  We propose a brand-new formulation of capacitated vehicle routing problem
(CVRP) as quadratic unconstrained binary optimization (QUBO). The formulated
CVRP is equipped with time-table which describes time-evolution of each
vehicle. Therefore, various constraints associated with time are successfully
realized. With a similar method, constraints of capacities are also introduced,
where capacitated quantities are allowed to increase and decrease according to
the cities which vehicles arrive. As a bonus of capacity-qubits, one also
obtains a description of state, which allows us to set a variety of traveling
rules, depending on each state of vehicles. As a consistency check, the
proposed QUBO formulation is also evaluated by quantum annealing with D-Wave
2000Q.
