Noisy intermediate-scale quantum (NISQ) hardware is almost universally incompatible with full-scale optimization problems of practical importance which can have many variables and unwieldy objective functions. As a consequence, there is a growing body of literature that tests quantum algorithms on miniaturized versions of problems that arise in an operations research setting. Rather than taking this approach, we investigate a problem of substantial commercial value, multi-truck vehicle routing for supply chain logistics, at the scale used by a corporation in their operations. Such a problem is too complex to be fully embedded on any near-term quantum hardware or simulator; we avoid confronting this challenge by taking a hybrid workflow approach: we iteratively assign routes for trucks by generating a new binary optimization problem instance one truck at a time. Each instance has $$\sim 2500$$ ∼ 2500 quadratic binary variables, putting it in a range that is feasible for NISQ quantum computing, especially quantum annealing hardware. We test our methods using simulated annealing and the D-Wave Hybrid solver as a place-holder in wait of quantum hardware developments. After feeding the vehicle routes suggested by these runs into a highly realistic classical supply chain simulation, we find excellent performance for the full supply chain. Our work gives a set of techniques that can be adopted in contexts beyond vehicle routing to apply NISQ devices in a hybrid fashion to large-scale problems of commercial interest.

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Problem instances of a size suitable for practical applications are not likely to be addressed during the noisy intermediate-scale quantum (NISQ) period with (almost) pure quantum algorithms. Hybrid classical-quantum algorithms have potential, however, to achieve good performance on much larger problem instances. One such hybrid algorithm on a problem of substantial importance: vehicle routing for supply chain logistics with multiple trucks and complex demand structure is investigated. Reinforcement learning with neural networks with embedded quantum circuits is used. In such neural networks, projecting high-dimensional feature vectors down to smaller vectors is necessary to accommodate restrictions on the number of qubits of NISQ hardware. However, a multi-head attention mechanism is used where, even in classical machine learning, such projections are natural and desirable. Data from the truck routing logistics of a company in the automotive sector is considered, and the methodology is applied by decomposing into small teams of trucks and results are found comparable to human truck assignment.

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