DB Schenker: Quantum Optimization for Air Freight Routing

The Challenge

Air freight routing is one of the most complex combinatorial optimization problems in logistics. DB Schenker operates a dense European hub network with dozens of origin-destination pairs, multiple aircraft types, strict weight and volume limits per flight, time-window constraints for perishable or priority cargo, and fuel cost functions that vary nonlinearly with aircraft load.

Classical solvers handle this through mixed-integer linear programming (MILP) and heuristic search, but solution quality degrades as network size grows. For a major hub like Frankfurt or Amsterdam, the planning window for overnight freight involves thousands of shipment units being assigned across hundreds of possible flight segments. Small inefficiencies compound across the network and show up directly in fuel burn and missed delivery windows.

DB Schenker’s logistics engineering team partnered with D-Wave to test whether quantum annealing could find better load assignments faster than MILP for the hardest subproblems in their air freight planning pipeline.

The Quantum Approach

The team reformulated the freight load assignment problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem. Each binary variable represents whether a specific shipment unit is assigned to a specific flight segment. The objective minimizes total fuel cost while penalizing constraint violations: weight limits, volume limits, and delivery deadline misses.

D-Wave Advantage’s hybrid solver was used rather than the pure quantum annealer, since real-world problem sizes exceed current native qubit counts. The hybrid workflow decomposes the full assignment problem into subproblems that fit on the annealer, solves them in parallel, and assembles the global solution classically.

import dimod
from dwave.system import LeapHybridSampler
from collections import defaultdict

# Shipments: list of (weight_kg, volume_m3, deadline_priority)
shipments = [
    {"id": 0, "weight": 320, "volume": 2.1, "priority": 1},
    {"id": 1, "weight": 150, "volume": 0.8, "priority": 2},
    {"id": 2, "weight": 480, "volume": 3.5, "priority": 1},
    {"id": 3, "weight": 210, "volume": 1.6, "priority": 3},
]

# Flights: list of (capacity_kg, capacity_m3, base_fuel_cost)
flights = [
    {"id": 0, "cap_kg": 600, "cap_m3": 5.0, "fuel_cost": 4200},
    {"id": 1, "cap_kg": 800, "cap_m3": 7.0, "fuel_cost": 5100},
]

n_s = len(shipments)
n_f = len(flights)
penalty = 5000.0

Q = defaultdict(float)

# Each shipment must be assigned to exactly one flight
for s in range(n_s):
    for f in range(n_f):
        var = f"x_{s}_{f}"
        Q[(var, var)] -= penalty
        for f2 in range(f + 1, n_f):
            var2 = f"x_{s}_{f2}"
            Q[(var, var2)] += 2 * penalty

# Penalize weight overload per flight
for f in range(n_f):
    cap = flights[f]["cap_kg"]
    for s in range(n_s):
        for s2 in range(s, n_s):
            w_s = shipments[s]["weight"]
            w_s2 = shipments[s2]["weight"]
            if w_s + w_s2 > cap:
                v1 = f"x_{s}_{f}"
                v2 = f"x_{s2}_{f}"
                Q[(v1, v2)] += penalty

# Minimize fuel cost scaled by load factor
for s in range(n_s):
    for f in range(n_f):
        var = f"x_{s}_{f}"
        load_fraction = shipments[s]["weight"] / flights[f]["cap_kg"]
        Q[(var, var)] += flights[f]["fuel_cost"] * (1 - load_fraction)

bqm = dimod.BinaryQuadraticModel.from_qubo(dict(Q))
sampler = LeapHybridSampler()
result = sampler.sample(bqm, time_limit=5)

best = result.first.sample
assignments = {
    (s, f): best.get(f"x_{s}_{f}", 0)
    for s in range(n_s) for f in range(n_f)
    if best.get(f"x_{s}_{f}", 0) == 1
}
print("Shipment-to-flight assignments:", assignments)

Results and Implications

Across a six-month evaluation covering DB Schenker’s European air freight network, the quantum-hybrid approach produced a 12% reduction in average fuel consumption per route compared to the incumbent MILP solver. Load factors improved by 8%, meaning aircraft flew closer to optimal capacity, reducing per-unit shipping costs.

The gains were largest on mid-density routes where the problem size fell into a sweet spot for the hybrid annealer. Very small problems were already solved near-optimally by classical methods; very large problems required more decomposition steps, eroding some advantage.

The project confirmed that quantum annealing is a viable near-term tool for logistics optimization when deployed as a hybrid component rather than a standalone solver. As D-Wave Advantage hardware scales and embedding quality improves, DB Schenker expects the solvable problem sizes to expand to cover full hub-scale planning without decomposition.