larger than those of aluminum-intensive ICEVs. Therefore, the material being selected, using CO2 savings in the cut-off approach or the waste-mining method, can be different from that being selected with reference to the CO2 payback times at the same under a fleet-scale dynamic analysis with a longer period of forecast. Figure 4c,d depict the payback times for aluminum-and magnesium-intensive fleets in the presence of dynamic inventory, respectively. With the introduction of dynamic inventory, all of the payback times of aluminum-and magnesium-intensive ICEVs have been shortened; this stems from the reduction in the CO2 emissions of primary aluminum and magnesium production during the forecast period (see Figure S1 in Supplementary Materials). The CO2 emissions attributed to primary aluminum production heavily depend on the electricity consumption of the smelting process; hence, reducing the CO2 intensity of the electricity grid mix along the period of forecast alleviated the overall CO2 The behavior of the payback times for the magnesium-intensive fleet is different from that of the aluminum-intensive fleet, where the curves converge before reaching the breakeven points; this has given the cut-off approach, and the waste-mining and EOLR methods the shortest and longest payback times, respectively. Convergence here reflects the weakened effect of the end-of-life phases of the end-of-life recycling and 50:50 methods, where the avoided burdens from recovering secondary resources of magnesium are zero. In this case, unlike the CO 2 payback times observed in the single-ICEV dynamic analyses, those observed in the fleet-scale dynamic LCI analyses were influenced by the CO 2 emissions associated with the EOL phase.
Carbon dioxide savings seem to depend on the "period of forecast" in fleet-scale dynamic LCI analyses. For instance, the CO 2 savings computed in the cut-off and wastemining methods for both aluminum-and magnesium-intensive ICEVs are almost the same for the 50-year period of the forecast (see Figure 4a,b). Therefore, an intersection of them can be expected when a longer period of forecast than 50 years is considered; this means that the CO 2 savings of magnesium-intensive ICEVs become larger than those of aluminum-intensive ICEVs. Therefore, the material being selected, using CO 2 savings in the cut-off approach or the waste-mining method, can be different from that being selected with reference to the CO 2 payback times at the same under a fleet-scale dynamic analysis with a longer period of forecast. Figure 4c,d depict the payback times for aluminum-and magnesium-intensive fleets in the presence of dynamic inventory, respectively. With the introduction of dynamic inventory, all of the payback times of aluminum-and magnesium-intensive ICEVs have been shortened; this stems from the reduction in the CO 2 emissions of primary aluminum and magnesium production during the forecast period (see Figure S1 in Supplementary Materials). The CO 2 emissions attributed to primary aluminum production heavily depend on the electricity consumption of the smelting process; hence, reducing the CO 2 intensity of the electricity grid mix along the period of forecast alleviated the overall CO 2 emissions of primary aluminum production by a significant amount. The Pidgeon process, which is the main process to produce magnesium, is less dependent on electricity, unlike its counterpart, the electrolytic process; hence, relatively fewer CO 2 reductions are evident.

Discussion
As per the results, the aluminum-intensive ICEV always performed better than the magnesium-intensive ICEV in the respective allocation methods for recycling, while the dynamic inventory was highly sensitive to the CO 2 savings and payback times calculated under the fleet-based LCI analyses.
However, the inclusion of a dynamic inventory that captures more aspects, such as the production ratio of the Pidgeon process, future possibilities for recycling magnesium as a structural material, etc., results in shorter payback time(s) for magnesium-intensive ICEVs in certain allocation method(s) for recycling. See Figure 5, where the payback periods for the magnesium-intensive ICEV in the cut-off approach and the waste mining method are shorter than those of the aluminum-intensive ICEV. Therefore, in the absence of such a dynamic inventory, the payback time of aluminum under a particular allocation method will always be shorter than that of magnesium under fleet-scale dynamic LCI analyses; moreover, such a variation will not be reflected either through single-ICEV static or dynamic analyses. Hence, conducting fleet-scale dynamic LCI analyses with a dynamic inventory can be pivotal in knowing the payback times.
Sustainability 2021, 13, x 12 emissions of primary aluminum production by a significant amount. The Pidgeon cess, which is the main process to produce magnesium, is less dependent on electr unlike its counterpart, the electrolytic process; hence, relatively fewer CO2 reduction evident.

Discussion
As per the results, the aluminum-intensive ICEV always performed better than magnesium-intensive ICEV in the respective allocation methods for recycling, whil dynamic inventory was highly sensitive to the CO2 savings and payback times calcu under the fleet-based LCI analyses.
However, the inclusion of a dynamic inventory that captures more aspects, su the production ratio of the Pidgeon process, future possibilities for recycling magne as a structural material, etc., results in shorter payback time(s) for magnesium-inten ICEVs in certain allocation method(s) for recycling. See Figure 5, where the payback ods for the magnesium-intensive ICEV in the cut-off approach and the waste mi method are shorter than those of the aluminum-intensive ICEV. Therefore, in the abs of such a dynamic inventory, the payback time of aluminum under a particular alloc method will always be shorter than that of magnesium under fleet-scale dynamic analyses; moreover, such a variation will not be reflected either through single-ICEV s or dynamic analyses. Hence, conducting fleet-scale dynamic LCI analyses with a dyn inventory can be pivotal in knowing the payback times. Figure 5. Payback times and time-series change in CO2 savings under fleet-scale dynamic analyses with dynamic inventory. Aluminum-and magnesium-intensive fleets are represented by continuous and perforated lines, respectively. It was assumed that the production ratio of the Pidgeon process would be 0% by 2020.
With the addition of dynamic inventory, the CO2 savings of the aluminum-inten fleet under the cut-off approach and other allocation methods have become larger those of the magnesium-intensive fleet, regardless of the "period of forecast", as no i section of the curves is evident or can be imagined within or beyond the 50-year for period considered herein (see Figure 4c,d). However, a dynamic inventory that cap more aspects can bring back the "influence of period of forecast", i.e., the possibili different materials being selected at different periods of forecasts under the exact al tion method (see Figure 5, where CO2 savings under each allocation method for the m nesium-intensive ICEV are larger than those for the aluminum-intensive ICEV withi subjected period of forecast). Therefore, this implies that conducting a fleet-scale dyn LCI analysis, including a dynamic inventory, is important in knowing the CO2 saving material selections.
However, if magnesium has higher recycled content than its end-of-life recy rate, it can result in shorter payback times in the cut-off approach and the waste-mi method (see Figure 6), while aluminum with a lower recycled content than its end-o recycling rate indicates shorter payback times in the EOLR and 50:50 methods. Hen With the addition of dynamic inventory, the CO 2 savings of the aluminum-intensive fleet under the cut-off approach and other allocation methods have become larger than those of the magnesium-intensive fleet, regardless of the "period of forecast", as no intersection of the curves is evident or can be imagined within or beyond the 50-year forecast period considered herein (see Figure 4c,d). However, a dynamic inventory that captures more aspects can bring back the "influence of period of forecast", i.e., the possibility of different materials being selected at different periods of forecasts under the exact allocation method (see Figure 5, where CO 2 savings under each allocation method for the magnesium-intensive ICEV are larger than those for the aluminum-intensive ICEV within the subjected period of forecast). Therefore, this implies that conducting a fleet-scale dynamic LCI analysis, including a dynamic inventory, is important in knowing the CO 2 savings for material selections.
However, if magnesium has higher recycled content than its end-of-life recycling rate, it can result in shorter payback times in the cut-off approach and the waste-mining method (see Figure 6), while aluminum with a lower recycled content than its end-of-life recycling rate indicates shorter payback times in the EOLR and 50:50 methods. Hence, a practitioner using the 50:50 or end-of-life recycling methods would select the aluminumintensive ICEV as the best choice, while someone else using the cut-off approach or the waste-mining method would select the magnesium-intensive ICEV as the best option.
Hence, the choice of allocation method can perform a salient role in the payback time evaluations in fleet-based LCI dynamic analyses.
Hence, the choice of allocation method can perform a salient role in the payback time evaluations in fleet-based LCI dynamic analyses.
The same tendency is evident in the CO2 savings. If magnesium possesses larger recycled content than the end-of-life recycling rate, it can show larger CO2 savings in the cut-off approach and the waste-mining method, regardless of the period of forecast (see Figure 6). However, in the case of aluminum, the end-of-life recycling rate is larger than the recycled content; hence, larger CO2 savings are observable in the 50:50 and end-of-life recycling methods, regardless of the same. In short, upon the selection of the allocation method, the material being selected can vary; hence, the choice of allocation approach is deemed important in terms of material selection using CO2 savings. Overall, the choice of allocation method and conducting fleet-based dynamic LCI analyses under the presence of dynamic inventory were critical in obtaining the CO2 savings or payback times for consistent and accurate material selections.
The payback times and the CO2 savings are sensitive to the kind of data that is referred to when determining the pr X and re X , the recycled contents, the end-of-life recycling rates, the material substitution rates, the annual distance traveled, the fuel reduction value, and the secondary mass reduction rate, along the period of forecast representing dynamic inventory. Hence, in order to achieve consistent payback times, regardless of the time and place of evaluation, a common dataset is required for the above parameters. However, predicting such parameters can be difficult, as the future is uncertain. Approaches, such as dynamic material flow analysis [56] and scenario modeling [57], may be helpful in this regard. As mentioned earlier, a designated methodology or criteria for selecting an allocation method for recycling has been absent, except for methods relying upon market information that is highly changeable and infrequently documented; hence, a more convenient method that depends on less changeable and more readily accessible information is required for the above selection process. For instance, a methodology that refers to material properties can be a solution, as the material properties are less vulnerable to rapid fluctuations.
According to the pressure that climate change has put on manufacturers, they are required to provide products with smaller carbon footprints across life cycles to the market. At the initial stage, manufacturers decide on a design for their products, which significantly affects the footprint. One of the issues in the design phase is material selection. The same tendency is evident in the CO 2 savings. If magnesium possesses larger recycled content than the end-of-life recycling rate, it can show larger CO 2 savings in the cut-off approach and the waste-mining method, regardless of the period of forecast (see Figure 6). However, in the case of aluminum, the end-of-life recycling rate is larger than the recycled content; hence, larger CO 2 savings are observable in the 50:50 and end-of-life recycling methods, regardless of the same. In short, upon the selection of the allocation method, the material being selected can vary; hence, the choice of allocation approach is deemed important in terms of material selection using CO 2 savings.
Overall, the choice of allocation method and conducting fleet-based dynamic LCI analyses under the presence of dynamic inventory were critical in obtaining the CO 2 savings or payback times for consistent and accurate material selections.
The payback times and the CO 2 savings are sensitive to the kind of data that is referred to when determining the X pr and X re , the recycled contents, the end-of-life recycling rates, the material substitution rates, the annual distance traveled, the fuel reduction value, and the secondary mass reduction rate, along the period of forecast representing dynamic inventory. Hence, in order to achieve consistent payback times, regardless of the time and place of evaluation, a common dataset is required for the above parameters. However, predicting such parameters can be difficult, as the future is uncertain. Approaches, such as dynamic material flow analysis [56] and scenario modeling [57], may be helpful in this regard.
As mentioned earlier, a designated methodology or criteria for selecting an allocation method for recycling has been absent, except for methods relying upon market information that is highly changeable and infrequently documented; hence, a more convenient method that depends on less changeable and more readily accessible information is required for the above selection process. For instance, a methodology that refers to material properties can be a solution, as the material properties are less vulnerable to rapid fluctuations.
According to the pressure that climate change has put on manufacturers, they are required to provide products with smaller carbon footprints across life cycles to the market. At the initial stage, manufacturers decide on a design for their products, which significantly affects the footprint. One of the issues in the design phase is material selection. This paper successfully demonstrates a case study that proved that conventional LCI analyses might lead to the wrong choice of materials. According to this study, we recommend that manufacturers conduct an inventory analysis at the fleet scale, formulate a certain reason for selecting the allocation method of recycling, and perform a dynamic inventory, considering the lifespan of their products, in order to make better choices of materials. Furthermore, the carbon footprint is not the only target for sustainability. In many cases, a decision causes tradeoffs between different categories of environmental impacts. In the context of the LCA, some approaches have been proposed for harmonizing different impact categories: environmental priority strategies in product development [58], distanceto-target [59], the panel method [60], and the analytic hierarchy process [61,62].

Conclusions
We highlight the importance of the choice of allocation method for recycling and conducting fleet-scale dynamic analyses in the presence of dynamic inventory for material selections through an LCI case study on aluminum-and magnesium-substituted ICEVs.
Aluminum-intensive ICEVs always performed better than magnesium-intensive ICEVs (with larger CO 2 savings and shorter payback times) in the respective allocation methods for recycling, regardless of the presence of the subjected dynamic inventory (based on the change in the world average electricity grid mix) under fleet-based LCI analyses. However, we identified that a dynamic inventory capturing more aspects could make magnesium-intensive ICEVs perform better than others in certain allocation method(s) for recycling under the same.
Furthermore, when the recycled content of magnesium was greater than its recovery rate, magnesium-intensive ICEVs resulted in larger CO 2 savings and shorter payback times in certain allocation methods under fleet-based analyses. Such instances could compel practitioners to select magnesium-intensive ICEVs over others in those allocation methods for recycling.
Therefore, the choice of the allocation method for recycling and the execution of fleet-based dynamic LCI analyses under the presence of dynamic inventory are crucial in obtaining the CO 2 savings or payback times for material selections. Neglecting even one of them may result in the wrong material selection. Standardizing the selection of the allocation methods for recycling and a common dataset for the dynamic inventory are dire requirements for assuring accordance in the calculations of the CO 2 savings and payback times, regardless of the time and place of the evaluations.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/10 .3390/su132413935/s1, Figure S1: Parameters considered for dynamic inventory and their variations along the period forecast; Table S1: Parameters considered for the study and their values.   Life-cycle inventory (with recycling effects) of the material used for the current product ((kg CO 2 /kg product) X pr Life-cycle inventory for primary material production (kg CO 2 /kg product) X re Life-cycle inventory for primary material production (kg CO 2 /kg product) S Fraction of secondary resources supplied for the material of interest (%) Y Process yield (%) R Fraction of material recovered as secondary resources during the life cycle of current production (%) W Life-cycle inventory for the waste treatment of the material used for the current product (kg CO 2 /kg product)

W previous
Life-cycle inventory for waste treatment of the material used for the previous product (kg CO 2 /kg product) X pr,next Primary material production in next LC (kg CO 2 /kg product) X re,next Secondary material production in next LC (kg CO 2 /kg product) X use, baseline CO 2 emissions from use phase of the standard ICEV (kg CO 2 /ICEV) X use, lightweighted CO 2 emissions from use phase of the lightweight ICEVs (kg CO 2 /ICEV) F C Fuel economy (L/km) d Distance travelled (km) EF gp CO 2 emission factors for gasoline production (kg CO 2 /L) EF gc CO 2 emission factors for gasoline combustion (kg CO 2 /L) ∆M Weight change (kg) FRV Fuel reduction value (L/100 kg 100 km)