## 2 Materials and Methods  
This section, structured in four steps, outlines the process for developing a methodology aimed at improving production and service systems, specifically within the context of solid waste management. It begins with the identification of sector-specific needs and challenges, followed by the proposal of a general definition of DTs, along with architecture and framework. Subsequently, a replicable methodology for the implementation of DTs is presented, and finally, the approach is validated through a real-world case study. Step 1: Contextual Analysis and Problem Definition: Assessment of the waste management sector's context, identifying challenges related to efficiency and sustainability in organic waste management. This review included the analysis of data on waste generation, current practices, and limitations of conventional systems. Step 2: Definition and Design of the DTs Architecture and Framework: In this step, the conceptual and technical framework guiding the implementation of the DTs is established. This process involves defining the functional layers that structure the system and detailing how they interact to ensure an efficient flow of information. The proposed architecture is designed to enable bidirectional interaction between the physical system and its digital counterpart, integrating advanced capabilities for real-time monitoring, analysis, and optimization. The proposed definition of DTs is illustrated in Figure 1, which highlights the characteristics, levels of implementation, and the feedback flow between the physical and virtual systems. Figure 2 shows the modular three-layer architecture and the associated implementation framework, which structures the bidirectional interaction between the physical environment and the digital twin. Figure 1: Proposed definition. Figure 2: Proposed architecture and framework: (**a**) proposed architecture; (**b**) proposed framework. * Physical Environment: Hosts the system under study with sensors to capture data and actuators to execute actions based on processed information. * Cloud Services: Facilitate the storage, analysis, and management of data, ensuring bidirectional information transfer and enabling both batch and real-time processing. * Virtual Environment: Digitally replicates the physical system, allowing for simulations, predictive analysis, and the generation of services such as process optimization, predictive maintenance, and training. Step 3: Methodology Development: This step focuses on designing a structured methodology for implementing DTs in production and service systems, considering the identified needs and the characteristics of the target system. Technical and operational procedures are defined, including the selection of tools, integration strategies, and guidelines for evaluating system performance. The modular and adaptive approach ensures the methodology is customizable, providing scalability, efficiency, and interoperability across various industrial environments. Figure 3 presents the proposed methodology, divided into two main stages (contextual and propositional), each comprising structured phases to guide implementation. The proposed methodology consists of two sequential stages: the contextual stage defines the system's suitability for DT implementation by establishing objectives, KPIs, and technical requirements; the propositional stage involves the design, modeling, and integration of the DT based on those parameters, enabling decision support and performance evaluation. Step 4: Validation of the Developed Methodology: In this step, the designed methodology was implemented and validated through a quasi-experimental setup carried out at a rural composting facility located in Cajamarca, Colombia. The validation involved the deployment of low-cost temperature and humidity sensors, a cloud-based data processing layer, and a virtual simulation environment to assess real-time operational performance.