Abstract
In this work we develop methods to optimize an industrially-relevant logistics problem using quantum computing. We consider the scenario of partially filled trucks transporting shipments between a network of hubs. By selecting alternative routes for some shipment paths, we optimize the trade-off between merging partially filled trucks using fewer trucks in total and the increase in distance associated with shipment rerouting. The goal of the optimization is thus to minimize the total distance travelled for all trucks transporting shipments. The problem instances and techniques used to model the optimization are drawn from real-world data describing an existing shipment network in Europe. We show how to construct this optimization problem as a quadratic unconstrained binary optimization (QUBO) problem. We then solve these QUBOs using classical and hybrid quantum-classical algorithms, and explore the viability of these algorithms for this logistics problem.
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Notes
- 1.
Simply increasing the bin capacity may worsen the situation. For instance, suppose that \(v(s) = c_\mathrm {vol} / 2\) for each shipment s so that \(b(s) = \left\lceil c_\mathrm {bin} / 2 \right\rceil \) . If \(c_\mathrm {bin} = 2\), then \(b(s) = 1\) so that we can put two shipments into a truck. But if \(c_\mathrm {bin} = 3\), then \(b(s) = 2\) so that we can put only one shipment into a truck.
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A Solver Parameters
A Solver Parameters
Here we present the time allocated to each solver in Table 2, and the corresponding parameters in Table 3. For the D-Wave HSS, we limit the 30 and 50 shipment instances to only 5 minutes of run-time. We note that these 5 minutes were sufficient for the problems tested. Because we could not control the usage of the QPU in the D-Wave HSS, we report the QPU run-time in the timing results rather than a parameter. All software solvers were executed using single-threaded programs.
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Yarkoni, S. et al. (2021). Solving the Shipment Rerouting Problem with Quantum Optimization Techniques. In: Mes, M., Lalla-Ruiz, E., Voß, S. (eds) Computational Logistics. ICCL 2021. Lecture Notes in Computer Science(), vol 13004. Springer, Cham. https://doi.org/10.1007/978-3-030-87672-2_33
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