Abstract: We propose a digitized version of the quantum annealing algorithm to solve logistic network design problems. Our algorithm employs improved heuristics for the selection of the parameters of the Hamiltonian encoding the problem. We also propose an evolution scheme which allows us to reach high fidelities with a circuit depth that grows linearly with the size of the problem I and the number of discretization steps nT on an ideal quantum computer, O(I,nT) = 2InT. We present an alternative evolution scheme based on digital-quantum computation, which can be implemented in a realistic quantum computer with a limited connectivity among qubits. We introduce the tools required to implement this algorithm in both digital and digital-analog paradigms. The results shows that our algorithm succeed in obtaining a high fidelity for a predictable selection of nT and total annealing times.