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# aHead Research employs simulation techniques to build a digital twin of production, logistics and industrial processes

### A Digital Twin, according to aHead Research

Starting from a real process -a supply chain, a production line, operations inside a warehouse- we rewrite in logical-mathematical form all elements that compose and regulate it, obtaining a replica called Digital Twin. A digital twin is therefore a mathematical model of a process or system that reproduces the functioning of such in a virtual environment. Obtaining a digital twin that is faithful to the original requires several steps of modeling and tuning of the parameters, and a discrete event simulation framework in that allows us to capture the evolution over time of dynamic processes.

### Creating a Digital Twin

The first step in creating a digital twin of complex systems like a warehouse or an industrial process is writing a mathematical model that has the capacity of simulating the real process. It is important to identify the various components of the system, such as resources, flows, buffers, transport vehicles, and create secondary models describing their features. The process logic is then reproduced by linking the various secondary models following the principles of discrete-event simulation, therefore obtaining a unified model of the entire process. For each of the secondary models, we determine the optimal set of parameters to describe their behavior, so that they are truthful to their real counterparts. This process is made more complex by the fact that numerous parameters are intrinsically hard to define -i.e., the interval between two instances of malfunctioning of a processing machine. Through statistical analysis, we obtain the probability distribution for such parameters, thanks to a model able to replicate stochastic aspects of reality. We implement the mathematical process in code, usually Java- or Python-base, through specific stacks dedicated to the simulation of discrete events, so that the model is then ready to exploit the potential of Digital Twin simulations.

### Creating a Digital Twin

The first step in creating a digital twin of complex systems like a warehouse or an industrial process is writing a mathematical model that has the capacity of simulating the real process. It is important to identify the various components of the system, such as resources, flows, buffers, transport vehicles, and create secondary models describing their features. The process logic is then reproduced by linking the various secondary models following the principles of discrete-event simulation, therefore obtaining a unified model of the entire process. For each of the secondary models, we determine the optimal set of parameters to describe their behavior, so that they are truthful to their real counterparts. This process is made more complex by the fact that numerous parameters are intrinsically hard to define -i.e., the interval between two instances of malfunctioning of a processing machine. Through statistical analysis, we obtain the probability distribution for such parameters, thanks to a model able to replicate stochastic aspects of reality. We implement the mathematical process in code, usually Java- or Python-base, through specific stacks dedicated to the simulation of discrete events, so that the model is then ready to exploit the potential of Digital Twin simulations.

### Using simulation to improve the process

As the design and implementation of a digital twin are finished, we employ simulation to optimize production processes and improving one or more KPI formerly identified with the experts. In the virtual environment we can easily edit some components -different resource allocation, different working shifts different settings for the machinery, introduction of more efficient machinery, etc. – and measure the effects of such changes on the KPIs. With a digital twin, we are able to perform various what-if analysis at low costs and with no risks pro the real process, therefore avoiding both prohibitive costs and the risk of compromising the entire production chain. The execution of several replicas of what-if simulation allows for the evaluation of the robustness of the KPIs in response to uncertain events that may present themselves in a minimal fraction of the runs.

### Using simulation to improve the process

As the design and implementation of a digital twin are finished, we employ simulation to optimize production processes and improving one or more KPI formerly identified with the experts. In the virtual environment we can easily edit some components -different resource allocation, different working shifts different settings for the machinery, introduction of more efficient machinery, etc. – and measure the effects of such changes on the KPIs. With a digital twin, we are able to perform various what-if analysis at low costs and with no risks pro the real process, therefore avoiding both prohibitive costs and the risk of compromising the entire production chain. The execution of several replicas of what-if simulation allows for the evaluation of the robustness of the KPIs in response to uncertain events that may present themselves in a minimal fraction of the runs.

### Simulation to foresee the future

A digital twin allows us to simulate the future and, therefore, to forecast how the process will behave in the following minutes, hours, days or even weeks. Such vision makes it possible to anticipate potential problems and to guide the implementation of corrective solutions to prevent such issues. To perform such an exercise, however, we need to predict the behavior of how each of the external processes to our digital twin that interact with it. Inevitably, such a prediction comes with uncertainty, which we can reduce thanks to machine-learning techniques and the prediction of time series. In aHead Research, we are able to understand how uncertainty is to be dealt with during decision-making processes to reduce the associated risk. In such context, the AI algorithms based on stochastic optimization provide a perfect support to the decision-making processes in uncertain situations

### Simulation to foresee the future

A digital twin allows us to simulate the future and, therefore, to forecast how the process will behave in the following minutes, hours, days or even weeks. Such vision makes it possible to anticipate potential problems and to guide the implementation of corrective solutions to prevent such issues. To perform such an exercise, however, we need to predict the behavior of how each of the external processes to our digital twin that interact with it. Inevitably, such a prediction comes with uncertainty, which we can reduce thanks to machine-learning techniques and the prediction of time series. In aHead Research, we are able to understand how uncertainty is to be dealt with during decision-making processes to reduce the associated risk. In such context, the AI algorithms based on stochastic optimization provide a perfect support to the decision-making processes in uncertain situations.