Applications › Routing, scheduling and assignment
Applications · Logistics & optimisation
Routing, scheduling and assignment
The classic combinatorial problems, at the scale where well-tuned classical heuristics begin to strain — and the formulation work that decides whether a quantum method can help.
The problem
Routing a fleet, scheduling a plant, assigning staff to shifts, packing a container: these are the same mathematics wearing different clothes, and they are the problems most often cited as early quantum applications. They are also the problems where classical methods are strongest, because sixty years of operations research has gone into them.
The interesting question is therefore not “can a quantum computer do this” — it can — but “at what problem size, constraint density and time budget does it become the better choice.” Answering that honestly requires doing the formulation work properly and benchmarking against a genuinely good classical baseline rather than a straw one.
QUBO and Ising formulation with careful penalty design; embedding onto the connectivity the hardware actually offers; probability-boosting techniques to improve the sampling distribution; and hybrid decomposition where the instance is larger than the device.
Strong. Commercial MILP solvers and mature metaheuristics handle industrial instances well. We benchmark against them rather than around them, and we report where they win.
Methods published; benchmarking in progress. The probability-boosting work is peer-reviewed. Domain-specific pilots are the natural next step and need an industrial partner.
Transport and distribution planning; production scheduling; workforce assignment; network design.
A real instance with real constraints — synthetic benchmarks systematically flatter quantum methods. An agreed classical baseline to compare against. Solver or hardware access appropriate to the instance size.
Evidence
- “Probability-boosting technique for combinatorial optimization.” PeerJ Computer Science 10:e2499 (2024). doi
- QUBO construction techniques developed in the cybersecurity work (see that page) are formulated so that they can be carried over to this domain.
- In preparation: a chained partial-sum formulation for knapsack QUBOs, which keeps the formulation exact while cutting the interaction density that decides whether an instance can be embedded on annealing hardware at all. What it does →
Talk to us about this
If you have an instance that your current solver takes too long on, that is exactly the conversation we want to have — including the outcome where we tell you to keep your solver.
Last updated 14 September 2026.