White Paper

Quantum Computing: the best ally for last mile optimisation

What is the optimal last-mile delivery path to guarantee a high level of service to the end user, while at the same time ensuring highly efficient logistics?

Quantum Computing: the best ally for last mile

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The logistics of complexity

Defining the optimal last-mile delivery path is a complex operation, one which over the past few years has been further complicated by an increasing number of often contradictory variables. On the one hand, traffic, balancing weekly work, the environmental impact and the protection of workers’ rights. On the other hand, the needs for flexibility, personalisation and the free delivery service requested by consumers.
Last-mile delivery models were, of course, further complicated by the pandemic. The restrictions imposed by the global situation have, in fact, led to an unprecedented explosion of online shopping, with e-commerce becoming the primary sales channel.


This shift has led to an enormous growth in volumes, the redefinition of delivery times (24/7/365) and processes, as well as to the expansion of the increasingly heterogeneous types, range and variety of goods marketed and sold.

Despite the increased number and complexity of variables however, most distribution partners continue to plan their itineraries without the support of an optimisation tool. Indeed, the management of courier routes is often based on the empirical experience of the individuals who, every morning, define the daily travel plan manually.

Optimise the last mile with Quantum Computing

Being able to count on computational speed and algorithmic flexibility capable of managing complex logistic processes therefore becomes a key requirement for operators in the sector. In this context, Quantum Computing can provide decisive support: the technology enables operators to overcome the limits of a good approximation, to achieve a modelling capability that is increasingly closer to the complexity of today’s scenario, and to close the gap towards the real-time optimisation of delivery routes.

Reply has taken full advantage of the potential offered by Quantum Computing, creating a Quantum-Inspired Algorithm for last-mile optimisation: Quadratic Unconstrained Binary Optimisation or QUBO.
The QUBO model has been designed to describe quadratic and binary variable combinatorial optimisation problems, and to be able to solve them efficiently through the quantum capability.

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Reply’s experimentation

The Reply team tested the optimisation performance through D-Wave’s python library, Qbsolv, using anonymised data from various customers. To compare the different solutions (Quantum Computing vs. non-Quantum Computing), various simulations were carried out, which clearly confirmed the superior performance of the quantum approach compared to the traditional one.

To offer customers a solution capable of automating and optimising the last mile with increasing efficiency, while ensuring quality and safety, the Reply team is working on defining a Quantum-Inspired algorithm prototype capable of running on traditional GPUs and thus addressing the key accessibility aspects associated with quantum hardware, in terms of costs.