## 1 Introduction
### Proposed Approach  
With this in mind, as our main contributions we present adapted formulations of well known dispatching approaches, specifically to make them better suited for a synchronous evaluation of dispatching decisions. For the validation of this approach, we present an agent-based simulation testbed and a modular DT, whose role it is to provide the interface between the target environment and the dispatching algorithm. We present an extensive experimental evaluation with a broad range of target application environments, from which we can draw more general insights about the performance of the methods, than would be possible with only a single target use case scenario (c.f., Figure 1). Based on the literature research, we select and adapt the MOD STTF method [20] for our experimental evaluation, both with reassignment feature (MOD STTF) and for comparison without (STTF). As stated before, methods found in the literature are typically designed around event-based triggers and proceed with an asynchronous evaluation of dispatching decisions. This does not translate well to continuous agent-based models or physical implementations with a fleet of AMR, where the specific events, designed around navigation constraints, are not available. Therefore, we introduce a timer-based mechanism to evaluate the dispatching decisions cyclicly in a synchronised fashion. We formulate the dispatching problem in terms of the Stable Marriage Problem (SMP), which yields \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Source** & **AMHS Type** & **Navigation Graph** & **Simulation Model** \\ \hline
[19] & AGV & unidirectional/bidirectional & DES \\
[20] & AGV & unidirectional/bidirectional & DES \\
[21] & AGV & unidirectional & DES \\
[22; 23] & OHT & unidirectional & ABM \\
[24] & OHT & unidirectional & DES \\
[15] & AGV & unidirectional & ABM \\
[6] & AGV & unidirectional/bidirectional & DES \\
[16] & AMR & unconstrained & unknown \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of previous evaluation setups regarding the modelled Automated Material Handling System (AMHS) (Automated Guided Vehicle, AGV; Overhead Hoist Transport, OHT; Autonomous Mobile Robot, AMR), its navigation constraints, and the employed simulation model (Discrete-Event Simulation, DES; Agent-Based Model, ABM). Figure 1: Dispatching method formulation and design of experimental evaluation. equivalent results to the original MOD STTF formulation, and the Linear Sum Assignment Problem, which performs a global optimisation according to the selected dispatching rule. The methods can then be implemented using the specific algorithms available to solve these problems. With our experimental evaluation we demonstrate the viability of the approach, which is the adaptation and application of the described methods to the domain of AMR-based AMHS, the presented modular simulation testbed, and the DT interface. We assess the performance of the approaches in a broad range of operation scenarios, i.e., the frequency and spatial distribution of transport requests, the fleet utilisation, and the size and structure of the environment. In order to achieve this, we use the following variations on the environment parameters. * The makespan is dominated by the travel time vs. processing duration,
* The vehicle utilisation is either high or low,
* Different degrees of complexity regarding agent navigation and spatial distribution of stations are considered. In our earlier work [25], we presented the testbed environment that includes an agent-based simulation and a digital twin. We will use this simulation environment for our experimental evaluation. The digital twin represents the backend for this simulation that encapsulates and provides access to its data and controls. Section 2 gives a brief literature overview and lays out the selected approaches for Task Allocation and Vehicle Dispatching. Section 3 provides the detailed description of the proposed digital twin concept and implementation.