# A Scheduling Solution for Robotic Arm-Based Batching Systems with Multiple Conveyor Belts +
## 2 Related Work
### Solution Algorithms for Scheduling Robotic Arm-Based Batching Systems  
Multiple solution approaches have been proposed to solve and analyze various robotic batching systems. [PERSON] et al. [18] took a wider view of the system and analyzed the layout of the batching process, determining the size and number of batching machines, the flexibility of different setups, as well as introducing solution approaches. [PERSON] [24] proposed an algorithm to be used in an online bin covering problem representing a system that pushes the items into trays instead of picking-and-placing. Furthermore, the authors investigated and proposed algorithms for the semi-online problem. [PERSON] [25] investigated the application of condition-based maintenance strategies. A selection method was proposed to choose the most relevant parts of a machine. Among others, it is based on failure rate and downtime costs and consequences. [PERSON] [26] analyzed different types of batching machines, modeled the machines mathematically (including an online bin covering variant), and proposed solution strategies for each. Finally, the performance of the batching machines is compared with different types of problem features. Soft computing methods have been also proposed to tackle robotic batching problems. [PERSON] et al. [21] proposed a hybrid genetic algorithm for a more simple batching machine. The problem is formulated as a \(k\)-bounded semi-online bin covering problem, which is a frequent model for these types of problems. [PERSON] et al. [23] investigated a deep reinforcement learning approach in the decision process of a robotic batching system and showed promising results. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Study** & **Target System/Problem** & **Decision** &
\begin{tabular}{l} **Tray/Bin** \\ **Lane Number** \\ \end{tabular} \\ \hline
[20] & \
\begin{tabular}{l} Poultry processing plants \\ with batches \\ \end{tabular} &
\begin{tabular}{l} Which tray? \\ (with respect to weights) \\ \end{tabular} & 1 \\ \hline
[21] & \
\begin{tabular}{l} Bin covering with \\ a target weight for \\ a poultry processing plant \\ \end{tabular} &
\begin{tabular}{l} Which tray? \\ (with respect to weights) \\ \end{tabular} & 1 \\ \hline
[22] & \
\begin{tabular}{l} Packing in a conveyor-based \\ automatic sorting system \\ \end{tabular} &
\begin{tabular}{l} Which action? \\ - Do [stay, put, pick] \\ - For [current box, buffer] \\ \end{tabular} & 1 \\ \hline
[23] & \
\begin{tabular}{l} A robotic arm system \\ with multiple conveyor belts \\ \end{tabular} &
\begin{tabular}{l} Which tray? \\ (with respect to weights and \\ conveyor belt track) \\ \end{tabular} & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._ \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Study** & **Conveyor Belt Type** & **Buffer** & **Machine Type** \\ \hline
[17] & Two conveyor belts & Yes &
\begin{tabular}{l} Grader \\ (diverter) \\ \end{tabular} \\ \hline
[18] & 4 track line conveyor belt & Yes &
\begin{tabular}{l} Grader \\ \end{tabular} \\ \hline
[19] & 1 track line conveyor belt & Yes &
\begin{tabular}{l} Grader \\ \end{tabular} \\ \hline
[20] & 1 track line conveyor belt & Yes &
\begin{tabular}{l} Batcher \\ (drop) \\ \end{tabular} \\ \hline
[21] & 1 track line conveyor belt & Yes &
\begin{tabular}{l} Batcher \\ (drop) \\ \end{tabular} \\ \hline
[22] & \
\begin{tabular}{l} Unidirectional 1 track conveyor belt \\ A circular conveyor for boxes \\ \end{tabular} &
\begin{tabular}{l} Yes \\ (for unused product) \\ \end{tabular} & Robotic arm \\ \hline
[23] & 2 track line conveyor belt & Yes & Robotic arm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Related work for a robotic arm-based batching system (cont?). It should be noted that the robotic arm-based system addressed in [PERSON] et al. [23] has the same system setting as our target system. However, our study tackles the scheduling problem involved in the system by applying a deterministic approach as will be explained in the following sections.