# A Hybrid IVFF-AHP and Deep Reinforcement Learning Framework for an ATM Location and Routing Problem
## 1 Introduction
A real case study using the Nearest Neighbor-First Iterated Local Search-Second Algorithm (NN-ILS) and real-time traffic data was discussed, and it was proved that lower cost, operational risk, and environmental impact were achieved compared to classical methods [18]. [PERSON] et al. (2023) [19] addressed the cash transport risk-constrained routing problem with multiple depots for cash transport vehicles with two models aiming at economic and environmental optimization. In the first model, emission and total distance minimization were performed, while in the second model, goal programming was used to optimize the objectives the decision-maker set. While the first model focused on minimizing total distance and emissions by providing a dual-objective optimization framework, the second model aimed to find optimal solutions to decision-makers' objectives using a goal-programming approach. Two different algorithms, the Hybrid Genetic Algorithm (HGAI) and the Self-Constraining Hybrid Genetic Algorithm (SHGA), were proposed in the study. The accuracy of these models was tested with real-time traffic data. One of the most important contributions of the study was developing a dynamic route update strategy sensitive to traffic flow and creating routes that minimized risks [19; 20]. In this study, a two-stage approach is proposed for ATM location selection and routing optimization that primarily considers security risk. In the first [19; 20] stage, districts are evaluated based on safety risk, and the most suitable ATM location within high-risk areas is determined using a novel methodology that combines clustering with interval-valued Fermatean fuzzy AHP (IVFF-AHP). In the second stage, the CIT routing problem is addressed using Deep Reinforcement Learning (DRL), which enables adaptive and cost-effective route planning. This integrated framework offers a unique contribution by simultaneously addressing strategic location planning and operational logistics within a risk-aware structure. Accordingly, the study aims to answer the following research question: \"How can banks optimize the placement of ATMs and the routing of cash transfers to ensure the efficient and secure delivery of services?\". Although many previous studies have focused on ATM location selection using GIS, clustering, MCDM, or statistical methods, they have primarily emphasized accessibility, customer density, or profitability. In contrast, this study introduces a novel perspective by incorporating security risk as a core factor in location decisions and further combines this with operational routing optimization, creating an integrated and realistic approach that is largely absent in the existing literature. The proposed approach demonstrates innovative applicability by addressing both strategic planning (location selection) and operational execution (cash-in-transit routing) within a unified framework. This dual-focus design enhances the real-world relevance of the study, especially for banks seeking to optimize both placement and logistics under safety constraints. The main contributions of this paper are as follows:  
1. It introduces a two-stage hybrid framework that combines clustering and IVFF-AHP for ATM location selection that primarily considers security risk. 2. It is the first study to apply the IVFF-AHP method in this domain, offering improved handling of uncertainty in multi-criteria decision-making. 3. It integrates DRL into the ATM cash-routing problem--an approach not previously explored in the literature. 4. It provides a realistic solution structure that banks can implement in practice to enhance both efficiency and security in ATM operations. The remainder of the article is organized as follows: Section 2 includes the main and sub-criteria considered in ATM location selection. Section 3 presents the proposed methodology. Section 4 contains a real case study applying the proposed method. Section 5 summarizes the results of this study and presents its limitations. The last section presents the results of this study and future research directions.