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arXiv · 2607.22675

A QUBO-Based Optimization Framework for ATM Cash Replenishment Scheduling

Riccardo Aiolfi·Giulia Montani·Valeria Zaffaroni·Luca Toffanetti·Davide Veronelli·Francesca Cibrario·Davide Caputo·Davide Corbelletto
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Abstract

The management of cash replenishment in Automated Teller Machine (ATM) networks requires scheduling recharges in order to minimize operational costs while maintaining high service levels and avoiding cash-outs, under uncertain and time-varying withdrawal demand. This work formulates the ATM cash replenishment problem through a Quadratic Unconstrained Binary Optimization (QUBO) model, which naturally captures nonlinear cost interactions, while incorporating operational constraints through penalty terms. The objective function combines fixed and variable replenishment costs with co-location discounts, as well as penalties for a late replenishment that could cause a service interruption. The resulting QUBO instances are solved using MegaQUBO, a GPU-accelerated QUBO solver. An empirical evaluation on a real dataset of 276 ATMs located in Italy, covering four representative months of 2022 (April, May, October, and November), benchmarks the proposed approach against a threshold-based operational policy. Results show consistent cost reductions of approximately 15%-18% while maintaining an excellent average service level (around 99.8%-99.9). Overall, the study demonstrates that QUBO-based optimization, coupled with GPU-based solving, can provide a practically deployable decision-support tool for large-scale ATM cash logistics.

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Riccardo Aiolfi, Giulia Montani, Valeria Zaffaroni, Luca Toffanetti, Davide Veronelli, Francesca Cibrario, Davide Caputo, Davide Corbelletto. 2026-07-10. A QUBO-Based Optimization Framework for ATM Cash Replenishment Scheduling. https://arxiv.org/abs/2607.22675

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