Lithium Supply Chain Optimization: A Global Analysis of Critical Minerals for Batteries

Abstract

Energy storage is a foundational clean energy technology that can enable transformative technologies and lower carbon emissions, especially when paired with renewable energy. However, clean energy transition technologies need completely different supply chains than our current fuel-based supply chains. These technologies will instead require a material-based supply chain that extracts and processes massive amounts of minerals, especially critical minerals, which are classified by how essential they are for the modern economy. In order to develop, operate, and optimize the new material-based supply chain, new decision-making frameworks and tools are needed to design and navigate this new supply chain and ensure we have the materials we need to build the energy system of tomorrow. This work creates a flexible mathematical optimization framework for critical mineral supply chain analysis that, once provided with exogenously supplied projections for parameters such as demand, cost, and carbon intensity, can provide an efficient analysis of a mineral or critical mineral supply chain. To illustrate the capability of the framework, this work also conducts a case study investigating the global lithium supply chain needed for energy storage technologies like electric vehicles (EVs). The case study model explores the investment and operational decisions that a global central planner would consider in order to meet projected lithium demand in one scenario where the objective is to minimize cost and another scenario where the objective is to minimize ${\mathrm{CO}}_2$ emissions. The case study shows there is a 6% cost premium to reduce ${\mathrm{CO}}_2$ emissions by 2%. Furthermore, the ${\mathrm{CO}}_2$ Objective scenario invested in recycling capacity to reduce emissions, while the Cost Objective scenario did not. Lastly, this case study shows that even with a deterministic model and a global central planner, asset utilization is not perfect, and there is a substantial tradeoff between cost and emissions. Therefore, this framework—when expanded to less-idealized scenarios, like those focused on individual countries or regions or scenarios that optimize other important evaluation metrics—would yield even more impactful insights. However, even in its simplest form, as presented in this work, the framework illustrates its power to model, optimize, and illustrate the material-based supply chains needed for the clean energy technologies of tomorrow.

1. Introduction

Energy storage and the other technologies that power the clean energy transition are more efficient and less carbon-intensive but more material-intensive than the technologies that power our current energy system [1]. The legacy energy system is fuel-intensive and relies on the continuous extraction of fossil fuels, which are then burned in order to produce energy. In contrast to the extract, burn, and repeat cycle of the legacy energy system, the emerging clean energy system relies on technologies that, while they require larger amounts of minerals, those minerals are not discarded until at the end of the lifecycle of the technology, minimizing the total amount of materials that must be extracted, especially if the minerals are then recycled afterward. For comparison, the current energy system extracts 15 billion tons of fossil fuels (coal, oil, and natural gas), while current mineral production for clean energy technologies is 7 million tons, with an optimistic projection of 28 million tons in 2040: orders of magnitude lower [1,2]. Nonetheless, even with the relatively lower amount of required materials, the clean energy system of tomorrow requires large-scale planning of the global material supply chain, which is especially true for critical minerals.

1.1. Critical Minerals and Lithium

A critical mineral is a mineral that has a high risk of supply chain disruption and/or serves an essential function in one or more energy technologies, including technologies that produce, transmit, store, and conserve energy [1,3,4]. Critical minerals are present in almost all electronic devices, including computers and telecommunication devices, and support critical industries like healthcare, transportation, advanced manufacturing, and public safety [5,6]. Critical minerals are essential for new energy technologies, including wind, solar, and batteries [7,8,9].

For energy storage technologies, these dynamics are most prevalent for one critical mineral: lithium. While there are alternatives to other critical minerals that make up cathodes—for example, replacing expensive or otherwise costly to acquire critical minerals that make up nickel–manganese–cobalt (NMC) chemistries with the cheaper minerals that make up lithium–iron–phosphate (LFP) chemistry batteries—for the foreseeable future, all batteries will require lithium [10,11,12]. This makes lithium particularly important to the overall energy storage and battery supply chain and the various benefits, especially emissions benefits, energy storage technologies can provide.

1.2. Benefits of Electric Vehicles

Globally, the energy sector, which includes electricity generation and heat, dominates global carbon emissions: comprising about 34%. This is followed by the industrial sector (24%), land use (22%), transportation (15%), and building (6%) [13]. However, in developed countries, transportation is or is becoming the largest end-use emitting sector, and in the US, it is the leading source of ${\mathrm{CO}}_2$ overall [13,14]. As electricity generation decarbonizes and transportation vehicle miles traveled (VMT) increase, transportation’s share of a country’s emissions profile starts to dominate.

Electrical vehicles (EVs), which use energy storage technology (i.e., batteries) have the potential to dramatically reduce operational-based ${\mathrm{CO}}_2$ emissions in the transportation sector. However, EVs require a substantial increase in mining output, where the mining industry already accounts for 4–7% of global emissions, which would increase the production-based ${\mathrm{CO}}_2$ emissions, potentially offsetting some of the operational emission gains [15]. Nonetheless, the lifecycle emissions of a typical vehicle, even current EVs powered by a relatively clean grid, are dominated by operational emissions, with production emissions only making up a small fraction of overall lifecycle emissions. Therefore, the reduction in ${\mathrm{CO}}_2$ and other emission gases like ${\mathrm{NO}}_x$ and ${\mathrm{SO}}_x$ enabled by EVs could slow down the effects of climate change and drastically improve air quality.

Because of the overall emission benefits, adopting EVs is seen as a technological necessity, but EVs have other advantages over legacy internal combustion engine vehicles (ICEVs) that may aid with their adoption [16]. EVs regularly outperform ICEVs in some performance metrics, such as instantaneous access to horsepower and linear torque, energy efficiency, handling, responsiveness, safety, and total cost of ownership, among others [17]. However, adoption has been limited because the technology is not quite mature. Current batteries, which are mostly lithium-ion batteries, are relatively heavy due to a lower specific energy (gravimetric energy density, kWh/kg) and their costs, while rapidly declining, are still high (USD/kWh). Nevertheless, these metrics are expected to improve, and the role of lithium-based batteries is expected to stay dominant. Therefore, developing and optimizing the lithium supply chain is of critical importance for EVs and all energy storage technologies [4].

1.3. Framework and Case Study Overview

This work creates a mixed integer programming framework for evaluating and optimizing the supply chain of the critical minerals needed for clean energy technologies. The framework is designed for flexibility and modularity, where the user inputs exogenously supplied projections for parameters, including demand, cost, carbon intensity, and any other metric or conversion factor needed for the model. Then, the framework will automatically populate the mathematical optimization model, which uses a multi-echelon supply chain format. Then, the user can set their desired objective, modify the model to explore other metrics, or add features that are of specific interest. The model can evaluate multiple minerals needed for a given technology or evaluate how the demand for a mineral from multiple technologies affects that mineral’s supply chain. The latter is the approach this study uses to evaluate the efficacy of the proposed framework.

This work develops and investigates a simplified (a single decision maker) and deterministic case study that compares the evolution of the global lithium supply chain in a scenario where the objective is to minimize cost versus a scenario where the objective is to minimize emissions. Figure 1 illustrates the lithium supply chain and the case study’s optimization model. The supply chain portion of the diagram is based on [11] and is illustrated in the dark blue circles, which correlate to the stage set (the icons are attributed to [18]). The sets, which include years, stages, and technologies, are listed along with their model acronyms. Each set is illustrated and color coded with years in light blue, stages in dark blue, and technologies in green. EV Stock and Scrap, which is specified exogenously, is also included and is colored peach. The demand parameters and objective parameters, listed with their model symbols in separate orange-outlined blocks, are also included. These parameters include the demand for lithium, the demand for EV battery packs, and the amount of scrap EV batteries that are available to be recycled. Finally, the key decision variables are shown in purple-outlined boxes. These decisions include how many facilities to open up, how big these facilities should be, and how much to produce at each facility: all with the goal of meeting demand.

The case study evaluated two scenarios: the Cost Objective scenario and the ${\mathrm{CO}}_2$ Objective scenario. Both scenarios tracked the annual discounted costs over the entire model period (2020–2100) and the annual ${\mathrm{CO}}_2$ emissions. The Cost Objective scenario’s objective was to minimize the sum of the annual discounted costs, while the ${\mathrm{CO}}_2$ Objective scenario’s objective was to minimize the sum of the annual ${\mathrm{CO}}_2$ emissions. The Cost Objective scenario output a total discounted cost of USD 9.51 trillion and total ${\mathrm{CO}}_2$ emissions of 56.8 gigatons. The ${\mathrm{CO}}_2$ Objective scenario reported a total discounted cost of USD 10.1 trillion and total ${\mathrm{CO}}_2$ emissions of 55.7 gigatons, for a cost premium of 6% for 2% emissions reduction. The facility investments in both scenarios mostly looked similar, with the ${\mathrm{CO}}_2$ Objective scenario investing in more facilities overall. However, the ${\mathrm{CO}}_2$ Objective scenario invested in 243 recycling facilities and only 29 mining facilities by 2050, whereas the Cost Objective scenario did not invest in any recycling facilities and invested in 36 mining facilities. The Cost Objective scenario’s general strategy was to maximize asset utilization rates to minimize costs, while the ${\mathrm{CO}}_2$ Objective scenario looked to maximize the utilization of the lowest-carbon-emitting technologies, even at the expense of existing assets.

The case study results show that even with one global decision maker who has perfect knowledge of demand and costs, by virtue of the deterministic modeling paradigm, there are still various tradeoffs that have to be made. Asset utilization, while high, is not perfect, even though the model brings new capacity online with perfect precision, which is unrealistic. Furthermore, there is a substantial difference in decision making between the Cost Objective and ${\mathrm{CO}}_2$ Objective scenarios, which suggests that less idealized scenarios will require complicated balancing of competing objectives. Nonetheless, this framework can provide scalable analysis for a variety of needs and help decision makers understand the supply chain and increasingly add complexity to evaluate more nuanced decisions.

The rest of the article is structured as follows. Section 2 provides additional context for the case study, including the different energy storage technologies and what minerals they require. Section 2 also explores details about the lithium supply chain and other research that explores it. Section 3 details the methods behind the framework and provides the structure for the optimization model. Section 3 also details case study data for the lithium supply chain model. Section 4 describes the results and key findings from the lithium supply chain case study. Section 5 discusses the implications of the case study results and the utility of the overall framework.

2. Case Study Background

Energy storage technology is advancing exponentially, and it has the potential to revolutionize renewable-powered grids, personal electronics, and vehicles. Similar to other transformative energy technologies, like carbon nanotubes, energy storage technologies could provide massive benefits [19,20]. Furthermore, energy storage is an enabling technology that could undergird new technologies like shared autonomous vehicles or tailored semiconductor advances [21,22]. Furthermore, energy storage technologies are constantly improving, and the developmental of new battery chemistries has the potential to accelerate these effects. However, as shown in other technologies, including distributed energy resources (DERs) [23,24,25], carbon capture and sequestration (CCS) [26], infrastructure [27], new semiconductors in EVs, and weatherization [28,29], most of the impacts and the challenges are from simply finding a way to increase adoption. Innovative technologies are usually faced with a limiting factor, preventing them from reaching their full potential. The impact new energy storage technologies can have is currently being hampered by the deficiency of their supply chains, which raises prices and lowers adoption, especially down the socioeconomic scale. While there is vast research on how to increase equitable adoption of technologies, like energy efficiency [30,31], vaccines [32,33] and solar [34], the main hindrance for equitable adoption in energy storage is the relatively nascent technology powering them and the cost of their supply chains.

To provide context for the rest of the article, this section will explore the different energy storage technologies, the materials they use, and why lithium is so important. Then, the section will detail the lithium supply chain and its different components. After that, this section will explain key battery metrics and how they influence demand, which affects the entire supply chain. Lastly, this section will present other lithium supply chain explorations found in the literature and explain how this article provides value and novelty.

2.1. Energy Storage Technologies

2.1.1. Lithium-Ion

Lithium-ion batteries are now the dominant form of energy storage and are characterized by their lithium metal oxide cathodes, lithium-based electrolytes (usually lithium–fluoride), and lithium-free, typically carbon-based anodes [35].

The earlier generation lithium-ion batteries included lithium–cobalt–oxide (LCO) and lithium–manganese–oxide (LMO) chemistries, with LCO having the highest theoretical specific energy but a short cycle life and high thermal instability. LMO has a better cycle life and thermal stability than LCO, and it does not use cobalt, but it has much lower energy density. These chemistries are typically not found in electric grid energy storage or EVs and are delegated to uses like in electronics or electric scooters and bikes [1,36].

Nickel–magnesium–cobalt (NMC) continues to have the most market share of any battery chemistry, with 60%. NMC batteries can contain different ratios of nickel, magnesium, and cobalt—for instance, with equal ratios, it would be NMC 111 (or NMC 333)—but as cobalt prices have skyrocketed and associated labor challenges have become more apparent, higher-nickel chemistries that use less cobalt, such as NMC 622 and NMC 811 (which use 60% and 80% nickel, respectively), have become more popular, even though it is harder to manufacture higher-nickel-percentage batteries [37].

Nickel–cobalt–aluminum (NCA) batteries have a higher theoretical specific energy density than NMC but a lower lifetime, and they are much more expensive due to the cobalt chemistries [37]. While higher-nickel and lower-cobalt chemistries like NCA+ have been developed, they still are not comparable in price. Nonetheless, high-performance cars sometimes use NCA chemistries, and they still have around an 8% market share [11].

Lithium–iron–phosphate (LFP) is used for its cost effectiveness, lifespan, and safety; however, it is less energy dense than many other chemistries [35]. Nonetheless, it has seen its market share grow as the ability to produce cheap batteries outweighs the importance of building more capable ones. In 2022, LFP was the second most common chemistry behind NMC, with a market share of just under 30% [10]. However, most of the demand for LFP batteries comes from Chinese EV makers, with BYD accounting for over half of demand, and 85% of the Tesla cars that use LFP are made in China.

Silicon anodes have the potential to store up to 10 times as many lithium ions as graphite, which is the current dominant anode material [38,39]. However, silicon expands and contracts dramatically, reducing the efficacy of the battery and shortening its life [35]. Nonetheless, silicon-doped graphite anodes are under commercial development, and as the silicon content increases, so likely will the specific energy of the cells [40].

2.1.2. Lithium Anode and Solid State Batteries

Lithium–sulfur batteries have a sulfur cathode and a lithium metal anode and promise much higher energy densities than current lithium-ion technology. However, sulfur and lithium react to make unwanted byproducts that destroy the lifespan of the battery. Nonetheless, if these problems can be solved, these batteries would offer much higher energy densities with a potentially lower environmental impact [41].

Lithium–metal anodes, like silicon anodes, can also store many more lithium ions than graphite, drastically increasing energy density [42]. However, they tend to have short lifespans when used with liquid electrolytes due to interactions that drastically shorten the life of the cell [43].

By using a solid electrolyte, solid-state batteries are the logical step to combat the problem lithium metal anodes have with liquid electrolytes [35]. Solid-state batteries have much higher theoretical densities that could enable a wide range of applications and improve the performance of other EVs dramatically [44]. However, major technical challenges exist, including reliance on unscalable production processes, to create usable batteries [11].

The holy grail for batteries is currently lithium–air batteries, which would use a lithium–metal anode, a solid or gooey electrolyte, and a lithium–oxygen cathode [45]. This would have a much higher energy density because at full charge, the air would not be stored in the battery, making it lighter, just like petrol cars that get lighter as they burn of fuel from the tank [46]. However, this technology is a long way off and has many practical problems, such as how to control the air flow, that need to be solved before any commercial applications could be realized [35].

2.1.3. Alternative Non-Lithium Chemistry Limitations

Sodium-ion or Na-ion batteries are cheaper alternatives to Li-ion batteries due to not needing critical minerals and relying on cheaper minerals overall [47]. However, while they have similar life cycles and can charge at higher rates due to their higher thermal stability, they are significantly less energy dense and are currently only being used in short-range, low-cost EVs [10]. Nonetheless, the production capacity for Na-ion batteries is growing [10,48].

Redox flow batteries use two tanks of chemical solutions—one as the anolyte and the other as the catholyte—and the electrochemical reaction between the solutions pushes the electrons through the circuit [49]. Most redox batteries use vanadium and can be recharged like a typical battery or by refilling the spent solutions with charged ones, like a gas tank. Flow batteries are easy to scale because if you want more energy, you add more solution, and if you want more power, you stack the scales [50]. They are also safer because they are non-flammable solutions that will simply cause a spill if they fall out, and this safety, in addition to their robustness and scalability, makes them ideal for energy storage [51]. While their applications for vehicles are still nascent, they could provide benefits for grid energy storage, for which size and energy density requirements are not as strict. Even though their low energy density and need for tanks, other components, and refilling infrastructure make their practicality for EVs low, they have seen some support in military applications where lithium ions might not be as good of a fit [50]. Researchers have found ways to increase the energy density of these solutions by using nanoparticles, making the tradeoffs worth it in some cases.

This subsection investigated the relevant energy storage battery chemistries: both past and future. It highlights that, while there are some non-lithium battery chemistries, the vast majority of the current and likely future battery chemistries will use lithium. Therefore, securing adequate supplies of lithium will be important for future battery and transportation technologies.

2.2. Lithium Supply Chain

Lithium is a critical mineral resource for the US and has applications in glass and pharmaceuticals but, most notably, for batteries, especially those for grid energy storage and EVs [52]. The lithium-based battery supply chain has multiple stages that go from the mine to the product, which is then recycled back into the supply chain at the end of its life [6]. These stages include: Raw Material Production,

which involves acquiring minerals from deposits, either in brine, clays, or rocks [1]; Material Purification and Refining, which involves processing the mineral from its raw form to lithium carbonate or hydroxide and then using the purified material for the next step; Component Manufacturing to manufacture anodes, cathodes, separators, and electrolytes; the Cell Manufacturing step then takes the refined materials, processes them, and manufactures them into battery cells; finally Pack Manufacturing involves taking the battery cells and assembling packs for grid energy storage or EVs; lastly, Recycling and Reuse involves collecting end-of-life products and recovering the materials to be used again, reducing the need for new raw materials and the subsequent processing. The lithium supply chain is global and, as a result has geospatial and geopolitical dimensions, and while they are beyond the scope of this work, they can be explored in [1,3,4,6].

2.2.1. Lithium Mining and Extraction

Lithium is traditionally mined from three types of deposits: brine, pegmatite, and sedimentary rock [53]. According to the USGS, lithium brine deposits account for 66% of the world’s lithium resources, pegmatites are 26%, and sedimentary rocks are 8% [5]. Most of the lithium extracted from brine comes from Chile, and most of the lithium extracted from pegmatite comes from Australia. However, the lithium in Thacker Pass, the largest reserve in North America, is in clay [54]. This requires an entirely new process to extract the lithium and turn it into lithium carbonate, which presents opportunities for building up a US-based lithium supply chain.

Mining requires a lot of investment to discover if a potential deposit is profitable. As the low-hanging-fruit mines have been discovered, the cost per discovery of every new mine is going up dramatically. Fortunately, mines are as productive or even more productive than ever, so when a profitable mine is identified, the other costs pale in comparison to the discovery cost. New technological developments aim to lower this cost/discovery, which increase the productivity of every mine.

2.2.2. Lithium Processing

Lithium extracted from the Earth needs to be processed, usually to lithium carbonate or lithium hydroxide, to be used in downstream applications. Cell component manufacturers, especially for cells that will be turned into EV packs, require even more stringent purity requirements. These lithium refiners will likely be collocated at lithium mines if possible; however, there will also be sole processing plants that will receive imported lithium or even processed lithium and produce high-purity lithium carbonate or lithium hydroxide as needed for downstream component, cell, and pack producers [1].

2.2.3. Component Production

Every battery has three major components: cathode, anode, and electrolyte. Cathodes for lithium-ion batteries are usually an alloy with lithium and another metal like iron, nickel, or magnesium and sometimes another element like potassium. The electrolytes are generally lithium ions in combination with a highly electronegative element like fluorine. Anodes are generally lithium free, and most of them are made with carbon-based graphite. Future anodes could be made of silicon or other elements but are unlikely to include lithium in the near future [11].

2.2.4. Cell Production

After the components for a battery are produced, each individual cell can be manufactured. Cylindrical cells dominate EV battery packs and are usually defined as 12,580 and 2480 models, which corresponds to the diameter and length, respectively. Other cell geometries, like coin cells and pouch cells, can also be fabricated but are typically used in R&D. Older EVs like the Nissan Leaf used boxy types of cells whereby components were stacked on top of each other, but this is much more expensive to fabricate. Cell fabrication seems to have settled on the cylindrical model, as it is easier to automate and increase throughput using machines. This step also can introduce defects in the batteries themselves that can cause them to perform below their specifications.

2.2.5. Pack Production

The last step for EV manufacturers is to combine dozens of hundreds of cells into a pack that will then be installed into a vehicle. These packs combine cells in series and parallel to achieve their associated voltage, current, and kWh targets. This is mostly an assembly step, and productivity advances in this area will come from improving manufacturing and assembly strategies. Like with the cell fabrication steps, errors in assembly can lead to defects in the pack, which can reduce the stated performance.

2.2.6. Recycling

Used lithium-ion batteries contain between 5–20% cobalt, 5–10% nickel, 5–7% lithium, 5–10% other metals (copper, aluminum, iron, and other), 15% organic compounds, and 7% plastics by mass. They also typically use LiPF6-based organic solvent electrolytes, a graphite anode, and a layered lithium metal oxide [55]. Furthermore, seven of the components (cobalt, lithium, copper, graphite, nickel, aluminum, and manganese) have been reported to comprise >90% of the economic value of a spent lithium-ion battery: Co (39%) and Li (16%, as LCE equivalent) followed by Cu (12%), graphite (10%), Ni (9%), Al (5%), and Mn (2%) [56].

Spent batteries available for recycling are expected to increase from near zero now to over 1300 GWh. In 2030, [11] expects around only 100 kt of recycled content to be on the market, versus 1200 kt by 2040, representing an 8% market share. There are a variety of techniques used to recover materials from lithium-ion batteries, with a special focus on lithium and the other critical minerals [57]. For example, Fenton-modified flotation is used to recycle electrode materials LiCoO2 and graphite [58], and a physical recycling method, grinding flotation, has been used to attempt to separate and recover LiCoO2 and graphite [59]. Other methods to recover cathode scraps have also been explored [60,61], and new companies are starting to be formed to recycle on an industrial scale [62]. In additional to these methods, different pyrometallurgy and hydrometallurgy processes and their recovery rates have been investigated [63,64].

2.3. Battery Metrics

There are three key battery metrics that correspond with a battery-based technology’s performance and a customer’s willingness to purchase it: cost, usually defined by USD/kilowatt-hour (kWh) of battery capacity; specific energy, usually defined by watt-hour (Wh)/kilogram (kg); and the final metric, efficiency, which has a variety of different metrics depending on the application. For EVs, the EPA uses the metrics kWh/100 miles and miles-per-gallon equivalent (mpge), which assumes the energy in 33.7 kWh of electricity is equal to that in one gallon of gasoline [17]. Another metric, mile/kWh, is a bit more intuitive since it increases as efficiency improves rather than decreases, like kWh/100 miles, and does not require an extra conversion, like mpge. For other energy storage applications, other efficiency metrics like self-discharge rate and number of cycles are more important.

Metrics that do not fall neatly into those three boxes, like range, which is cited as a critical metric for EV adoption, are usually functions of the other three metrics, as the range of the car is directly determined by the cost, the specific energy of the battery, and the efficiency of the car. Nonetheless, the survey in [65] shows that the median customer desires an EV with a max 20-min charge time and 30-min total detour and wait time, 350 miles of range, and a max price of USD 50,000. While these metrics are quite more demanding than may seem necessary, they provide a good benchmark for what the three key metrics should look to accomplish.

The cost metric as of 2023 was USD 139/kWh at the pack level [66,67]. Approximately USD 100/kWh at the pack level is the approximate target for ICE parity [68]. The specific energies for the most common types of lithium-ion batteries are between 200–250 Wh/kg, whereas a targeted metric of 500 Wh/kg is desired to make applications like electric flight feasible [10,69]. A 500 Wh/kg energy storage is still significantly less energy than a gallon of gas, which has a a gravimetric energy density (specific energy) of approximately 12,000 Wh/kg. However, EVs are much more efficient and do not lose as much energy to heat as internal combustion engine vehicles (ICEVs). When comparing the useful energy from gasoline using a tank-to-wheel efficiency of 12% (the average for the US fleet) for petrol cars, researchers typically use a specific energy value of 1700 Wh/kg, which is still far higher than the approximately 200 Wh/kg of current lithium-ion batteries but is an achievable target with foreseeable technological advancements [35,45].

Finally, efficiency metrics have a broad range, but the “typical” EV has an efficiency of 36 kWh/100 miles or 93.6 mpge (2.78 miles/kWh) [17], which is much worse than the top-selling Model Y RWD’s efficiency of 26 kWh/100 miles (129 mpge or 3.85 miles/kWh). As specific energy increases, efficiency will naturally increase as well, since the weight of the car will go down, which should increase range. While range targets like 300 miles per charge are more common [70], Lucid Motors recently stated an efficiency target of 10 km/kWh (6.2 miles/kWh), which would allow a 300 km (186 mile) range with only a 30 kWh battery, illustrating the relationship between not only efficiency and range but efficiency and material needs [71].

However, currently an EV’s weight is a major limiting factor on efficiency, especially when compared to ICEVs, which balance their thermodynamic inefficiency with their overall energy density. An EV with a battery size of 62 kWh and an efficiency of 4.35 miles/kWh (23 kWh/100 miles, 146 mpge) would have a range of 270 miles, and if it used Tesla’s 4680 cells (230 Wh/kg, [72]), the battery alone would weigh 300 kgs, with the motor weighing another 100 kg ([73]). On the other hand, a 45 mpg ICEV equipped with an engine and the 6 gallons of gas needed to go 270 miles would only weigh 150 kgs (engine weight: 136 kg [74]).

Nonetheless, one of the main short-term targets for specific energy, 500 Wh/kg, would lower the weight to near ICEV parity. A 4.35 mile/kWh, an EV with a 435 mile range would have a 100 kWh pack, which, at current energy densities, would weigh almost 500 kg. However, for an EV with a 500 Wh/kg specific energy, the same 100 kWh pack would weigh 200 kg, and the range of the car would increase dramatically as well. These compounding technological shifts will affect the supply chain on both the demand side, as the advantages of EVs increase overtime, and the supply side, as they affect how much of each critical mineral goes into each EV battery pack.

2.4. Lithium Supply Chain Modeling

The lithium supply chain network has been modeled and evaluated from numerous perspectives [75]. It has been modeled to evaluate environmental concerns [76,77]. Other studies have evaluated the whole supply chain as a value chain and network [78,79]. Models have been used to manage the materials in the supply chain for efficient production [80,81,82,83]. Since one of the advantages of mineral supply chains is their ability to be reused in the supply chain, many studies have investigated the “closed loop” supply chain [84,85,86,87,88,89,90].

These models either focus on one stage (such as recycling, even if they include all the stages of the supply chain), look at a specific geopolitical area, or evaluate the environmental impact of the supply chain. Few studies look explicitly at what decisions must be made regarding what facilities to build and what materials to produce. Large forecasting models such as [1,11] that are based on predictions do order-of-magnitude calculations about how many facilities are needed but do not attempt to meaningfully evaluate the cost and the strategic decisions investors will have to make. This work aims to fill that gap with a modular framework that specifically looks at what investment and operational decisions must be made to meet future demand for the minerals needed for clean energy technologies.

3. Methods

The proposed framework uses a supply chain optimization structure to formulate and solve a mixed-integer programming model parameterized by exogenously provided data profiles, as shown in Figure 1. Supply chain optimization is a method that models a supply chain, usually as a mathematical program, using data available to the decision maker and then uses a mathematical solver to solve that model according to some objective, which is usually to minimize cost [91]. The decisions that make up supply chain management take place at three different levels: operational, which are short-term decisions; tactical, which are intermediate-term decisions; and strategic, which are long-term decisions [92].

Supply chain management, the parent field of supply chain optimization, is relatively new, as the term “Supply Chain Management” was famously coined in 1982 by Keith Oliver in an interview with Arnold Kransdorff from the Financial Times [93]. However, with the increase in computational power and the increasing global importance of supply chains, supply chain modeling is now a powerful tool that can guide decision makers. The presented framework leverages these developments, and the global lithium supply chain case study illustrates the power of these techniques.

The global lithium supply chain case study in this article is evaluated from 2020–2100, where 2020–2024 is used to calibrate the model. A long time horizon (81 years) is used due to the long-term nature of building and operating these assets. The current lead time for a mine globally is 16 years, but once built, some mines remain in operation for multiple decades, with mines for minerals like copper still operating from the 1910s [15]. The case study uses current demand, cost, and carbon intensity data from a variety of sources and then combines multiple future projections for those same parameters into a model using logistic and decay curves. Then, the case study evaluates the investment, capacity, and operational decisions that a hypothetical global central planner would make to meet demand for lithium, which includes electric vehicles, batteries for energy storage, and other uses. This case study evaluates two objectives disparately: cost minimization and ${\mathrm{CO}}_2$ emission minimization.

3.1. Mathematical Formulation

This section presents all five parts of an optimization problem’s mathematical formulation: sets, decision variables, parameters, objective function, and constraints.

3.1.1. Sets

There are three main sets, or groups of data classified together because of shared characteristics, in this formulation that correspond with a key: Years, Stages, and Technologies. They are presented visually in Figure 1 and are explored in more detail below.

$\mathbf{Major}\mathbf{Set}$	$\mathbf{Years}$
$y\in Y:2020–2100$	$\mathrm{All}\mathrm{Years}$
$y_{start}\in Y:2020–2024$	$\mathrm{Calibration}\mathrm{Years}$
$y_{warm}\in Y:2025–2100$	$\mathrm{Decision}\mathrm{Years}$
Major Set	Stages
s ∊ S: mine, proc, cath, cell, pack, rec	Stages
Major Set	Technology
t ∊ T: ${\mathrm{T}}_{\mathrm{mine}}$, ${\mathrm{T}}_{\mathrm{proc}}$, ${\mathrm{T}}_{\mathrm{cath}}$, ${\mathrm{T}}_{\mathrm{cell}}$, ${\mathrm{T}}_{\mathrm{pack}}$, ${\mathrm{T}}_{\mathrm{rec}}$	Technology
$T_{\mathit{mine}}:\{\mathit{spod},\mathit{brine},\mathit{clay}\}$	Extraction Technologies
$T_{\mathit{proc}}:\{\mathit{lce},\mathit{loh}\}$	Processing Technologies
$T_{\mathit{cath}}:\{\mathit{nmc},\mathit{lfp}\}$	Cathode Technologies
$T_{\mathit{cell}}:\{{\mathit{Gwh}}_{\mathit{nmc}},{\mathit{Gwh}}_{\mathit{lfp}}\}$	Cell Production Technologies
$T_{\mathit{pack}}:\{{\mathit{bev}}_{\mathit{nmc}},{\mathit{bev}}_{\mathit{lfp}}{\mathit{pbev}}_{\mathit{nmc}}{\mathit{pbev}}_{\mathit{lfp}}\}$	Pack Production Technologies
$T_{\mathit{rec}}:\left\{\mathit{lce}\mathit{loh}\right\}$	Recycling Technologies
$t_{\mathit{in}}∊T$	Input Technologies
$t_{\mathit{out}}∊T$	Output Technologies

The first major set group represents the model years and their subsets. This includes y, which covers all model years (2020–2100); $y_{start}$, which includes the calibration years (2020–2024); and $y_{warm}$, which are the decision years (2025–2100), where the model can make endogenous decisions.

The second major set group, s, represents all of the stages in the lithium supply chain: extraction (mine), processing ($proc$), component (cathode) manufacturing ($cath$), cell production ($cell$), pack production ($pack$), and recycling ($rec$).

The third major set represents the technologies that are produced at each stage. The extraction stage outputs spodumene concentrate ($spod$), lithium brine ($brine$), or lithium clays ($clay$). The processing stage outputs lithium carbonate ($lce$) and lithium hydroxide ($loh$). The component manufacturing stage outputs lithium–iron–phosphate oxide ($lfp$) and nickel–manganese–cobalt oxide ($nmc$). The cell production stage outputs nmc cells ($GW{h}_{nmc}$) and lfp cells ($GW{h}_{lfp}$). The pack production stage outputs 62 kWh nmc or lfp packs for battery electric vehicles ($be{v}_{nmc}$, $be{v}_{lfp}$) and 15 kWh nmc or lfp packs for plug-in hybrid electric vehicles ($phe{v}_{nmc}$, $phe{v}_{lfp}$). The reported units for this technology are in millions of cars (MM units). The recycling stage outputs lce and loh.

Note that technologies can be an input for a stage or an output (i.e., product) of a stage and are designated with $t_{in}$ and $t_{out}$, respectively, as appropriate, in later variables and constraints. For example, the processing stage ($proc$) inputs mining technologies ($T_{mine}$) and outputs (produces) processing technologies ($T_{proc}$), where the input technologies are denoted with $t_{in}$ and the output technologies are denoted with $t_{out}$.

3.1.2. Decision Variables

The decision variables are variables that the model can modify endogenously. Some decision variables correspond to different decisions that must be made at various stages, while other decision variables track certain statuses necessary for certain constraints. Figure 1 visualizes some of the key decision variables; all decision variables are explored in detail below.

$$\begin{array}{cc}Pro{d}_{y,s,t_{in},t_{out}}\hfill & \mathrm{Production} \mathrm{in} \mathrm{year} y \mathrm{of} \mathrm{stage} s, \mathrm{technologies} t_{in} \& t_{out}\hfill \\ Activ{e}_{y,s,t_{in},t_{out}}\hfill & \mathrm{Active} \mathrm{Facilities} \mathrm{in} \mathrm{year} y \mathrm{of} \mathrm{stage} s, \mathrm{technologies} t_{in} \& t_{out}\hfill \\ Inves{t}_{y,s,t_{in},t_{out}}\hfill & \mathrm{Investments} \mathrm{in} \mathrm{year} y \mathrm{of} \mathrm{stage} s, \mathrm{technologies} t_{in} \& t_{out}\hfill \\ NewCa{p}_{y,s,t_{in},t_{out}}\hfill & \mathrm{New} \mathrm{Capacity} \mathrm{in} \mathrm{year} y \mathrm{of} \mathrm{stage} s, \mathrm{technologies} t_{in} \& t_{out}\hfill \\ Capacit{y}_{y,s,t_{in},t_{out}}\hfill & \mathrm{Total} \mathrm{Capacity} \mathrm{in} \mathrm{year} y \mathrm{of} \mathrm{stage} s, \mathrm{technologies} t_{in} \& t_{out}\hfill \end{array}$$

The production decision variable ($Prod$) represents how much of a technology ($t_{out}$) is produced at a given stage in a year using the corresponding technology ($t_{in}$) as its input. The active facilities ($Active$) decision variable represents how many active facilities there are in a given year for a given stage, with the ability to produce $t_{out}$ from a certain $t_{in}$. The invest ($Invest$) decision variable represents which facilities for a given stage s with the ability to convert a $t_{in}$ into $t_{out}$ are invested in for a year (y). The new capacity ($NewCap$) decision variable represents how much new capacity is added at time t, and the capacity ($Capacity$) decision variable represents how much capacity is available to be used for a given stage, input technology $t_{in}$, and output technology $t_{out}$.

3.1.3. Parameters

In this model, there are three main sets of parameters, or exogenously provided information, that inform the model: demand parameters, cost parameters, and emission parameters. These parameters are illustrated in Figure 1, and the sources and assumptions used in this model for these parameter sets will be explained below. Furthermore, there are miscellaneous parameters, including needed conversions, that will be listed and explored as well.

Demand Parameters

The demand parameters correspond to exogenously and extrapolated demand profiles for the outputs of each stage. They are listed below.

$$\begin{array}{cc}{D}_{y,s}^{Mine}\hfill & \mathrm{Mine} \mathrm{Li} \mathrm{demand} \mathrm{in} \mathrm{year} y \mathrm{and} \mathrm{stage} s;\hfill \\ D_{y,s,t_{proc}}^{Proc}\hfill & \mathrm{Processing} \mathrm{Li} \mathrm{demand} \mathrm{in} \mathrm{year} y \mathrm{of} \mathrm{stage} s, \mathrm{technologies} t_{proc};\hfill \\ D_{y,s,t_{cath}}^{Cath}\hfill & \mathrm{Cathode} \mathrm{Li} \mathrm{demand} \mathrm{in} \mathrm{year} y \mathrm{of} \mathrm{stage} s, \mathrm{technologies} t_{cath};\hfill \\ D_{y,s,t_{cell}}^{Cell}\hfill & \mathrm{Cell} \mathrm{Li} \mathrm{demand} \mathrm{in} \mathrm{year} y \mathrm{of} \mathrm{stage} s, \mathrm{technologies} t_{cell};\hfill \\ D_{y,s,t_{pack}}^{Pack}\hfill & \mathrm{Pack} \mathrm{Li} \mathrm{demand} \mathrm{in} \mathrm{year} y \mathrm{of} \mathrm{stage} s, \mathrm{technologies} t_{pack};\hfill \\ D_{y,s,t_{rec}}^{Rec}\hfill & \mathrm{Li} \mathrm{available} \mathrm{for} \mathrm{recycling} \mathrm{in} \mathrm{year} y \mathrm{of} \mathrm{stage} s, \mathrm{technologies} t_{rec}.\hfill \end{array}$$

We calibrate our demand profile using projections and assumptions for total vehicles and electric vehicles (EVs) (where EVs include battery electric vehicles (BEVs) that are solely powered by batteries and plug-in hybrid electric vehicles (PHEVs) that have a secondary power source), scrapped vehicles, total lithium demand, lithium demand for all batteries (including EV batteries), lithium demand for EVs, and lithium demand for other uses. The demands for each of these categories for key years (2020, 2030, 2040, 2050, and 2100) are shown in

Table 1. Demand parameter values for key years.

Demand Category (Units)	2020	2023	2030	2040	2050	2100	Notes	Sources
Total Cars (MM)	85.24	93	119	129	142.5	234.35	2% growth rate from 2025	[68]
BEVs (MM)	2.27	9.92	22.18	47.13	83.31	221.38	S-curve from Equation (1) from 2023	[1,11,21]
PHEVs (MM)	0.97	4.25	8.94	16.1	23.4	12.98	S-curve until 2060. After: (Total − BEVs)	[1,11,21]
Stock EVs (MM)	19	40.16	190.9	569	1188.1	5344.5	= (Cumulative EV Demand − Scrap)	[68]
Recoverable Li (GWh)	0	82.7 *	276	838.3	1796	9191.3	3% scrap rate starting 2024 *	[68]
Total Li (kt Li)	85.5	180	259.56	516.26	880.23	2345.32	= (EV + Battery + Other)	[5,94,95,96]
Battery Li (kt Li)	58.58	156.6	222.66	466.68	813.59	2053.21	(EV Li/0.8) from 2030	[5,11,94,95,96]
EV Li (kt Li)	18.34	80.07	178.13	373.34	650.87	1642.57	Based on EV demand	[5,11,94,95,96]
Other Uses (kt Li)	23.93	30	36.9	49.59	66.64	292.14	3% growth rate from 2023	[5,94,95,96]

. Table 1 also includes the calibration year 2023, where the projections for the future are based or the calibration curve is initiated from.

There are not any readily available datasets for yearly demand predictions: only predictions for demand at key years such as 2030, 2040, and 2050. Therefore, this study uses a classic logistic (i.e., S-shaped) diffusion curve to create the demand profile. According to this model, the adoption of a new technology is initially slow because technological challenges remain, costs are relatively high, and consumers are skeptical about its benefits, which perfectly describes the present scenario for EVs and energy storage in general. Adoption then accelerates as the technology improves and becomes less expensive, and consumers and future customers start to see the benefits of the technology. Eventually, the technology saturates the market, and adoption plateaus [21].

This model uses the form below, where $D\left(y\right)$ represents the demand in year y:

$$D\left(y\right)=\frac{k}{1+e^{-b(y-\tau )}}.$$

(1)

The diffusion curve in Equation (1) features three parameters. The parameter k is the market saturation percentage, and this study assumes pure EVs (BEVs) comprise 95% of vehicle sales by 2100, so $k=0.99$. This study assumes PHEVs reach a maximum saturation of 20% of total car sales in 2060. Then, the model assumes that PHEVs make up the balance between total car sales, which the model assumes grows at a 2% growth rate, and BEVs as the BEVs work to their saturation point of 95%.

Since this model uses predicted demand information from [1,11], the parameters that control the shape of the curve were tuned to match the general predicted range for electric vehicle demand, which was between 20–40 MM EV sales and 30–70 million EV sales in 2040. Therefore, for the parameter $\tau$, which is the year when adoption occurs at its highest rate and demand is exactly half of the maximum market saturation (i.e., $D\left(\tau \right)=k/2$), the model used $\tau =2045$ for BEVs and $\tau =2035$ for PHEVs. The parameter b controls the steepness of the diffusion curve, or how gradually the adoption process proceeds, and was set to $b=0.10$ for both PHEVs and BEVs.

The model also had to define raw lithium demand since lithium is used for more than just batteries. Therefore, using data for the last 7 years of global worldwide lithium production and the market share for its uses, including electric vehicles, battery storage, and construction from [5,94,95,96], a 10% growth rate starting in 2023 was found to be reasonable. We also used these datasets to define the resources available by resource type (i.e., clay, brine, and spodumene). The resources or quota of all lithium found as of the 2024 U.S. Mineral Commodities report [5] is enough for all lithium demand until 2100. However, the current reserves are insufficient, but it is likely that the resources will be converted to reserves at the needed pace, so the only constraints placed were on the reserve values for each resource.

The market share of demand for batteries was assumed to grow from 71% in 2020 to 93% by 2100, with the remaining market share to remain for other uses of lithium. The electric vehicle market share, which is included in the battery market share, is expected to grow from 22% in 2020 to 74% in 2100, with the remainder of the battery market share to be used for other energy storage technologies like grid energy storage, which we assume to be 10% of the lithium demand for batteries in order to align with the 100 GW prediction for 2040 from [11], or electronics.

Miscellaneous Parameters

All other demands, except the recycling demand, which is calculated via a scrap rate (see Table 1), were derived from the calculated EV demand by calculating how much lithium is needed at each step. The mass of lithium per kg for different battery chemistries was calculated using the bill of materials from [97]. For an NMC battery pack, there is 0.127 kg of lithium per kWh, and for an LFP battery pack, there is 0.096 kg of lithium per kWh. In an NMC pack, the cathode weighs about 1.71 kg/kWh, and of that, about 7.2% is lithium. For an LFP pack, the cathode weighs about 2.07 kg/kWh, and the lithium only makes up about 4.6% of that. Raw lithium from any extraction source is measured in kg or kilotons (kt) of lithium, but when it is processed, it is usually measured in kilotons of lithium carbonate equivalent (LCE). However, most lithium is processed into lithium hydroxide (LOH) since that is what is needed for the more popular NMC batteries, which the model assumes will continue to have a 70% market share. The chemical equation for LCE is ${\mathrm{Li}}_2$${\mathrm{CO}}_3$, and thus, there are 5.23 kg of LCE/kg of lithium. The chemical equation for LOH is LiOH, and as a result, there are 3.45 kg of LOH/kg of lithium. The battery pack size for a pure battery electric vehicle (BEV) was assumed to be 62 kWh, and for a plug-in hybrid electric vehicle (PHEV), it was assumed to be 15 kWh, corresponding to the average battery sizes in 2023 [98].

Cost Parameters

The cost parameters correspond to exogenously specified costs for investing in and operating the facilities required for each stage. They are visualized in Figure 1 and are explored in detail below.

$$\begin{array}{cc}P{C}_{y,s,t_{in},t_{out}}\hfill & \mathrm{Production} \mathrm{Cost} \mathrm{in} \mathrm{year} y \mathrm{of} \mathrm{stage} s, \mathrm{technologies} t_{in} \& t_{out}\hfill \\ V{C}_{y,s,t_{in},t_{out}}\hfill & \mathrm{Variable} \mathrm{Cost} \mathrm{in} \mathrm{year} y \mathrm{of} \mathrm{stage} s, \mathrm{technologies} t_{in} \& t_{out}\hfill \\ F{C}_{y,s,t_{in},t_{out}}\hfill & \mathrm{Fixed} \mathrm{Cost} \mathrm{in} \mathrm{year} y \mathrm{of} \mathrm{stage} s, \mathrm{technologies} t_{in} \& t_{out}\hfill \end{array}$$

The lithium supply chain is growing at a rapid rate, and cost information is changing just as rapidly as technology and management practices improve. However, metrics such as USD/kWh have been recorded with a decent degree of accuracy, and the cost curve is clearly exponential. According to [66,67], battery prices have fallen from USD 780/kWh in 2013 to USD 211 in 2018 and finally to USD 139/kWh in 2023.

Table 2. Cost parameters: fixed, variable, and production costs for all stages and technologies in the year 2023.

Stage	Tech In	Tech Out	Average Size (kt, GWH)	2023 Fixed Cost (USD MM)	2023 Variable Cost (USD MM/kt [GWh])	2023 Production Cost (USD MM/kt [GWh])	USD/kWh	Annuitized (Fixed + Variable) 2023 Average Cost (USD MM)	Notes	Sources
mine	earth	clay	8	1000	150	15	4.37	176.5		[54,99,100]
mine	earth	spod	8	1000	150	19	4.85	176.5		[11,99]
mine	earth	brine	8	1000	200	20	5.44	208.6		[11,99]
proc	spod	loh	50	500	50	24.56	19.90	240.7	baseline	[11,99,101]
proc	spod	lce	80	500	30	30	16.88	232.7	same as loh cost	[11,99]
proc	brine	lce	80	500	20	24.56	13.68	168.5	baseline	[11,99]
proc	brine	loh	50	500	50	27.9	22.17	240.7	USD 2500/kg LCE premium	[11,99]
proc	clay	lce	80	500	30	17.5	10.47	232.7	baseline	[11,99]
proc	clay	loh	50	500	50	42.5	32.06	240.7	USD 2500/kg LCE premium	[11,99]
cath	lce	lfp	7	500	50	345	34.18	68.2		[11,66,99]
cath	loh	nmc	7	500	50	250	33.06	68.2	30% more than lce	[66,99,102]
cell	lfp	GWh_lfp	35	2500	50	44	53.74	341.0		[11,67,99]
cell	nmc	GWh_nmc	35	2500	50	44	53.74	341.0		[11,67,103]
pack	lfp	bev_lfp	0.5	2000	2000	1500	31.96	240.7		[11,67,99]
pack	lfp	phev_lfp	0.5	2000	2000	15	33.10	240.7		[11,67,99]
pack	nmc	bev_nmc	0.5	2000	2000	1500	31.96	240.7		[11,67,99]
pack	nmc	phev_nmc	0.5	2000	2000	15	33.10	240.7		[11,67,99]
rec	GWh	lce	8	500	100	8	10.79	104.3		[11,99]
rec	GWh	loh	8	500	100	8	14.25	104.3		[11,99]

lists all variations of cost used in the model for every stage and technology in the year 2023.

From Catsaros [67], the cost of pack production is given as USD 32 in 2023. Then, the remaining USD 107 split between cell, component, processing, and mining costs was calculated using data from [11,99]. New lithium processing plants help provide some cost and size information to help calibrate costs [101,104]. Similarly, new mines also help provide cost data [100]. According to Stoikou [66], cathode materials cost between USD 35–USD 54 for the cell producers to buy; thus, using the conservative amount, then the cell cost would be around USD 53/kWh. New information on new cathode plants [102] and new cell and pack manufacturers [103] help further calibrate the cost data. Continuing the extrapolation, the mine costs would be about USD 4.50/kWh, with spodumene transformation being the most expensive and clay being in between. The processing cost would be USD 13.5/kWh for brine to LCE, and the extra conversion to LOH adds more cost. Lastly, the remaining cost for the production of the active cathode material from the processed lithium would be around USD 34/kWh.

A typical supply chain model will take into account three distinct costs: the cost to invest in a facility, which incurs a fixed cost (USD/facility); the cost of building the facility up to the desired capacity, which incurs a variable cost (USD/units of capacity installed); and production costs (USD/units produced). The large upfront investment costs are usually financed, so the model assumes a 5% interest rate and a 20-year loan for the fixed and variable costs. Thus, each stage had a set of annualized finance cost and the production cost (calculated at the average production size) to match with the disaggregated USD/kWh metric described earlier. The annualized financed cost ranged from USD 1–4, which is a typical headline figure for these facilities, with the production cost making up the rest with a nearly 50/50 split between the annualized cost and the production cost per year.

Using the year 2023 as the calibration year, the exponential decay function shown in Equation (2) was used to create a reasonable declining price curve for the battery metric USD/kWh, where a represents the USD/kWh in year $\tau$ (2023). Thus, a is equal to USD 139/kWh, and the decay factor (b) is 0.05 or 5%.

$$C\left(y\right)=a{(1-b)}^{(y-\tau )}.$$

(2)

In the model to account for the time value of money, all costs are discounted from the year 2023 ($\tau$) with a discount rate of 0.05 (b), as shown in Equation (3).

$$Valu{e}_y=Valu{e}_{\tau }{(1-b)}^{(y-\tau )}.$$

(3)

Emission Parameters

The emission parameters correspond to exogenously specified carbon intensity profiles for the facilities and production of each stage. They are illustrated in Figure 1 and are listed below.

$$\begin{array}{cc}PCO{2}_{y,s,t_{in},t_{out}}\hfill & \mathrm{Production} {\mathrm{CO}}_2 \mathrm{in} \mathrm{year} y \mathrm{of} \mathrm{stage} s, \mathrm{technologies} t_{in} \& t_{out}\hfill \\ VCO{2}_{y,s,t_{in},t_{out}}\hfill & \mathrm{Variable} {\mathrm{CO}}_2 \mathrm{in} \mathrm{year} y \mathrm{of} \mathrm{stage} s, \mathrm{technologies} t_{in} \& t_{out}\hfill \\ FCO{2}_{y,s,t_{in},t_{out}}\hfill & \mathrm{Fixed} {\mathrm{CO}}_2 \mathrm{in} \mathrm{year} y \mathrm{of} \mathrm{stage} s, \mathrm{technologies} t_{in} \& t_{out}\hfill \end{array}$$

The carbon emissions at different parts of the lithium supply chain will vary greatly depending on the region, energy sources, resource type, etc. However, like for cost, there is a general metric, ${\mathrm{CO}}_2$/kWh, that can be disaggregated to provide a rough guide for carbon emissions. Multiple sources report a range of values for the carbon intensity of EV production [99,105,106,107,108,109]. However, they mostly have the same magnitude and coalesce around 140 kg ${\mathrm{CO}}_2$/kWh, with about 25% of emissions coming from mining to cathode production, 40% from cell production, and the remaining 35% from pack production. These values are used to inform our emission ratios for all the technologies in the model. This information is tabulated for 2023 in

Table 3. ${\mathrm{CO}}_2$ parameter: ${\mathrm{CO}}_2$ emission ratios for all stages and technologies in the year 2023.

Stage	Tech In	Tech Out	Max Size (kt, GWH)	kg ${\mathrm{CO}}_2$/ kWh	kt ${\mathrm{CO}}_2$/ kt (GWh)	kt ${\mathrm{CO}}_2$/ Average Facility	Notes	Source
mine	earth	clay	25	0.508	4.306	34.45		[11,54,99,107]
mine	earth	spod	25	0.508	4.306	34.45		[11,99,107]
mine	earth	brine	25	0.508	4.306	34.45	baseline	[11,99,107]
proc	spod	loh	100	7.6	18.7	935.9	5× baseline	[11,99,107]
proc	spod	lce	100	4.6	7.3	582.4	3× baseline	[11,99,107]
proc	brine	lce	100	1.5	2.4	194.1	baseline	[11,99,107]
proc	brine	loh	100	3.0	7.5	374.4	2× baseline	[11,99,107]
proc	clay	lce	100	3.0	4.9	388.3	2× baseline	[11,99,107]
proc	clay	loh	100	5.3	13.1	655.1	3.5× baseline	[11,99,107]
cath	lce	lfp	12	33.0	279.4	1956		[11,99,107]
cath	loh	nmc	12	33.0	279.4	1956	baseline	[11,99,107]
cell	lfp	GWh_lfp	100	56.0	56.0	1960		[11,99,107]
cell	nmc	GWh_nmc	100	56.0	56.0	1960	baseline	[11,99,107]
pack	lfp	bev_lfp	1	49.0	3038.0	1519		[11,99,107]
pack	lfp	phev_lfp	1	49.0	735.0	367.5		[11,99,107]
pack	nmc	bev_nmc	1	49.0	3038.0	1519		[11,99,107]
pack	nmc	phev_nmc	1	49.0	735.0	367.5	baseline	[11,99,107]
rec	GWh	lce	15	0.8	1.46	11.70		[11,99,107]
rec	GWh	loh	15	0.8	1.71	13.66		[11,99]

, where the maximum size, based on the largest planned facilities highlighted in the previous subsection plus a bit of capacity for growth, of each facility is also recorded.

After 2023, the model assumes a steady decline in ${\mathrm{CO}}_2$ emissions. It also uses the decay curve shown in Equation (2), but where a represents the kg ${\mathrm{CO}}_2$/kWh in year $\tau$ (2023). Therefore, in this case, a is equal to 140 kg ${\mathrm{CO}}_2$/kWh, and the decay factor (b) is 0.01 or 1%.

3.1.4. Objective Function

There are two objective functions evaluated in this study. Equation (4) represents the cost objective, where the production is multiplied by the production cost, the installed capacity is multiplied by the variable cost, and the facilities invested in are multiplied by the fixed cost for each stage, year, and technology. Equation (5) is the same, except instead of multiplying by cost, the production, new capacity, and investments are multiplied by the appropriate carbon intensity for each stage, year, and technology.

$$\begin{array}{c}\hfill TotalCos{t}_{y,s,t_{in},t_{out}}=\sum _y\sum _s\sum _t\sum _{t}P{C}_{y,s,t_{in},t_{out}}\times Pro{d}_{y,s,t_{in},t_{out}}+\\ \hfill \sum _y\sum _s\sum _t\sum _{t}V{C}_{y,s,t_{in},t_{out}}\times NewCa{p}_{y,s,t_{in},t_{out}}+\\ \hfill \sum _y\sum _s\sum _t\sum _{t}F{C}_{y,s,t_{in},t_{out}}\times Inves{t}_{y,s,t_{in},t_{out}}\end{array}$$

(4)

$$\begin{array}{c}\hfill TotalCO{2}_{y,s,t_{in},t_{out}}=\sum _y\sum _s\sum _t\sum _{t}PCO{2}_{y,s,t_{in},t_{out}}\times Pro{d}_{y,s,t_{in},t_{out}}+\\ \hfill \sum _y\sum _s\sum _t\sum _{t}VCO{2}_{y,s,t_{in},t_{out}}\times NewCa{p}_{y,s,t_{in},t_{out}}+\\ \hfill \sum _y\sum _s\sum _t\sum _{t}FCO{2}_{y,s,t_{in},t_{out}}\times Inves{t}_{y,s,t_{in},t_{out}}\end{array}$$

(5)

3.1.5. Constraints

This model has two main groups of constraints: constraints that ensure demand is met and constraints that ensure production is bounded by available capacity. All constraints are listed below.

Demand Constraints

Equation (6) ensures that production exceeds demand for every technology output. Any stage that can output a given technology can contribute; however, in this model, that is only relevant for the recycling stage, which, like the processing stage, can also output lce or loh. Equation (7) ensures enforcement of the specified demand for lithium from all sources, which includes EVs, battery storage, and medical uses. The lithium can come from any mine source. Equation (8) ensures that you can only recycle the scrapped EV batteries available, where $D_{y,rec,t_{in}}$ represents the demand for recycled batteries. Note, in this equation, the demand represents the amount available to be recycled rather than a demand that must be met. Equation (9) ensures that a downstream stage (denoted with $(s+1)$) can only use use a technology ($t_{out\left(s\right)}$) as an input in order to produce that stage’s output ($t_{o}ut(s+1)$) if a previous stage produced that technology from its own inputs ($t_{in}$). The equation includes the appropriate unit conversion parameter to ensure the units match. Note, the mine stage is limited by reserves instead of a previous stage’s outputs.

$$\sum _{t_{in}}\sum _{s}Pro{d}_{y,s,t_{in},t_{out}}\ge D_{y,t_{out}}\hspace{1em}\forall \hspace{1em}y\in Y,t\in T$$

(6)

$$\sum _{t_{out}}Pro{d}_{y,mine,t_{out}}\ge D_{y,mine}\hspace{1em}\forall \hspace{1em}y\in Y$$

(7)

$$\sum _{t_{in}}Pro{d}_{y,rec,t_{in},t_{out}}\le D_{y,rec,t_{in}}\hspace{1em}\forall \hspace{1em}y\in Y,s\in S,t\in T$$

(8)

$$Pro{d}_{y,(s+1),t_{out\left(s\right)},t_{out(s+1)}}\le UnitConversio{n}_{t_{in},t_{out\left(s\right)}}\times Pro{d}_{y,s,t_{in},t_{out\left(s\right)}}\hspace{1em}\forall \hspace{1em}y\in Y,t\in T,s\in S$$

(9)

Capacity Constraints

Equation (10) is a tracking constraint that counts the number of active facilities of each type every year. Equation (11) ensures that the newly added capacity cannot exceed the number of facilities invested in multiplied by the maximum capacity of each facility. Equation (12) updates the usable capacity available by adding capacity that has just come online (assuming it requires 5 years to build and commission a facility) to the available capacity from the year prior. Equation (13) ensures that production in each time period cannot exceed available capacity. Note, some constraints are only applicable for the Decision Years ($y_{warm}$), starting with 2025. The previous year’s capacity and number of available and invested in units are set exogenously to align with existing conditions.

$$Activ{e}_{y,s,t_{in},t_{out}}=Activ{e}_{(y-1),s,t_{in},t_{out}}+Inves{t}_{(y-5),s,t_{in},t_{out}}\hspace{1em}\forall \hspace{1em}y\in Y_{warm},s\in S,t\in T$$

(10)

$$newCa{p}_{y,s,t_{in},t_{out}}\le maxCa{p}_s\times Inves{t}_{y,s,t_{in},t_{out}}\hspace{1em}\forall \hspace{1em}y\in Y_{warm},s\in S,t\in T$$

(11)

$$Ca{p}_{y,s,t_{in},t_{out}}=Ca{p}_{(y-1),s,t_{in},t_{out}}+newCa{p}_{(y-5),s,t_{in},t_{out}}\hspace{1em}\forall \hspace{1em}y\in Y_{warm},s\in S,t\in T$$

(12)

$$Pro{d}_{y,s,t_{in},t_{out}}\le Ca{p}_{y,s,t_{in},t_{out}}\hspace{1em}\forall \hspace{1em}y\in Y,s\in S,t\in T$$

(13)

4. Results

This section highlights the key results from compiling and solving the model specified above for both the Cost Objective and ${\mathrm{CO}}_2$ Objective scenarios. The model for both scenarios was compiled using Python version 3.12, translated by the GurobiPy Python package and solved with the Gurobi Optimizer, where the GurobiPy and the optimizer were part of Gurobi version 11.0.1. The computer resources used to compile and solve the model included an Intel(R) Core(TM) i9-10900 2.80GHz CPU with 10 physical cores, 20 logical processors, and 20 threads.

The Cost Objective scenario’s model had 13,556 rows, 10,706 continuous variables, and 2673 integer variables. The presolver removed 5862 rows and 5325 columns in 0.67 s, leaving 7694 rows, 5546 continuous variables, and 2508 integer variables. The solver ran for 100,800 s (28 h) before the algorithm was terminated and produced an objective value of $9.51\times {10}^6$, which corresponds to a total discounted cost of USD 9.51 trillion (as shown in

Table 4. Main results: facilities open in select years, total costs, and total emissions by scenario.

Facility/Year (Scenario)	2023	2030 (Cost)	2040 (Cost)	2050 (Cost)	2100 (Cost)	2023	2030 (${\mathrm{CO}}_2$)	2040 (${\mathrm{CO}}_2$)	2050 (${\mathrm{CO}}_2$)	2100 (${\mathrm{CO}}_2$)
Mining Facilities	8	13	21	36	96	8	14	20	29	77
Processing Facilities	8	12	21	32	70	8	13	27	41	97
Cathode Production Facilities	15	19	36	59	145	15	20	37	66	157
Cell Production Facilities	30	30	39	64	153	30	30	39	67	160
Pack Production Facilities	22	33	65	110	261	22	35	68	112	266
Recycling Facilities	0	0	0	0	0	0	100	150	243	283
Total Discounted Cost		USD 9.51 trillion					USD 10.1 trillion
Total ${\mathrm{CO}}_2$ Emissions		56.8 gigatons					55.7 gigatons

) for the entire time period of the model, with an optimality gap of 0.0176%. While the model did not reach optimality, it reached a solution with a 0.1% optimality gap in 44 s and a 0.02% optimality gap in 1080 s, which is virtually the same optimality gap as after 100,800 s. Therefore, it can be surmised that the rest of the solve time was attempting to fathom the trees in order to provide a provably optimal solution.

The ${\mathrm{CO}}_2$ Objective scenario’s model had the same 13,556 rows, 10,706 continuous variables, and 2673 integer variables as the Cost Objective scenario’s model. However, the presolver removed 5862 rows and 5329 columns in 0.65s leaving, 7694 rows, 5542 continuous variables, and 2508 integer variables: a small difference. A major noteworthy difference between the two models was that the ${\mathrm{CO}}_2$ Objective scenario’s model solved in 4.49 s, which was much faster than the Cost Objective scenario’s model. The ${\mathrm{CO}}_2$ Objective scenario’s model produced an objective value of $5.57\times {10}^7$, which corresponds to 55.7 gigatons of ${\mathrm{CO}}_2$ emissions (as shown in Table 4) for the entire time period of the model, with a relative tolerance of $1\times {10}^{-4}$.

Table 4 records some of the key results from both scenarios. It lists the total discounted costs and total ${\mathrm{CO}}_2$ emissions for both scenarios and also details what facilities each scenario opened in select years. Overall, in 2050, the total number of lithium facilities is less than 100 for all stages except for pack production and recycling in the ${\mathrm{CO}}_2$ Objective scenario. By 2100, only the pack production and recycling facilities have more than 160 locations open. The ${\mathrm{CO}}_2$ Objective scenario opened more of all the facilities except for mining facilities, for which production was replaced by the recycling plants. The rest of this section will explore in more detail the dynamics behind the results of each scenario.

4.1. Cost Objective Scenario

4.1.1. Cost Objective: Production and Capacity

Figure 2 shows the production at each stage over the model period. Since demand is deterministic and the objective function is to minimize cost, this represented the demand curve as well. Figure 3 also illustrates the deterministic nature of the model. However, it does not start to perfectly match demand even after the initial start period, where it has extra capacity from already existing facilities. Since each facility has a certain fixed cost associated with installation, there is a jagged nature between the installations and the capacity as the model attempts to match demand as well as possible. This is highlighted in Figure 4, which stays pretty close to the maximum capacity of each stage but deviates substantially in some years.

The capacity and production output from the aggregated stage data almost perfectly track the demand data, and the same is true for most stages, since the number of EVs by type is input as a parameter, which means that there needs to be a certain number of NMC and LFP batteries produced, which corresponds to the appropriate kilotons of cathode active material. Theoretically, the associated kilotons of LOH and LCE, precursors for NMC and LFP chemistries, respectively, can be sourced from different types of processing plants; since there is no recycling capacity in the solution for the Cost Objective scenario, these simply match what material is mined. However, for the mine stage, the model makes the decision.

Figure 5 shows that there is a clear strategy to produce from spodumene and clay in the earlier years, and when the spodumene mines plateau, the model brings online the brine mines to make up the difference. Since spodumene and clay are the cheapest and next cheapest ways, respectively, to produce LOH, they dominate the market share, as the model clearly invests in and produces from those technologies first. It even chooses to convert some of that production into LCE rather than bring brine mines online. However, as demand increases and the spodumene reserves run low, then brine production is brought online.

4.1.2. Cost Objective: Total Cost and Emissions

Figure 6 shows that the costs mostly maintain the ratios that were set when disaggregating the USD/kWh metric. The cell costs are a little higher than their initial ratio; the cathode costs are as well, while the pack cost is down, but the magnitude is similar. The total discounted cost for this scenario is USD 9.51 trillion.

Figure 7 shows that emissions are dominated by cell and pack production. Cathode production also has significant emissions as well. Since the emissions from pack and cell production are associated with the emissions related to industrial facilities, these could be lowered by adopting renewable energy at these facilities. Unfortunately, it seems that emissions cannot be substantially lowered by making different investment decisions. The total ${\mathrm{CO}}_2$ emissions for this scenario is 56.8 gigatons.

4.2. ${\mathrm{CO}}_2$ Objective

4.2.1. ${\mathrm{CO}}_2$ Objective: Total Cost and Emissions

Figure 8 highlights the first change between the two objectives: that the ${\mathrm{CO}}_2$ scenario invests in recycling in order to lower emissions. This clearly lowers mine and processing production, so their costs decrease, and the stages no longer maintain their ratios from the USD/kWh metric. The total discounted cost for this scenario is USD 10.1 trillion, which is about 6% higher than the Cost Objective scenario, meaning that the emissions savings come with a nearly 6% cost premium.

Figure 9 shows that emissions are still dominated by the cell and pack production, and the cathode production emissions are unchanged. However, the mine and processing emissions go down by a large percentage. Unfortunately, it seems that emissions cannot be substantially lowered by making different investment decisions, but since they are dominated by industrial facility emissions, they might be easier to decarbonize than if mining and processing emissions dominated. The total ${\mathrm{CO}}_2$ emissions for this scenario are 55.7 gigatons, which is slightly lower than for the Cost Objective scenario (a little less than 2% lower) but not significantly so. This emissions-savings-to-cost-savings ratio of one third might still be justified depending on the decision makers’ preferences.

4.2.2. Production and Investments

Figure 10 and Figure 11 show that since there is now recycling capacity, the production for mining and processing no longer follow the demand curve. As more recyclable material becomes available, the recycling production increases accordingly. Like the Cost Objective scenario, the ${\mathrm{CO}}_2$ scenario cannot perfectly align capacity with demand. However, Figure 12 and Figure 13 show how unit investments are not necessarily made with the goal of maximizing asset utilization to lower cost but to maximize available capacity of the lowest-emitting facilities. The model heavily invests in additional units, constantly hitting the unit investment limit for recycling. This will lower the utilization rate of the new facilities and existing ones but dramatically lower the production emissions once the facilities are online.

5. Discussion

Clean energy transition technologies will require an entirely new supply chain with different characteristics and stages than our current energy system. The complexities of energy storage, including the variety of chemistries that can power it, its multiple use cases (especially EVs), and the variety of critical minerals needed to build them highlight the shift in perspective needed for the new clean energy supply chains. Critical minerals, currently produced in relatively small quantities, will have to be rapidly scaled up to meet new demand. New technological directions that lower costs, increase energy density, or provide new capabilities (e.g., wireless charging) could require completely different materials, shifting the supply chain. These challenges and the general uncertainty on how to manage clean energy transition supply chains are why new flexible and robust decision tools are needed.

This study introduced a flexible framework for modeling, optimizing, and managing the mineral supply chains for clean energy technologies. This framework uses exogenously provided information to parameterize a mathematical-optimization-based model that can provide critical insights into mineral supply chains. To evaluate this framework, a global lithium supply chain case study was explored.

5.1. Key Insights from the Global Lithium Supply Chain Case Study

The case study evaluated the lithium supply chain with a global central planner with perfect access to demand and cost information under two scenarios. The Cost Objective scenario’s objective was to minimize the total discounted cost of the entire supply chain from 2020–2100 and reported a total discounted cost of USD 9.51 trillion, which was about 6% cheaper than the ${\mathrm{CO}}_2$ Objective scenario. In contrast, the ${\mathrm{CO}}_2$ Objective scenario’s objective was to minimize the total ${\mathrm{CO}}_2$ emissions of the entire supply chain from 2020–2100 and reported 55.7 gigatons of ${\mathrm{CO}}_2$ emissions over the model period, which was about 2% less than that of the Cost Objective scenario.

Both scenarios made similar investments in cell and pack production facilities but deviated substantially in the number of mining, processing, cathode production, and recycling facilities. This is most prevalent in the decision to invest in recycling facilities, where the Cost Objective scenario did not invest in any recycling facilities and the ${\mathrm{CO}}_2$ Objective scenario invested in a substantial number to replace more-carbon-intensive mining facilities. Furthermore, the ${\mathrm{CO}}_2$ Objective scenario opened up more facilities overall to maximize utilization of the less-carbon-intensive facilities, even though that resulted in lower asset utilization, driving up costs. In contrast, the Cost Objective scenario sought to open as few facilities as possible and maximize asset utilization to drive down costs.

Even under the ideal conditions of having perfect access to demand, cost, and carbon intensity, there are nuances in decision making under both scenarios. Asset utilization shifts as demand grows, and the new assets cannot be brought online perfectly in sync with the new demand. Furthermore, when different technologies can be implemented to produce the same end product, the model maximizes the utilization of the cheapest one earlier before starting the more expensive options. Since this model discounts future costs, this makes logical sense for the Cost Optimization scenario. Therefore, the main strategy of the Cost Optimization scenario was to maximize utilization of the lowest cost facilities. However, when emissions are considered, the strategy changes: no longer is the model attempting to maximize the utilization ratio, but rather, it is attempting to ensure that the lowest-emitting technologies have the capacity to meet more demand. So the ${\mathrm{CO}}_2$ Optimization scenario invested in a large number of less-carbon-intensive units, like recycling facilities, at one time rather than gradually, like the Cost Optimization scenario, which dramatically lowers the utilization ratio.

The case study also allowed us to compare the scale of the minerals required for the clean energy transition to the fossil fuels required for the legacy energy system. For the case study, in the year 2100, the maximum number of facilities opened by either scenario for each stage was as follows: 96 lithium mining facilities, 97 processing plants, 157 cathode production facilities, 160 cell production facilities, 266 pack production facilities, and 283 recycling facilities, for a total of 1059 facilities. In contrast, there were over 1 million active oil wells in 2017, and in 2014, there were 550 gas processing plants and 114 oil refineries [110]. There are also currently 550 coal mines, down from nearly 1500 mines in 2008 [14]. Lastly, in the case study, the total aggregate global lithium demand for all 81 model years was 9100 kt (0.0091 gigatons), while our fossil fuel energy system requires 15 gigatons of fossil fuels every year. However, the mineral weight can be misleading as massive amounts of materials must be extracted and processed to acquire the minerals. Nonetheless, even when accounting for the material requirements of lithium, which add a factor of 170 to the mineral weight needed and would increase the 81-year lithium tonnage demand to 1.55 gigatons of material, the material tonnage for lithium is orders of magnitude lower than the fossil fuel energy system’s tonnage [2,111,112]. Thus, this model further highlights how the existing energy system is much more material, mineral, and even capital intensive than the new energy system, even when accounting for the fact that a clean energy system will require more critical minerals.

While the total discounted costs produced by the model are difficult to compare to the costs of existing systems since the model assumes orders of magnitude increases in lithium production and the future discount rate is unknowable, the total ${\mathrm{CO}}_2$ emissions are more easily evaluated. In 2022, total fossil fuel emissions totaled almost 10 gigatons, where 32% came from oil, 41% came from coal, and 21% came from natural gas [113]. Therefore, in one year, the current energy system emits over a sixth of the ${\mathrm{CO}}_2$ emissions that the entire lithium supply chain does during the entire 81-year case study time period. If we assume 2022’s level of fossil fuel ${\mathrm{CO}}_2$ emissions over that same 81-year time period, that would be 8100 gigatons of emissions. If we conservatively assume that lithium-enabled technologies can only replace 10% of those total emissions, then the lithium supply chain would save 753 gigatons of ${\mathrm{CO}}_2$ emissions. However, energy storage technologies powered by lithium are likely in that long of a time horizon to replace most oil-based transportation technologies and enable intermittent renewables to almost completely replace all coal- and natural-gas-powered plants via cheap energy storage. Thus, the lithium supply chain could help eliminate terratons of future ${\mathrm{CO}}_2$ emissions, and being able to model and optimize the supply chain is critical to that effort.

The case study showcases the ability of the framework to produce insights even with simplistic and ideal scenarios. Furthermore, if a decision maker wants to evaluate different scenarios, they can simply modify their exogenously provided dataset and explore entirely new scenarios. This flexibility and ease of use can be used to quickly evaluate potential scenarios from different decision makers’ perspectives. Furthermore, as decision makers start to deal with more complex issues, this framework can be modified, expanded, and tailored as needed to address the complexities of the global critical mineral supply chain.

5.2. Future Work

The framework developed in this article is useful, but it is currently in its most raw and simplistic form, but if expanded, the problems it can solve can be much more complex. The first potential addition to explore would be geospatial capabilities, where instead of treating the planet as one region with one decision maker, the model can balance multiple players in different regions with competing objectives. Next would be to expand to other critical minerals beyond lithium or to evaluate the supply chains of multiple critical minerals that would be needed for a given technology. A major limitation of this work is the deterministic nature of the evolving demand, cost, and emission profiles; incorporating uncertainty and creating a stochastic model would bring even more generalizable insights.

Furthermore, the supply chain does not operate in isolation: it exists to provide materials for people to build the new clean energy technologies. Thus, this model could be linked to a capacity expansion type model to inform the demand for the materials and to policy makers on how investments in the supply chain can increase the rate of decarbonization, improving air quality and carbon emissions. This would also provide feedback to users of those types of models, who assume the materials are ready whenever they want to build. Being able to implement material availability could help them make better technological investments.

The geopolitics of the world are shifting, and countries are wanting to capture more industrial benefits for their constituents. The model should account for labor, capital, and other macro- and macroeconomic effects to quantify those benefits and provide information that could be used for other economic and social models. Lastly, this model could incorporate functions that take into account how certain investments can accelerate technical innovation through network effects or lower the costs via learning-by-doing mechanisms. The functional forms for these interactions are typically non-linear, which would complicate the model, but surrogate modeling techniques could be applied to speed up analysis.

This framework provides a foundational tool that will help evaluate a critical piece of the clean energy transition: the mineral supply chain. The framework offers a way for decision makers to make multi-objective decisions at various scales and will provide a basis for future analysis.