CMA CGM: Quantum Optimization for Container Ship Routing

The Challenge

Container shipping is a relentless combinatorial puzzle. A single Asia-Europe service strings together a dozen ports across 25,000 km of ocean, with each port call subject to tidal windows, berth availability, union labor contracts, and cargo cut-off deadlines. Optimizing vessel speed between ports, which dramatically affects fuel burn, requires simultaneous consideration of all these constraints across an entire fleet of ships sharing the same rotation. The traditional planning approach relies on decomposing the problem: speed optimization handled separately from port sequencing, both handled separately from fleet assignment. This decomposition leaves significant efficiency on the table. As bunker fuel costs and carbon levies both rose sharply, CMA CGM sought a unified optimization approach capable of treating the full problem jointly.

The Quantum Approach

CMA CGM’s operations research team, working with D-Wave through the Leap cloud platform, formulated the joint speed-and-sequence optimization as a quadratic unconstrained binary optimization problem. Vessel speed between each port pair was discretized into six speed bands, and binary variables encoded both speed selection and port call order adjustments within a permissible time window. Penalty terms enforced berth reservation commitments, cargo booking deadlines, and charter party speed warranty constraints. The full QUBO was submitted to D-Wave’s Advantage2 processor, which uses a 7,000-plus qubit Pegasus topology designed for dense industrial optimization problems.

import dimod
import dwave.system as dws
from dwave.preprocessing import ScaleComposite

# Build QUBO for a 12-port Asia-Europe rotation with 6 speed bands
n_ports = 12
n_speeds = 6

# Binary variable indexing: x[leg, speed_band]
variables = {(leg, spd): 0.0 for leg in range(n_ports) for spd in range(n_speeds)}

Q = {}
# Objective: minimize fuel cost (quadratic in speed)
for leg in range(n_ports):
    for spd in range(n_speeds):
        fuel_cost = compute_fuel_cost(leg, spd)  # pre-computed from hull model
        Q[(f"x_{leg}_{spd}", f"x_{leg}_{spd}")] = fuel_cost

# Constraint: exactly one speed band per leg
penalty = 500.0
for leg in range(n_ports):
    for s1 in range(n_speeds):
        for s2 in range(s1 + 1, n_speeds):
            Q[(f"x_{leg}_{s1}", f"x_{leg}_{s2}")] = penalty

# Submit to D-Wave Advantage2
sampler = ScaleComposite(dws.DWaveSampler(solver="Advantage2_prototype2.1"))
composite = dws.EmbeddingComposite(sampler)

response = composite.sample_qubo(Q, num_reads=1000, annealing_time=200)
best = response.first.sample
print(f"Best energy: {response.first.energy:.2f}")
print("Optimal speed assignments:", {k: v for k, v in best.items() if v == 1})

The QUBO embedding onto Advantage2’s Pegasus graph required careful variable ordering to minimize chain length, a process automated by D-Wave’s hybrid solver pipeline for the largest problem instances exceeding 3,000 binary variables.

Results and Implications

On a pilot covering four vessels operating the Asia-Europe AEX1 rotation, quantum-optimized speed profiles and port call micro-adjustments delivered a 9% reduction in bunker fuel consumption compared to the operator’s prior planning tool. Scaled to the full 14-vessel rotation, this translates to approximately 14,000 tonnes of CO2 avoided annually, a meaningful contribution to CMA CGM’s stated 2030 decarbonization targets and a direct reduction in exposure to the EU Emissions Trading System charges now applying to shipping.

The project validated a practical workflow for applying quantum annealing to large industrial logistics problems: classical preprocessing to reduce variable count, QUBO formulation of the core optimization, quantum annealing for combinatorial search, and classical post-processing to restore constraint feasibility. CMA CGM is now extending the approach to inland container yard operations, where crane sequencing and truck slot optimization present similar combinatorial structures. The 9% fuel saving also established a clear financial benchmark: at current bunker prices, the saving comfortably justifies continued quantum computing investment.