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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 $\sim 2500$ 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.