Every EAF heat starts with a scrap charging decision that will define the chemistry of the heat, the energy consumption of the melt, the tap-to-tap time, and the cost of the liquid steel produced — and most melt shops make that decision using a combination of experience, habit, and whatever grades happen to be available in the scrap yard that shift. The cost of a sub-optimal scrap mix decision is not catastrophic in any individual heat; it is chronic and compound across thousands of heats per year. A melt shop producing 800,000 tonnes per year that is paying $3.50 per tonne of liquid steel more than the mathematically optimal mix for its chemistry requirements and scrap inventory is leaving $2.8 million on the floor annually — without ever missing a chemistry specification or triggering a customer complaint. Book a session with the iFactory EAF optimization team to see how AI-driven mix planning closes that gap.
EAF Energy · Metallurgical Process Optimization
EAF Scrap Mix Optimization: Linear Programming, Residual Element Control, and Alternative Iron Unit Integration for Minimum-Cost Steel Chemistry
A process metallurgist's technical reference for EAF scrap mix optimization — covering grade taxonomy, linear programming objective functions and constraints, residual element strategy, DRI and HBI integration, and real-time mix planning connected to scrap yard inventory and market pricing.
$2–8
Per tonne of liquid steel saved by LP-optimized vs. manual mix selection on equivalent inventory
30–90 min
Manual scrap mix calculation time per heat in typical EAF operations without optimization software
Cu + Sn
The two residual elements that most consistently constrain scrap mix flexibility in flat-product EAF heats
15–25%
Energy penalty of DRI charge relative to equivalent scrap weight — quantified and optimizable
Chemistry Fundamentals
Why Scrap Mix Selection Is a Multi-Dimensional Constrained Optimization Problem
The scrap mix for an EAF heat must simultaneously satisfy four categories of constraint that frequently conflict with each other. Metallurgical constraints define the chemistry window the mix must achieve — carbon content for the refining reaction, phosphorus and sulfur limits for the final product, and residual element ceilings that cannot be exceeded because EAF has no primary refining capability to remove them. Physical constraints define what can be charged — bucket weights, basket sizes, crane capacity, and yard availability. Economic constraints define what should be charged — relative costs of available grades, energy penalties of alternative iron units, and opportunity costs of premium grades. And process constraints define how the heat will run — electrical energy delivery, oxygen lance practice, and tap-to-tap time targets. An experienced metallurgist holds all four constraint categories in working memory and selects a mix that satisfies most of them most of the time. A linear programming optimizer satisfies all of them simultaneously, every heat, and finds the minimum cost solution in the feasible region that human judgment rarely locates.
Metallurgical
C aim, P ≤ limit, S ≤ limit, Cu ≤ ceiling, Sn ≤ ceiling, Cr ≤ ceiling, Ni ≤ ceiling, Mo ≤ ceiling. The chemistry window the mix must hit — non-negotiable constraints.
Physical
Basket weight limits, crane lifts per basket, scrap density vs. furnace volume, tap weight target ± tolerance. The physical envelope within which the chemistry solution must fit.
Economic
$/t for each available scrap grade, energy cost per kWh, electrode consumption per tonne, oxygen cost, DRI premium vs. energy penalty. The objective function to minimise.
Process
Target tap-to-tap time, electrical energy delivery (kWh/t), oxygen balance for decarburisation, foamy slag practice constraints. Process window within which the economics are valid.
Scrap Grade Taxonomy
From Shredded to Prime: How Scrap Grades Map to Chemistry Variability and Cost
The scrap grade hierarchy is not simply a quality ranking — it is a map of chemistry variability, residual element risk, and cost premium. Understanding where each grade sits on all three dimensions simultaneously is the prerequisite for rational mix optimization. The table below covers the principal grades used in EAF operations from lowest to highest specification.
| Grade | Cu range (%) | Sn range (%) | Fe yield (%) | Typical cost premium | Primary application |
|---|---|---|---|---|---|
| Shredded (obsolete) | 0.20–0.45 | 0.010–0.030 | 95–97% | Base price | Long products, commodity billets |
| HMS 1&2 (heavy melt) | 0.08–0.20 | 0.005–0.015 | 96–98% | +$10–30/t | Long and flat products — general use |
| Turnings / borings | 0.05–0.15 | 0.003–0.010 | 88–93% | −$5–15/t (yield discount) | Mixed — density limitations at high % |
| Bundles (pressed) | 0.04–0.12 | 0.003–0.008 | 96–98% | +$15–35/t | Flat products, automotive-grade billets |
| No. 1 busheling | 0.02–0.08 | 0.002–0.006 | 97–99% | +$30–65/t | Cold-rolled, galvanised, exposed panel |
| Prompt industrial | 0.015–0.05 | 0.001–0.004 | 98–99% | +$40–80/t | AHSS, API, critical flat products |
| DRI / HBI | <0.005 | <0.001 | 88–94% met Fe | +$50–120/t (vs. shredded) | Dilution for residual management |
Residual Element Risk — Visualised
Copper and Tin Concentration by Scrap Grade — The Constraint Map That Drives Mix Logic
The heatmap below shows the typical Cu and Sn residual ranges across the principal scrap grades. The constraint ceiling for a cold-rolled flat product specification (Cu ≤ 0.08%, Sn ≤ 0.008%) is marked. Mix optimization must ensure the weighted average residual contribution from all grades stays below the ceiling — with margin for measurement uncertainty.
The constraint ceiling for cold-rolled flat products (Cu ≤ 0.08%, Sn ≤ 0.008%) means shredded scrap cannot exceed approximately 15–22% of the charge weight without breaching copper limits on most heats. This constraint is the primary driver of scrap grade premium costs for flat product EAF melt shops.
Linear Programming Framework
The Objective Function, Decision Variables, and Constraint Structure for EAF Mix Optimization
A linear programming model for EAF scrap mix optimization is structurally elegant: it finds the combination of available scrap grades that minimises total charge cost while satisfying all chemistry, physical, and process constraints. The model structure below is the basis for all commercial and in-house EAF charge optimization systems.
Objective Function — Minimise
Cost = Σ (xᵢ × pᵢ) + Σ (xⱼ × pⱼ × eⱼ)
Where xᵢ = tonnes of scrap grade i charged, pᵢ = $/t cost of grade i, xⱼ = tonnes of alternative iron unit j charged, pⱼ = $/t cost of unit j, and eⱼ = energy cost adjustment factor for unit j (DRI carries a +15–25% energy penalty relative to prime scrap). The objective is the total variable cost of the metallic charge per heat — the number the LP minimises subject to all constraints below.
Chemistry Constraints
Carbon aim
Σ (xᵢ × Cᵢ) / W ≥ C_aim
Total C in charge ÷ tap weight ≥ minimum carbon for refining reaction
Copper ceiling
Σ (xᵢ × Cuᵢ) / W ≤ Cu_max
Weighted Cu contribution ÷ tap weight ≤ specification ceiling minus safety margin
Tin ceiling
Σ (xᵢ × Snᵢ) / W ≤ Sn_max
Typically the binding constraint for flat products — tighter relative to available scrap composition than Cu
Phosphorus
Σ (xᵢ × Pᵢ) / W ≤ P_max
P is partially removed in EAF slag practice — the constraint must account for refining efficiency
Total metallic Fe
Σ (xᵢ × Feᵢ × yᵢ) = W_tap
Mass balance — yield-adjusted Fe from all sources must equal target tap weight
Cr, Ni, Mo ceilings
Σ (xᵢ × Elᵢ) / W ≤ El_max
Applicable for grade-critical heats — structural, API, or AHSS specifications
Physical and Inventory Constraints
Grade availability
xᵢ ≤ Inventory_available_i
Cannot charge more of any grade than is in the scrap yard at time of heat scheduling
Basket weight
Σ xᵢ_basket ≤ W_basket_max
Each basket is limited by crane SWL and furnace roof opening diameter
DRI/HBI fraction
x_DRI / W_total ≤ DRI_fraction_max
Maximum DRI fraction limited by tap-to-tap time impact and energy availability
Minimum grade fractions
xᵢ ≥ xᵢ_min (for some i)
Operational minimums for certain grades due to density requirements or fixed supply contracts
The LP optimal solution (★) uses less shredded and slightly more DRI than the typical manual selection — achieving the same tap weight and chemistry at lower total charge cost because the energy penalty of DRI is more than offset by the reduction in prime scrap required to maintain the Cu ceiling. This trade-off is invisible to manual calculation but immediately obvious to the LP solver.
Residual Element Strategy
Managing Cu, Sn, Cr, Ni, and Mo Across a Heat Campaign — Not Just a Single Heat
Residual element management is inherently a campaign-level problem, not a heat-level one. A single heat that pushes copper to 0.078% against a 0.080% ceiling is acceptable. Three consecutive heats at 0.077–0.079% while ladle analysis uncertainty is ±0.005% creates a statistical expectation of product exceeding specification. The mix optimizer must maintain a rolling residual budget across the shift or campaign, not simply check each heat in isolation.
Cu
Copper — The Primary Constraint
Not removable by any current EAF-BOF-ladle metallurgy route. Once in the melt, it stays. Copper accumulation in product recycle streams is a global secular trend — rising Cu in shredded scrap is structurally inevitable as the installed base of copper wiring and electronics reaches end-of-life. The optimal long-term strategy is dilution via prime scrap and DRI, combined with dedicated low-Cu heat families that maximise shredded usage when product specifications allow.
Strategy: Grade segmentation — route high-Cu heats to tolerant products; protect low-Cu campaigns with prime and DRI
Sn
Tin — The Hidden Binding Constraint
Tin is present at lower absolute concentrations than copper but has tighter specification limits in critical flat products (Sn ≤ 0.006–0.010%) and causes severe surface quality defects (hot shortness) at levels that would not raise concern for copper. Its co-distribution with copper in shredded scrap means the Sn constraint often becomes binding before the Cu constraint does in flat product heats. The Sn/Cu ratio in shredded scrap is relatively stable at approximately 0.055–0.075 — meaning the Cu constraint proxy is usually sufficient, but Sn must be tracked independently for high-specification products.
Strategy: Track Sn independently on AHSS, API, and exposed panel grades — do not rely on Cu proxy alone
Cr/Ni/Mo
Tramp Alloys — Grade-Specific Concerns
Chromium, nickel, and molybdenum enter the charge primarily through alloy steel scrap (turnings from machine shops, prompt scrap from automotive stamping of AHSS). They are beneficial — even required — in some product grades and harmful in others. A melt shop producing both commodity and structural grades must maintain scrap segmentation that routes alloy-bearing grades to heats where the alloy content is acceptable or specified, and protects commodity heats from alloy contamination. This is a yard management and logistics problem as much as a metallurgical one.
Strategy: Grade and yard segmentation with digital tagging — not solvable by LP alone without physical source control
Alternative Iron Units
DRI, HBI, and Pig Iron — When They Add Value and When They Cost More Than They Save
Alternative iron units (AIUs) are not simply premium-cost scrap substitutes. They serve a specific function: diluting residual elements from the scrap charge to reach chemistry specifications that the available scrap cannot achieve alone. The economic case for AIUs depends entirely on the premium of the AIU over the scrap it displaces, the value of the residual dilution it provides (what prime scrap would alternatively be required), and the energy penalty it carries relative to scrap.
| AIU Type | Residual content | Energy penalty | Typical cost vs. HMS | Optimal use case | Key limitation |
|---|---|---|---|---|---|
| DRI (direct reduced iron) | Cu <0.005%, essentially zero Sn | +15–25% kWh/t (gangue melting) | +$50–100/t | Diluting Cu/Sn when prime scrap premium exceeds DRI energy cost | Gangue oxide load (SiO₂, Al₂O₃) increases slag volume and refractory wear |
| HBI (hot briquetted iron) | Cu <0.005%, essentially zero Sn | +12–20% kWh/t | +$55–110/t | Same as DRI but better for continuous charging — higher density, less fines | Same gangue load as DRI; slightly lower reducibility than DRI pellets |
| Pig iron (blast furnace) | Near-zero Cu, Sn, Ni, Cr, Mo | −5 to +5% (high C aids EAF) | +$40–90/t | Carbon source for EAF refining AND residual dilution — dual function | Carbon management — high C input requires careful O₂ balance |
| Hot metal (from adjacent BOF) | Near-zero residuals | Negative — significant energy input | Variable — integration-specific | Integrated plants — residual dilution with energy benefit | Requires integrated plant logistics; not available in standalone EAF |
The AIU Economic Decision Rule
The break-even condition for substituting DRI for prime scrap is: DRI premium ($/t) + DRI energy penalty ($/t) ≤ prime scrap premium avoided ($/t). When prime scrap (No.1 busheling) is priced at $80/t above HMS and DRI is at $75/t above HMS with a $12/t energy penalty, the calculation is: DRI cost uplift = $75 + $12 = $87/t vs. prime scrap avoided = $80/t → DRI is $7/t more expensive than the alternative for equivalent Cu dilution effect. This calculation updates with every scrap price movement — which is why real-time pricing integration in the LP model is not optional for melt shops using significant AIU fractions.
Connect LP Optimization to Your Live Scrap Inventory and Pricing
iFactory's EAF Mix Optimizer Runs the LP Calculation Per Heat with Live Yard Inventory and Daily Scrap Prices
Most scrap mix optimization tools require manual data entry of prices and inventory before each calculation. iFactory connects directly to your scrap yard management system and market price feeds, running the LP optimization automatically at the start of each shift — delivering a ready-to-execute mix recommendation for every scheduled heat before the shift begins.
Real-Time Mix Planning
From Shift Plan to Heat-Level Execution — Five Steps That Close the Loop
01
Shift Scrap Inventory Snapshot
At shift start, the optimizer pulls a real-time inventory snapshot from the scrap yard management system — tonnes available by grade, location in yard, and confirmed incoming deliveries within the shift. This defines the feasible set of grades for the LP model. Any grade with zero inventory is automatically excluded from the solution space.
02
Heat Schedule and Chemistry Requirements
The production schedule for the shift — which steel grades are being produced, in what sequence, at what tap weights — defines the chemistry constraints for each heat. A shift producing both structural (high Cu tolerance) and cold-rolled (low Cu) heats requires different mix solutions for different positions in the schedule. The optimizer plans all heats simultaneously to manage total inventory depletion efficiently.
03
Live Scrap Price Integration
Daily scrap prices from the melt shop's procurement system or market price feed update the objective function coefficients in the LP model. When a grade's price changes — either from a new delivery at a different contract price or from a spot market purchase — the optimizer recalculates the optimal mix for remaining heats immediately. A $15/t increase in No.1 busheling may shift 3–5 heats to a higher DRI fraction if the DRI energy break-even condition is now satisfied.
04
Post-Tap Chemistry Feedback
After each heat, the actual tap chemistry is fed back into the optimizer. If copper is trending toward the ceiling (actual readings consistently in the top 20% of the specification window), the optimizer tightens the Cu constraint for subsequent heats using a dynamic safety margin — effectively building in an adaptive buffer that prevents specification exceedances under measurement uncertainty.
05
End-of-Shift Inventory Reconciliation
At shift end, actual consumption by grade is compared to the planned consumption. Variances — typically from basket weight variability or manual charge adjustments — are fed back into the opening inventory snapshot for the next shift. Over time, this feedback loop improves the accuracy of the yield factors used in the mass balance constraints, making the LP model progressively more accurate.
Melt Shop KPIs
Six Metrics That Quantify Scrap Mix Optimization Programme Value
Metallic Charge Cost per Tonne LS
Trend: decreasing
Total cost of all metallic charge materials (scrap, DRI, HBI, pig iron) divided by liquid steel tonnes produced. The primary economic output metric of mix optimization. Should be tracked against the theoretical minimum-cost solution for the same inventory and chemistry requirements — the gap between actual and theoretical minimum is the optimization opportunity.
Chemistry Aim Achievement Rate
Target: >97%
Percentage of heats where tap chemistry falls within specification for all residual elements. Below 95% indicates either the mix optimization is not constraining residuals correctly or the scrap grade chemistry data in the model does not reflect actual grade composition — both correctable with calibration.
Prime Scrap Utilisation Rate
Target: minimise subject to chemistry
Percentage of total metallic charge from premium-priced prime grades (No.1 busheling, prompt). The LP optimizer minimises this implicitly in the objective function. Tracking it separately allows the melt shop to assess whether chemistry relaxations in some product grades could allow a shift from prime to lower-cost grades, improving economics without product specification changes.
Residual Element Safety Margin
Target: 15–25% of ceiling
Average gap between actual tap chemistry residual and specification ceiling, expressed as a percentage of the ceiling. A margin consistently below 10% indicates the optimizer is running heats too close to the boundary — increasing specification exceedance risk. A margin consistently above 35% suggests prime scrap is being over-used when lower-cost alternatives could still deliver adequate margin.
AIU Break-Even Utilisation
Monitor vs. price spread
Percentage of heats where DRI or HBI was used, compared to the percentage where the price spread calculation justified its use. Tracks whether the melt shop is using AIUs economically or habituously — a common issue when DRI supply contracts obligate minimum consumption regardless of the prime scrap price differential.
Mix Calculation Lead Time
Target: <5 minutes per heat
Time from heat scheduling to delivery of a complete, LP-optimized mix recommendation to the scrap yard and furnace crew. Manual calculation averages 30 to 90 minutes. LP optimization with live data integration delivers in under 2 minutes. Reducing calculation lead time increases the planning horizon available for scrap yard logistics, reducing charging delays.
From the Melt Shop
“
The conversation about scrap mix optimization in EAF operations often gets framed as a technology question — do we implement LP software or not? But in my experience managing melt shops, the technology is the easier part. The hard part is the data quality underneath it. A linear program is only as good as the grade chemistry data you feed it. If your No.1 busheling is actually ranging from 0.025% to 0.085% copper and you are modelling it at a fixed 0.04%, your optimizer is solving for a ghost. The first thing I tell any melt shop starting an optimization programme is: invest in incoming scrap chemistry verification before you invest in the solver. Sample every grade on arrival, build grade-specific chemistry distributions, and update those distributions monthly. Once the data quality is there, the LP solution is remarkably powerful — I have seen metallic charge cost reductions of $4 to $9 per tonne of liquid steel from optimizer deployment in melt shops that already thought they were managing their scrap mix well. Those savings come entirely from the optimizer finding mix combinations that are mathematically superior but outside the experience range of the metallurgists who were making the decisions by hand.
Dr. Viktor Holubchenko
Process Metallurgist · EAF Melt Shop Technical Director · 28 years in EAF steelmaking across Eastern Europe, Turkey, and Southeast Asia · Former Chief Metallurgist, 2.4 Mt/year flat product EAF plant · Specialist in scrap mix optimization and residual element management
Melt Shop Technical Questions
EAF Scrap Mix Optimization — Frequently Asked
How accurately does LP optimization actually predict tap chemistry when scrap grade composition varies from heat to heat?
LP optimization predicts tap chemistry as accurately as the grade chemistry data input to the model — no more, no less. This is the central accuracy limitation of all charge optimization systems. Shredded scrap, which has the highest natural chemistry variability (Cu ranging 0.20–0.45% across different lots), produces the largest prediction error when modelled at a single representative value. The practical solution is probabilistic modelling: rather than a fixed chemistry for each grade, the optimizer uses the mean plus one standard deviation of each residual element — building in a safety margin that accounts for natural grade variability. iFactory's EAF mix optimizer uses grade chemistry distributions updated from incoming sample data, not static values, and tightens residual constraints automatically as the campaign progresses and actual readings reveal within-shift grade variability. For a detailed walkthrough of the grade chemistry calibration methodology, book a technical session with our EAF metallurgy team.
What is the practical maximum DRI fraction in an EAF heat, and what determines the limit?
The practical maximum DRI fraction in a conventional EAF heat (scrap basket charging followed by DRI continuous feed) is typically 30 to 40% of total metallic charge weight. The binding constraint at high DRI fractions is not metallurgical but electrical: DRI carries a gangue oxide load (SiO₂ and Al₂O₃ from the pellet binder and gangue) that requires additional kWh to reduce and melt, extending tap-to-tap time by 4 to 10 minutes at 30% DRI fraction versus an all-scrap heat. In a plant operating at maximum transformer capacity, this tap-to-tap extension reduces heats per day and offsets the residual dilution benefit economically. Plants with a dedicated DRI shaft furnace feeding the EAF can handle significantly higher DRI fractions (50–100%) because the DRI is preheated and charged hot, substantially reducing the electrical energy penalty. The LP model handles this constraint by including a tap-to-tap time term in the constraints — DRI fraction is limited such that the resulting heat duration remains within the target tap-to-tap window. iFactory's model uses plant-specific DRI energy and time coefficients calibrated from your actual heat data. Contact our support team for DRI integration specifications.
How does the optimizer handle a situation where the LP has no feasible solution — for example, when scrap inventory is insufficient to meet chemistry requirements?
An infeasible LP — where no combination of available grades simultaneously satisfies all constraints — is the most operationally important output of a well-configured optimizer, because it means the current inventory cannot produce the planned heat family without a chemistry risk or a scheduling change. When infeasibility is detected, iFactory's optimizer provides a ranked infeasibility diagnosis: which constraint is binding, by how much, and what the minimum corrective action would be. Typically the corrective options are: source additional AIU quantity to relax the residual ceiling, reschedule the heat to a later position in the campaign when a prime scrap delivery is expected, downgrade the product specification for that heat if the commercial and quality systems permit it, or accept a constrained feasible solution with a documented residual risk flag. The optimizer never silently selects an infeasible mix — it escalates the infeasibility to the shift metallurgist with a specific diagnosis before the scrap yard begins loading the basket.
How should we handle scrap grades with high chemistry uncertainty — lots where we do not have incoming test data?
Scrap lots without incoming test data should be assigned the worst-case chemistry from their grade's historical distribution rather than the mean — this is a conservative approach that slightly over-estimates charge cost for unknown lots but protects against specification exceedance. As soon as incoming test results are available (typically within 4 to 8 hours of delivery at most yards with NIR or spark OES analysis), the lot's chemistry is updated and the optimizer recalculates remaining heats using the actual data. Lots with persistently high chemistry uncertainty — certain obsolete scrap sources or merchant aggregators with poor grade control — should be assigned a more conservative distribution with a wider standard deviation to reflect the higher prediction risk. Over time, the grade chemistry database builds statistical confidence in each supply source, allowing the safety margin to be calibrated to the actual measurement uncertainty rather than a uniform conservative assumption. iFactory's grade chemistry module tracks per-supplier and per-delivery distributions separately, allowing the optimizer to distinguish between a reliable premium supplier's No.1 busheling and an unreliable source claiming the same grade.
Can LP scrap mix optimization work in a melt shop that does not have a digital scrap yard management system?
Yes — the LP model itself requires only four inputs per grade: tonnes available, cost per tonne, chemistry (or chemistry distribution), and density or volume characteristics for basket loading. These inputs can be manually entered at shift start if a digital scrap yard system is not available, and the LP calculation still runs in under 2 minutes. The operational value of LP optimization exists regardless of digital infrastructure — it is primarily a calculation tool, not a data integration tool. The additional value from digital integration (live inventory updates, automatic price feeds, post-tap chemistry feedback) amplifies the base value but is not a prerequisite. Most melt shops that begin LP optimization without a digital yard management system implement yard digitisation within 12 to 18 months because the optimizer reveals how much value is being lost to inventory visibility gaps. Book a session to discuss the implementation path that matches your current yard management maturity level.
Every Heat Is a Cost Optimization Problem. Most Melt Shops Are Solving It Manually.
LP-Optimized Scrap Mix Planning — Connected to Your Yard Inventory and Market Prices — Starts Here
iFactory's EAF mix optimizer connects linear programming scrap selection to your live scrap yard inventory, daily grade prices, production schedule, and post-tap chemistry feedback. The system delivers a fully optimized, constraint-verified mix recommendation for every heat before the shift begins — saving $2 to $8 per tonne of liquid steel across your annual production volume without changing your scrap supply relationships or product specifications.
