基于二次无约束二进制优化的自动取款机现金补充调度优化框架
A QUBO-Based Optimization Framework for ATM Cash Replenishment Scheduling
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中文总结 AI 辅助
研究针对ATM现金补充调度问题，通过QUBO模型结合惩罚项制定问题，用MegaQUBO求解，在意大利276台ATM真实数据集上实证评估，相比阈值策略，能降本15%-18%且维持高服务水平，为ATM现金物流提供决策支持工具。
中文摘要 AI 辅助
自动取款机（ATM）网络中的现金补充管理需要进行充值调度，以便在不确定和时变取款需求下，在维持高服务水平并避免现金耗尽的同时，将运营成本降至最低。本文通过二次无约束二进制优化（QUBO）模型来制定ATM现金补充问题，该模型自然地捕捉非线性成本相互作用，并通过惩罚项纳入运营约束。目标函数将固定和可变补充成本与同地折扣相结合，以及对可能导致服务中断的延迟补充进行惩罚。使用GPU加速的QUBO求解器MegaQUBO来解决由此产生的QUBO实例。对位于意大利的276台自动取款机的真实数据集进行实证评估，涵盖2022年四个有代表性的月份（4月、5月、10月和11月），将所提出的方法与基于阈值的运营策略进行基准测试。结果表明，在保持出色的平均服务水平（约99.8%-99.9%）的同时，成本持续降低约15%-18%。总体而言，该研究表明，基于QUBO的优化与基于GPU的求解相结合，可以为大规模ATM现金物流提供一个实际可部署的决策支持工具。
英文摘要
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.
