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<!DOCTYPE html>
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<!-- ══════════════════════════════════════════════════════ SIDEBAR -->
<nav id="sidebar">
<div class="sidebar-logo">
<div class="project-name">BLEECAM</div>
<div class="project-ver">API Reference · April 2026</div>
</div>
<div class="sidebar-section">Modules</div>
<span class="sidebar-module">config.py</span>
<a href="#config-constants" class="sidebar-link">Constants & Configuration</a>
<span class="sidebar-module">data_loader.py</span>
<a href="#load_all_data" class="sidebar-link">load_all_data()</a>
<a href="#validate_csvs" class="sidebar-link">validate_csvs()</a>
<a href="#validate_slca" class="sidebar-link">validate_slca()</a>
<span class="sidebar-module">REE.py</span>
<a href="#parse_args" class="sidebar-link">_parse_args()</a>
<a href="#total_cost_rule" class="sidebar-link">total_cost_rule()</a>
<a href="#total_emissions_rule" class="sidebar-link">total_emissions_rule()</a>
<a href="#total_child_labor_rule" class="sidebar-link">total_child_labor_rule()</a>
<a href="#print_diagnostics" class="sidebar-link">print_diagnostics()</a>
<span class="sidebar-module">constraints.py</span>
<a href="#fix" class="sidebar-link">_fix()</a>
<a href="#fix_inactive" class="sidebar-link">fix_inactive_process_locations()</a>
<a href="#fix_disallowed" class="sidebar-link">fix_disallowed_trade_flows()</a>
<a href="#clay_mining" class="sidebar-link">clay_mining_constraints()</a>
<a href="#clay_refining" class="sidebar-link">clay_refining_constraints()</a>
<a href="#beneficiation" class="sidebar-link">beneficiation_constraints()</a>
<a href="#h2so4" class="sidebar-link">sulfuric_acid_digestion_constraints()</a>
<a href="#hcl" class="sidebar-link">hydrochloric_acid_digestion_constraints()</a>
<a href="#mse" class="sidebar-link">molten_salt_electrolysis_constraints()</a>
<a href="#mr" class="sidebar-link">metallothermic_reduction_constraints()</a>
<a href="#ct" class="sidebar-link">chemical_transformation_constraints()</a>
<a href="#magnet_mfg" class="sidebar-link">magnet_manufacturing_constraints()</a>
<a href="#magnet_mix" class="sidebar-link">magnet_market_mix_constraints()</a>
<a href="#demand" class="sidebar-link">demand_fulfillment_constraints()</a>
<a href="#weibull" class="sidebar-link">weibull_historic_retirement()</a>
<a href="#use_phase" class="sidebar-link">use_phase_stock_constraints()</a>
<a href="#fix_eol_t0" class="sidebar-link">fix_eol_outflows_at_t0()</a>
<a href="#eol_lagged" class="sidebar-link">_eol_lagged_constraints()</a>
<a href="#direct_reuse" class="sidebar-link">direct_reuse_constraints()</a>
<a href="#m2m" class="sidebar-link">magnet_to_magnet_recycling_constraints()</a>
<a href="#hydro" class="sidebar-link">hydrometallurgical_constraints()</a>
<a href="#pyro" class="sidebar-link">pyrometallurgical_constraints()</a>
<a href="#cryo" class="sidebar-link">cryogenic_constraints()</a>
<a href="#stock" class="sidebar-link">add_stock_constraints()</a>
<a href="#capacity" class="sidebar-link">apply_capacity_constraints()</a>
<a href="#unused_oxides" class="sidebar-link">add_unused_oxides_tracking()</a>
</nav>
<!-- ══════════════════════════════════════════════════════ MAIN -->
<main id="main">
<div class="page-header">
<h1>BLEECAM API Reference</h1>
<p>
<span class="badge">Pyomo</span>
<span class="badge">IPOPT</span>
<span class="badge">NdFeB Supply Chain</span>
Auto-generated from source docstrings · National Renewable Energy Laboratory
</p>
</div>
<!-- ═══════════════════════════════════ config.py -->
<div class="module-section">
<span class="anchor" id="config-constants"></span>
<div class="module-header">
<h2>config.py</h2>
<span class="module-path">bleecam/config.py</span>
</div>
<p class="module-desc">Global model configuration — process lists, location lists, material lists, active process-location mappings, and all scalar penalty constants. Edit here to add new processes, locations, or change penalty rates.</p>
<div class="section-label">Constants</div>
<table class="const-table">
<thead><tr><th>Name</th><th>Value</th><th>Units</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="const-name">FLOW_SCALE</td><td class="const-val">1000.0</td><td>dimensionless</td><td>Divisor applied to all capacity/demand values on CSV load. Internal model variables operate in tonnes (kg ÷ 1000). Output flows are multiplied back by FLOW_SCALE before writing to CSV/HTML.</td></tr>
<tr><td class="const-name">num_time_periods</td><td class="const-val">5</td><td>periods</td><td>Number of model time periods (t = 0 … 4), representing annual snapshots 2025–2029.</td></tr>
<tr><td class="const-name">DEMAND_LOCATION</td><td class="const-val">'US'</td><td>—</td><td>The single demand node for hp_magnet consumption.</td></tr>
<tr><td class="const-name">ALLOY</td><td class="const-val">'neodynium dysprosium iron alloy'</td><td>—</td><td>Canonical string name for the NdFeB alloy material.</td></tr>
<tr><td class="const-name">PENALTY_UNUSED_OXIDE_COST</td><td class="const-val">80</td><td>$/kg</td><td>Penalty rate for NdOx/DyOx co-products routed to incompatible processes (misrouting penalty).</td></tr>
<tr><td class="const-name">PENALTY_UNUSED_OXIDE_GWP</td><td class="const-val">15</td><td>kg CO₂-eq/kg</td><td>GWP equivalent of the unused oxide penalty under the emissions objective.</td></tr>
<tr><td class="const-name">PENALTY_UNUSED_OXIDE_SLCA</td><td class="const-val">0.001</td><td>worker-hr/kg</td><td>Social LCA equivalent of the unused oxide penalty.</td></tr>
<tr><td class="const-name">DEFAULT_MAX_STOCK_CAPACITY</td><td class="const-val">4,000,000 / FLOW_SCALE</td><td>tonnes (internal)</td><td>Fallback stock capacity (4,000 tonnes) used when no explicit cap is found for a (t, material) pair.</td></tr>
<tr><td class="const-name">DEFAULT_STOCK_HOLDING_COST</td><td class="const-val">0.1</td><td>$/tonne·period</td><td>Default inventory holding cost per unit per period.</td></tr>
<tr><td class="const-name">list_of_processes</td><td class="const-val">17 processes</td><td>—</td><td>Ordered list of all process names: mining, beneficiation, clay mining, clay refining, H₂SO₄ digestion, HCl digestion, molten salt electrolysis, metallothermic reduction, chemical transformation, magnet manufacturing, magnet_market_mix, use phase, and 5 EOL routes.</td></tr>
<tr><td class="const-name">locations</td><td class="const-val">['CN','JP','AU','US','MM','MY','EE','CA','BR']</td><td>—</td><td>All country/region codes active in the model.</td></tr>
<tr><td class="const-name">materials</td><td class="const-val">12 materials</td><td>—</td><td>Nd, Dy, Fe, ion adsorption clay, NdFeB alloy, NdOx, DyOx, phosphate, flurocarbonate, monazite, bastnasite, hp_magnet.</td></tr>
<tr><td class="const-name">ACTIVE_PROCESS_LOCATIONS</td><td class="const-val">dict</td><td>—</td><td>Maps each process name to the list of locations where that process is active. Controls which flowQ variables are fixed to zero during model setup.</td></tr>
</tbody>
</table>
</div>
<!-- ═══════════════════════════════════ data_loader.py -->
<div class="module-section">
<div class="module-header">
<h2>data_loader.py</h2>
<span class="module-path">bleecam/data_loader.py</span>
</div>
<p class="module-desc">Reads all input CSVs from the data directory, applies FLOW_SCALE to capacity and demand, and returns a single data dictionary used to build the Pyomo model. Also provides validation utilities that flag missing data entries before a solve.</p>
<!-- load_all_data -->
<span class="anchor" id="load_all_data"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">load_all_data</span><span class="fn-paren">(</span><span class="fn-param">data_dir</span><span class="fn-colon">=</span><span class="fn-default">'./data'</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Load all CSV input data and return as a unified dictionary, with capacity and demand values scaled by <code>FLOW_SCALE</code>. This is the single data-ingestion call — all downstream model code works from the returned dict.</p>
<div class="section-label">Parameters</div>
<table class="params-table">
<thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">data_dir</td><td class="ptype">str or Path</td><td>Path to directory containing all input CSVs. Defaults to <code>'./data'</code>.</td></tr>
</tbody>
</table>
<div class="returns-box">
<div class="returns-label">Returns</div>
<div><span class="returns-type">dict</span> with keys: <code>demand_df</code> (DataFrame), <code>high_perf_magnet_required</code> (dict[int, float]), <code>yield_factor</code>, <code>recovery_rate</code>, <code>processing_cost</code>, <code>domestic_transport_cost</code>, <code>shipping_cost</code>, <code>tariff_cost</code>, <code>ef_factor</code>, <code>ct_mass_ratio_by_t</code>, <code>allowed_trade_arcs</code> (set), <code>max_output_capacity</code>, <code>slca_factors</code>. All flow quantities divided by <code>FLOW_SCALE</code>.</div>
</div>
</div>
</div>
<!-- validate_csvs -->
<span class="anchor" id="validate_csvs"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">validate_csvs</span><span class="fn-paren">(</span><span class="fn-param">time_periods</span>, <span class="fn-param">yield_factor</span>, <span class="fn-param">recovery_rate</span>, <span class="fn-param">processing_cost</span>, <span class="fn-param">domestic_transport_cost</span>, <span class="fn-param">ef_factor</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Check all active <code>(process, location, material, time)</code> combinations for missing entries across all major input CSVs. Prints a formatted warning listing every missing tuple. Call this before a solve to catch data gaps that would silently set parameters to 0.</p>
<div class="section-label">Parameters</div>
<table class="params-table">
<thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">time_periods</td><td class="ptype">list[int]</td><td>Model time period indices to validate against.</td></tr>
<tr><td class="pname">yield_factor</td><td class="ptype">dict</td><td>Keyed by <code>(t, process, location, material)</code>.</td></tr>
<tr><td class="pname">recovery_rate</td><td class="ptype">dict</td><td>Keyed by <code>(t, src, src_loc, dst, dst_loc, mat)</code>.</td></tr>
<tr><td class="pname">processing_cost</td><td class="ptype">dict</td><td>Keyed by <code>(t, process, location, material)</code>.</td></tr>
<tr><td class="pname">domestic_transport_cost</td><td class="ptype">dict</td><td>Keyed by <code>(t, process, location, material)</code>.</td></tr>
<tr><td class="pname">ef_factor</td><td class="ptype">dict</td><td>Keyed by <code>(t, process, location, material)</code>.</td></tr>
</tbody>
</table>
<div class="returns-box">
<div class="returns-label">Returns</div>
<div><span class="returns-type">None</span> — prints warnings to stdout.</div>
</div>
</div>
</div>
<!-- validate_slca -->
<span class="anchor" id="validate_slca"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">validate_slca</span><span class="fn-paren">(</span><span class="fn-param">time_periods</span>, <span class="fn-param">slca_factors</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Check SLCA impact factor coverage for all active process/location/material/time combinations across all five impact categories (child labor, forced labor, fatal injury, non-fatal injury, unemployment). Prints per-category OK or missing-entry status.</p>
<div class="section-label">Parameters</div>
<table class="params-table">
<thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">time_periods</td><td class="ptype">list[int]</td><td>Model time period indices.</td></tr>
<tr><td class="pname">slca_factors</td><td class="ptype">dict[str, dict]</td><td>Maps impact category name to <code>{(t, process, location, material): float}</code>.</td></tr>
</tbody>
</table>
<div class="returns-box">
<div class="returns-label">Returns</div>
<div><span class="returns-type">None</span> — prints per-category status to stdout.</div>
</div>
</div>
</div>
</div>
<!-- ═══════════════════════════════════ REE.py -->
<div class="module-section">
<div class="module-header">
<h2>REE.py</h2>
<span class="module-path">bleecam/REE.py</span>
</div>
<p class="module-desc">Main model entry point. Loads data, applies scenario overrides, builds the Pyomo ConcreteModel, invokes IPOPT, post-processes and scales outputs, writes results to CSV and HTML, and spawns the dashboard.</p>
<!-- _parse_args -->
<span class="anchor" id="parse_args"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">_parse_args</span><span class="fn-paren">()</span>
</div>
<div class="func-body">
<p class="func-summary">Parse CLI arguments for the single-objective BLEECAM solve. Accepts <code>--data</code> (path to input CSV directory) and <code>--out</code> (path for output files).</p>
<div class="returns-box">
<div class="returns-label">Returns</div>
<div><span class="returns-type">argparse.Namespace</span> with fields <code>.data</code> (Path) and <code>.out</code> (Path).</div>
</div>
</div>
</div>
<!-- total_cost_rule -->
<span class="anchor" id="total_cost_rule"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">total_cost_rule</span><span class="fn-paren">(</span><span class="fn-param">model</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Return the total cost objective expression for the Pyomo model. Sums processing cost, domestic transport cost, shipping cost, and tariff cost over all <code>flowQ</code> variables, plus stock holding costs, the unused-oxide penalty (<code>PENALTY_UNUSED_OXIDE_COST × total_unused_oxides</code>), and the demand slack penalty (<code>slack_penalty_cost × Σ(slack_pos + slack_neg)</code>).</p>
<div class="section-label">Parameters</div>
<table class="params-table">
<thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model instance.</td></tr>
</tbody>
</table>
<div class="returns-box">
<div class="returns-label">Returns</div>
<div><span class="returns-type">Pyomo expression</span> — passed directly to <code>Objective(rule=..., sense=minimize)</code>. Note: objective value = real cost / FLOW_SCALE during solve; multiply by FLOW_SCALE for display.</div>
</div>
</div>
</div>
<!-- total_emissions_rule -->
<span class="anchor" id="total_emissions_rule"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">total_emissions_rule</span><span class="fn-paren">(</span><span class="fn-param">model</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Return the total GWP emissions objective expression. Weights each <code>flowQ</code> variable by its emission factor from <code>ef_factor</code>, adds the unused-oxide GWP penalty and demand slack penalty. Use by setting <code>ACTIVE_OBJECTIVE = 'gwp'</code>.</p>
<div class="section-label">Parameters</div>
<table class="params-table">
<thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model instance.</td></tr>
</tbody>
</table>
<div class="returns-box">
<div class="returns-label">Returns</div>
<div><span class="returns-type">Pyomo expression</span> — total GWP weighted by emission factors.</div>
</div>
</div>
</div>
<!-- total_child_labor_rule -->
<span class="anchor" id="total_child_labor_rule"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">total_child_labor_rule</span><span class="fn-paren">(</span><span class="fn-param">model</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Return the total child-labor Social LCA objective expression. Weights each <code>flowQ</code> variable by its child-labor impact factor from <code>slca_factors['child_labor']</code>. Four additional SLCA categories (forced labor, fatal injury, non-fatal injury, unemployment) are loaded but not currently used as primary objectives. Use by setting <code>ACTIVE_OBJECTIVE = 'slca'</code>.</p>
<div class="section-label">Parameters</div>
<table class="params-table">
<thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model instance.</td></tr>
</tbody>
</table>
<div class="returns-box">
<div class="returns-label">Returns</div>
<div><span class="returns-type">Pyomo expression</span> — total child-labor SLCA impact in worker-hours.</div>
</div>
</div>
</div>
<!-- print_diagnostics -->
<span class="anchor" id="print_diagnostics"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">print_diagnostics</span><span class="fn-paren">(</span><span class="fn-param">model</span>, <span class="fn-param">high_perf_magnet_required</span>, <span class="fn-param">label</span><span class="fn-colon">=</span><span class="fn-default">'DIAGNOSTIC REPORT'</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Print a structured diagnostic summary of the solved model to stdout. Reports per-period demand fulfillment vs. slack, magnet market mix mass balance, recycling flow levels, and objective components. Used after solve to quickly validate results before inspecting HTML outputs.</p>
<div class="section-label">Parameters</div>
<table class="params-table">
<thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>Solved BLEECAM Pyomo model.</td></tr>
<tr><td class="pname">high_perf_magnet_required</td><td class="ptype">dict[int, float]</td><td>Mapping of time period to required hp_magnet demand (in FLOW_SCALE units).</td></tr>
<tr><td class="pname">label</td><td class="ptype">str</td><td>Header label printed at the top of the diagnostic block.</td></tr>
</tbody>
</table>
<div class="returns-box">
<div class="returns-label">Returns</div>
<div><span class="returns-type">None</span> — prints to stdout.</div>
</div>
</div>
</div>
</div>
<!-- ═══════════════════════════════════ constraints.py -->
<div class="module-section">
<div class="module-header">
<h2>constraints.py</h2>
<span class="module-path">bleecam/constraints.py</span>
</div>
<p class="module-desc">All Pyomo constraint rules, organized by supply chain stage. Each function serves two purposes: fixing structurally zero flowQ variables (reducing model size and preventing solver degeneracy) and adding mass-balance / yield / recovery-rate equations for that stage.</p>
<!-- _fix -->
<span class="anchor" id="fix"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">_fix</span><span class="fn-paren">(</span><span class="fn-param">var</span>, <span class="fn-param">val</span><span class="fn-colon">=</span><span class="fn-default">0</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Fix a Pyomo variable to a given value, suppressing errors if already fixed. This is the low-level utility called throughout constraints to zero out structurally impossible flows.</p>
<div class="section-label">Parameters</div>
<table class="params-table">
<thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">var</td><td class="ptype">pyomo.environ.Var</td><td>The Pyomo variable element to fix.</td></tr>
<tr><td class="pname">val</td><td class="ptype">float</td><td>Value to fix the variable to. Default <code>0</code>.</td></tr>
</tbody>
</table>
</div>
</div>
<!-- fix_inactive_process_locations -->
<span class="anchor" id="fix_inactive"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">fix_inactive_process_locations</span><span class="fn-paren">(</span><span class="fn-param">model</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Zero out all <code>flowQ</code> variables whose source or destination location is not active for that process, per <code>ACTIVE_PROCESS_LOCATIONS</code>. This is the first constraint call — it dramatically reduces the number of free variables before any process-specific constraints are applied.</p>
<div class="section-label">Parameters</div>
<table class="params-table"><thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody><tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model.</td></tr></tbody>
</table>
</div>
</div>
<!-- fix_disallowed_trade_flows -->
<span class="anchor" id="fix_disallowed"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">fix_disallowed_trade_flows</span><span class="fn-paren">(</span><span class="fn-param">model</span>, <span class="fn-param">allowed_trade_arcs</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Zero out all cross-country <code>flowQ</code> variables that are not in the permitted trade arc set. Same-country flows are always allowed. Trade topology is defined in <code>trade_topology.csv</code>.</p>
<div class="section-label">Parameters</div>
<table class="params-table"><thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model.</td></tr>
<tr><td class="pname">allowed_trade_arcs</td><td class="ptype">set[tuple]</td><td>Set of <code>(proc_from, loc_from, proc_to, loc_to, material)</code> tuples defining permitted cross-country flows.</td></tr>
</tbody>
</table>
</div>
</div>
<!-- clay_mining_constraints -->
<span class="anchor" id="clay_mining"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">clay_mining_constraints</span><span class="fn-paren">(</span><span class="fn-param">model</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Restrict clay mining outflows so that only same-location clay refining receives ion adsorption clay. All other inflows and outflows are fixed to zero. Enforces that ion adsorption clay does not cross borders.</p>
<div class="section-label">Parameters</div>
<table class="params-table"><thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody><tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model.</td></tr></tbody>
</table>
</div>
</div>
<!-- clay_refining_constraints -->
<span class="anchor" id="clay_refining"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">clay_refining_constraints</span><span class="fn-paren">(</span><span class="fn-param">model</span>, <span class="fn-param">yield_factor</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Enforce mass-balance and co-product ratio constraints for clay refining. NdOx and DyOx outputs must equal yield-factor multiples of clay input. The NdOx:DyOx ratio flowing to each downstream reactor (MSE or MR) is locked proportionally — no selective routing of one oxide without the other.</p>
<div class="section-label">Parameters</div>
<table class="params-table"><thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model.</td></tr>
<tr><td class="pname">yield_factor</td><td class="ptype">dict</td><td>Mapping of <code>(t, process, location, material)</code> to float yield fraction.</td></tr>
</tbody>
</table>
</div>
</div>
<!-- beneficiation_constraints -->
<span class="anchor" id="beneficiation"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">beneficiation_constraints</span><span class="fn-paren">(</span><span class="fn-param">model</span>, <span class="fn-param">yield_factor</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Link beneficiation outputs to mining inputs via yield factors. Phosphate output routes to H₂SO₄ digestion; flurocarbonate output routes to HCl digestion. All other outflows are fixed to zero.</p>
<div class="section-label">Parameters</div>
<table class="params-table"><thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model.</td></tr>
<tr><td class="pname">yield_factor</td><td class="ptype">dict</td><td>Mapping of <code>(t, process, location, material)</code> to float yield fraction.</td></tr>
</tbody>
</table>
</div>
</div>
<!-- sulfuric_acid_digestion_constraints -->
<span class="anchor" id="h2so4"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">sulfuric_acid_digestion_constraints</span><span class="fn-paren">(</span><span class="fn-param">model</span>, <span class="fn-param">yield_factor</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Enforce that NdOx and DyOx outputs from H₂SO₄ digestion equal yield-factor multiples of phosphate input. NdOx:DyOx ratio is locked proportionally across downstream receivers (MSE and MR). All other flows fixed to zero.</p>
<div class="section-label">Parameters</div>
<table class="params-table"><thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model.</td></tr>
<tr><td class="pname">yield_factor</td><td class="ptype">dict</td><td>Keyed by <code>(t, process, location, material)</code>.</td></tr>
</tbody>
</table>
</div>
</div>
<!-- hydrochloric_acid_digestion_constraints -->
<span class="anchor" id="hcl"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">hydrochloric_acid_digestion_constraints</span><span class="fn-paren">(</span><span class="fn-param">model</span>, <span class="fn-param">yield_factor</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Enforce that NdOx and DyOx outputs from HCl digestion equal yield-factor multiples of flurocarbonate input. Parallel structure to H₂SO₄ digestion but processes bastnasite/monazite ores via the HCl route.</p>
<div class="section-label">Parameters</div>
<table class="params-table"><thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model.</td></tr>
<tr><td class="pname">yield_factor</td><td class="ptype">dict</td><td>Keyed by <code>(t, process, location, material)</code>.</td></tr>
</tbody>
</table>
</div>
</div>
<!-- molten_salt_electrolysis_constraints -->
<span class="anchor" id="mse"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">molten_salt_electrolysis_constraints</span><span class="fn-paren">(</span><span class="fn-param">model</span>, <span class="fn-param">yield_factor</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Link Nd metal output from molten-salt electrolysis to NdOx input via yield factor. Fixes all other flows. MSE is the primary route for reducing neodymium oxide to Nd metal.</p>
<div class="section-label">Parameters</div>
<table class="params-table"><thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model.</td></tr>
<tr><td class="pname">yield_factor</td><td class="ptype">dict</td><td>Keyed by <code>(t, process, location, material)</code>.</td></tr>
</tbody>
</table>
</div>
</div>
<!-- metallothermic_reduction_constraints -->
<span class="anchor" id="mr"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">metallothermic_reduction_constraints</span><span class="fn-paren">(</span><span class="fn-param">model</span>, <span class="fn-param">yield_factor</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Link Dy metal output from metallothermic reduction to DyOx input via yield factor. Fixes all other flows. Metallothermic reduction is the primary route for reducing dysprosium oxide to Dy metal.</p>
<div class="section-label">Parameters</div>
<table class="params-table"><thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model.</td></tr>
<tr><td class="pname">yield_factor</td><td class="ptype">dict</td><td>Keyed by <code>(t, process, location, material)</code>.</td></tr>
</tbody>
</table>
</div>
</div>
<!-- chemical_transformation_constraints -->
<span class="anchor" id="ct"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">chemical_transformation_constraints</span><span class="fn-paren">(</span><span class="fn-param">model</span>, <span class="fn-param">yield_factor</span>, <span class="fn-param">ct_mass_ratio_by_t</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Enforce mass-balance for NdFeB alloy production. Alloy output = yield_factor × iron input. Nd and Dy metal inputs are determined by time-varying mass-ratio fractions read from <code>Demand_Input_Template.csv</code> (the <code>mass ratio Nd</code> and <code>mass ratio Dy</code> columns).</p>
<div class="section-label">Parameters</div>
<table class="params-table"><thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model.</td></tr>
<tr><td class="pname">yield_factor</td><td class="ptype">dict</td><td>Keyed by <code>(t, process, location, material)</code>.</td></tr>
<tr><td class="pname">ct_mass_ratio_by_t</td><td class="ptype">dict[int, tuple[float, float]]</td><td>Maps time period to <code>(Nd_mass_ratio, Dy_mass_ratio)</code> fractions.</td></tr>
</tbody>
</table>
</div>
</div>
<!-- magnet_manufacturing_constraints -->
<span class="anchor" id="magnet_mfg"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">magnet_manufacturing_constraints</span><span class="fn-paren">(</span><span class="fn-param">model</span>, <span class="fn-param">yield_factor</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Link hp_magnet output from magnet manufacturing to alloy input via yield factor. Fixes all irrelevant flows. The final step before the product enters the market mix node.</p>
<div class="section-label">Parameters</div>
<table class="params-table"><thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model.</td></tr>
<tr><td class="pname">yield_factor</td><td class="ptype">dict</td><td>Keyed by <code>(t, process, location, material)</code>.</td></tr>
</tbody>
</table>
</div>
</div>
<!-- magnet_market_mix_constraints -->
<span class="anchor" id="magnet_mix"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">magnet_market_mix_constraints</span><span class="fn-paren">(</span><span class="fn-param">model</span>, <span class="fn-param">high_perf_magnet_required</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Route the magnet market mix output to the use phase at the demand location (US). Fixes the market-mix → use-phase flow equal to total hp_magnet demand for each period. This is the "aggregation node" that collects supply from all manufacturing locations.</p>
<div class="section-label">Parameters</div>
<table class="params-table"><thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model.</td></tr>
<tr><td class="pname">high_perf_magnet_required</td><td class="ptype">dict[int, float]</td><td>Mapping of time period to required hp_magnet demand (in FLOW_SCALE units).</td></tr>
</tbody>
</table>
</div>
</div>
<!-- demand_fulfillment_constraints -->
<span class="anchor" id="demand"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">demand_fulfillment_constraints</span><span class="fn-paren">(</span><span class="fn-param">model</span>, <span class="fn-param">high_perf_magnet_required</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Add soft demand constraints using slack variables. Total hp_magnet inflow to the use phase must equal demand per period, but slack variables <code>demand_slack_pos</code> (unmet demand) and <code>demand_slack_neg</code> (over-supply) allow infeasibility to be detected and penalized rather than hard-infeasible. Slack is penalized by <code>slack_penalty_cost</code> in the objective.</p>
<div class="section-label">Parameters</div>
<table class="params-table"><thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model.</td></tr>
<tr><td class="pname">high_perf_magnet_required</td><td class="ptype">dict[int, float]</td><td>Mapping of time period to required hp_magnet demand (in FLOW_SCALE units).</td></tr>
</tbody>
</table>
</div>
</div>
<!-- weibull_historic_retirement -->
<span class="anchor" id="weibull"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">weibull_historic_retirement</span><span class="fn-paren">(</span><span class="fn-param">model</span>, <span class="fn-param">data_dir</span><span class="fn-colon">=</span><span class="fn-default">'./data'</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Compute historic in-use magnet retirements per time period using a Weibull lifetime distribution fitted to fleet deployment data. Loads <code>historic_installs.xlsx</code>, reads the <code>original</code> column (actual kg install data), and applies a Weibull CDF with shape k=1.5 and mean life 31.1 years to calculate what fraction of each installation cohort retires in each model period.</p>
<p style="margin-top:8px; color:#c0392b; font-size:13px;"><strong>Important:</strong> Must read the <code>original</code> column, not <code>installs</code> (which is all zeros, a legacy artifact). The <code>installs2</code> column (= original/1000) also works but <code>original</code> is authoritative.</p>
<div class="section-label">Parameters</div>
<table class="params-table"><thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model (used for TimePeriods set).</td></tr>
<tr><td class="pname">data_dir</td><td class="ptype">str or Path</td><td>Directory containing <code>historic_installs.xlsx</code>.</td></tr>
</tbody>
</table>
<div class="returns-box">
<div class="returns-label">Returns</div>
<div><span class="returns-type">dict[int, float]</span> — time period to historic retirement quantity in FLOW_SCALE units (tonnes). Typical values: ~34–38 tonnes per period with current install base.</div>
</div>
</div>
</div>
<!-- use_phase_stock_constraints -->
<span class="anchor" id="use_phase"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">use_phase_stock_constraints</span><span class="fn-paren">(</span><span class="fn-param">model</span>, <span class="fn-param">retirement_rate</span><span class="fn-colon">=</span><span class="fn-default">0.02</span>, <span class="fn-param">initial_use_stock</span><span class="fn-colon">=</span><span class="fn-default">0.0</span>, <span class="fn-param">historic_retirements_by_t</span><span class="fn-colon">=</span><span class="fn-default">None</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Add stock balance constraints for the in-use magnet fleet. Outflows from the use phase (to EOL routes) are bounded by the sum of the simple rate-based retirement and Weibull-computed historic retirements. Stock is updated each period: stock[t] = stock[t−1] + inflow − rate_retirement.</p>
<div class="section-label">Parameters</div>
<table class="params-table"><thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model.</td></tr>
<tr><td class="pname">retirement_rate</td><td class="ptype">float</td><td>Annual fraction of in-use stock that retires. Default 0.02 (2%).</td></tr>
<tr><td class="pname">initial_use_stock</td><td class="ptype">float</td><td>Initial installed magnet stock at t=0 in FLOW_SCALE units.</td></tr>
<tr><td class="pname">historic_retirements_by_t</td><td class="ptype">dict[int, float] or None</td><td>Pre-computed Weibull retirements from <code>weibull_historic_retirement()</code>. If None, uses rate-based calculation only.</td></tr>
</tbody>
</table>
</div>
</div>
<!-- fix_eol_outflows_at_t0 -->
<span class="anchor" id="fix_eol_t0"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">fix_eol_outflows_at_t0</span><span class="fn-paren">(</span><span class="fn-param">model</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Fix all end-of-life outflows from the use phase at t=0 to zero. No retirements occur at the first period because there is no t−1 stock and Weibull retirements are zero for the initial period.</p>
<div class="section-label">Parameters</div>
<table class="params-table"><thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody><tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model.</td></tr></tbody>
</table>
</div>
</div>
<!-- _eol_lagged_constraints -->
<span class="anchor" id="eol_lagged"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">_eol_lagged_constraints</span><span class="fn-paren">(</span><span class="fn-param">model</span>, <span class="fn-param">recovery_rate</span>, <span class="fn-param">current_process</span>, <span class="fn-param">destination_process</span>, <span class="fn-param">input_output_map</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Generic lagged mass-balance constraint for an end-of-life recycling route. Links t−1 retirement outflows from the use phase to t outputs from the recycling process via recovery rates. This one-period lag represents the time required to process retired magnets. The five named EOL constraint functions below are wrappers that call this with route-specific arguments.</p>
<div class="section-label">Parameters</div>
<table class="params-table"><thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model.</td></tr>
<tr><td class="pname">recovery_rate</td><td class="ptype">dict</td><td>Mapping of <code>(t, src, src_loc, dst, dst_loc, mat)</code> to float recovery fraction.</td></tr>
<tr><td class="pname">current_process</td><td class="ptype">str</td><td>Name of the EOL recycling process (e.g. <code>'direct reuse'</code>).</td></tr>
<tr><td class="pname">destination_process</td><td class="ptype">str</td><td>Name of the downstream process receiving recovered material.</td></tr>
<tr><td class="pname">input_output_map</td><td class="ptype">dict</td><td>Maps each output material to its corresponding input material and recovery key. E.g. <code>{'hp_magnet': 'hp_magnet'}</code> or <code>{'hp_magnet': ALLOY}</code>.</td></tr>
</tbody>
</table>
</div>
</div>
<!-- direct_reuse / m2m / hydro / pyro / cryo -->
<span class="anchor" id="direct_reuse"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">direct_reuse_constraints</span><span class="fn-paren">(</span><span class="fn-param">model</span>, <span class="fn-param">recovery_rate</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Apply lagged EOL constraints for the <strong>direct reuse</strong> pathway. Retired hp_magnets flow directly back to <code>magnet_market_mix</code> (as hp_magnet) with a one-period lag.</p>
<div class="section-label">Parameters</div>
<table class="params-table"><thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>
<tr><td class="pname">model</td><td class="ptype">pyomo.environ.ConcreteModel</td><td>The BLEECAM Pyomo model.</td></tr>
<tr><td class="pname">recovery_rate</td><td class="ptype">dict</td><td>Keyed by <code>(t, src, src_loc, dst, dst_loc, mat)</code>.</td></tr>
</tbody>
</table>
</div>
</div>
<span class="anchor" id="m2m"></span>
<div class="func-entry">
<div class="func-signature">
<span class="fn-keyword">def </span><span class="fn-name">magnet_to_magnet_recycling_constraints</span><span class="fn-paren">(</span><span class="fn-param">model</span>, <span class="fn-param">recovery_rate</span><span class="fn-paren">)</span>
</div>
<div class="func-body">
<p class="func-summary">Apply lagged EOL constraints for the <strong>magnet-to-magnet recycling</strong> pathway. Similar to direct reuse but involves reprocessing; outputs hp_magnet back to the market mix node.</p>
<div class="section-label">Parameters</div>
<table class="params-table"><thead><tr><th>Name</th><th>Type</th><th>Description</th></tr></thead>
<tbody>