CARMA — Marginal Abatement Cost for Intermodal Supply Chain Routing

Carbon compliance regime classification via parametric MILP

Paper: Marginal Abatement Cost as a Carbon Decision Signal in Intermodal Supply Chain Routing: A Parametric MILP Framework for Mode Shift, Allowance Purchase, and Regime Classification — Supply Chain Analytics (Elsevier, under review)

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Overview

CARMA answers the question prior routing models skip: should a logistics network shift modes or buy carbon allowances?

The framework applies RHS-parametric MILP to the carbon-budget constraint of an intermodal routing model. By solving the integer programme at sequential budget levels and differencing the results, it recovers a finite-difference marginal abatement cost (MAC) curve — bypassing LP-relaxation duals, which are structurally zero in mixed-integer mode-assignment models. Each (network, budget) point is then classified into one of five carbon-compliance regimes by comparing the network's MAC against an observable carbon price.

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Five-Regime Taxonomy

Regime	Condition	Decision
R1 — Mode shift preferred	λ̂ < 0.90π	Reconfigure logistics network
R2 — Parity	0.90π ≤ λ̂ ≤ 1.10π	Margin-neutral; decide on strategic grounds
R3 — Allowance purchase preferred	λ̂ > 1.10π	Buy ETS allowances
R4 — Co-benefit	Carbon constraint non-binding	No carbon instrument needed
R5 — Infeasible	No feasible modal assignment exists	Network redesign required

where λ̂(r) = [Z(r) − Z(r−Δr)] / [E(r−Δr) − E(r)] in €/kg CO₂e, and π is the observable carbon price.

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Key Results

Three Network Archetypes

Network	Type	Routes	Modes	Result at 65 €/t ETS
Salamanca	Rail-limited domestic	12	Truck / Rail	R3 — Allowance preferred (MAC 245–4,366 €/t, 3.8–67× ETS)
Iberian	Maritime-accessible	12	Truck / Rail / Ship	R4 — Co-benefit (77.1% emission cut, 55.7% cost saving)
Frankfurt	Hub-limited	14	Truck / Rail / Air	R4 → R3 → R5 (infeasible above 25% budget)

Within-Class Consistency (150 Generated Networks, 1,650 MILP Solves)

Family	At 20% budget	Median MAC (binding cases)
Rail-limited domestic (50 networks)	54% non-binding, 46% allowance-preferred, 0% shift-preferred	1,398 €/t (21× ETS)
Maritime-accessible (50 networks)	100% non-binding	—
Hub-limited (50 networks)	52% infeasible	—

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Method

Parametric MILP

For carbon reduction target r ∈ {0, 5, 10, …, 50}%:

min   Σ_{r,m} c_{rm} · x_{rm}
s.t.  Σ_{r,m} ef_{rm} · x_{rm} ≤ E₀ · (1 − r/100)
      Σ_m x_{rm} = 1   ∀r
      x_{rm} ∈ {0, 1}

LP-relaxation duals on the carbon-budget constraint equal zero in all 33 base-archetype solves (3 networks × 11 budget levels) — an expected consequence of the integer-programme value function being non-smooth.

Finite-Difference MAC

λ̂(r) = [Z(r) − Z(r−Δr)] / [E(r−Δr) − E(r)]     (€/kg CO₂e)
B*(r) = λ̂(r) × 1000                               (€/t CO₂e — for comparison with π)

The RHS-parametric MILP technique (Jenkins 1982) solves the integer programme at point values of the carbon-budget parameter and joins results across flat regions. The contribution is not the parametric MILP procedure itself but its application to the carbon-compliance decision: comparing B*(r) against π to classify the compliance regime.

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Quick Start

Installation

git clone https://github.com/sthangavel/CARMA-ALGORITHM.git
cd CARMA-ALGORITHM
pip install -r requirements.txt

Run Experiments

# Parametric MAC sweep — all three network archetypes
python experiments/parametric_abatement.py

# Budget step-size robustness (Δr = 2.5%, 5%, 10%)
python experiments/budget_step_robustness.py

# Parameter sensitivity sweep (cost rates, emission factors)
python experiments/parameter_sensitivity.py

# 150-network within-class consistency study
python experiments/generated_network_robustness.py

# Generate all paper figures
python experiments/generate_figure1.py   # Fig. 1 — framework pipeline
python experiments/generate_figures.py   # Fig. 2 — MAC curves, Fig. 3 — regime heatmaps

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Repository Structure

CARMA-ALGORITHM/
│
├── algorithm/
│   ├── optimization/
│   │   └── carbon_milp.py              — Parametric MILP solver (CarbonBudgetMILP)
│   └── utils/
│       └── metrics.py                  — Evaluation utilities
│
├── experiments/
│   ├── parametric_abatement.py         — Core MAC sweep (3 archetypes, 11 budget levels)
│   ├── budget_step_robustness.py       — Step-size sensitivity
│   ├── parameter_sensitivity.py        — Cost/emission factor sensitivity
│   ├── generated_network_robustness.py — 150-network within-class consistency
│   ├── generate_figure1.py             — Fig. 1: CARMA framework pipeline
│   └── generate_figures.py             — Fig. 2: MAC curves, Fig. 3: regime heatmaps
│
├── paper/
│   ├── CARMA_manuscript_v3.md          — Full manuscript (Supply Chain Analytics)
│   └── figures/
│       ├── fig1_carma_pipeline.png
│       ├── fig2_mac_curves.png
│       └── fig3_regime_heatmaps.png
│
├── config.py
└── requirements.txt

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Network Definitions

Emission Factors (kg CO₂e / tonne-km)

Mode	Factor	Source
Truck	0.0762	HBEFA 4.2 HDV Euro VI
Rail (Spain)	0.0285	Eurostat 2022 Spanish grid
Rail (Germany)	0.0570	Eurostat 2022 EU-27 average
Ship	0.0110	Eurostat 2022 short-sea
Air	0.6800	ICAO CORSIA 2022

Terminal Costs (€ per shipment, mode change from truck)

Mode	Terminal cost
Rail	€680
Ship	€750
Air	€350

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Dependencies

Package	Used for
pulp	MILP solver (CBC backend)
numpy	Numerical arrays
pandas	Result DataFrames
matplotlib	Figure generation

pip install pulp numpy pandas matplotlib

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License

MIT License — see LICENSE for details.