# Motion Trajectory Prediction in Warehouse Management Systems: A Systematic Literature Review
## 5 Findings
### TSP-Based Methods  
In this subsection, publications will be presented, that treat the problem of trajectory prediction in a warehouse as a travelling salesman problem (TSP) in order picking scenario. A work that breaks out a bit from the array of methods about trajectory prediction is presented by [PERSON] et al. [76]. The paper accomplished several goals related to the problem of sequencing and routing order pickers in warehouse systems. First, they evaluated the use of reformulating and solving the problem as a classical TSP, which resulted in up to 47% average savings in routing distance using the LKH TSP heuristic. Second, they examined the potential usefulness of combining problem-specific solution concepts from dedicated heuristics with high-quality local search features. Finally, they investigated whether a subset of features can be used to generate high-quality solutions for routing warehouse order pickers, or whether it is necessary to use \"state-of-the-art\" local search heuristics. They explored an innovative approach of reformulating the problem as a classical Travelling Salesman Problem (TSP). Utilizing the Lin Kernighan Helsgaun (LKH) TSP heuristic, the team achieved impressive savings in routing distance. However, the has limitations in solely relying on construction heuristics. While the method can harness the unique aspects of the Steiner TSP, their singular search methods, like aisle by aisle, can limit the exploration of the full solution space. Local search operators like the 2 opt, however, could effectively expand the searched solution area, leading to superior solutions without significant computational time increases. Future work could delve into fine-tuning these hybrid heuristic methods and exploring their application to other logistics and routing challenges. An article that also presents a solution to the order picking problem as a TSP problem is presented by [PERSON] and [PERSON] [77]. In the paper, the authors mathematically try to prove that the construction of minimal subgraphs of the transition to collect products is able to be solved on a microcomputer in a minute. However, this solution was not tested for scalability and the warehouse was very small and simple because a mathematical simulation was used to validate the method. Innovation that has been introduced was an algorithm that is capable of solving the order picking problem using minimal subgraphs. However, limitations in the study arose due to its scope. The research was based on a simple and small warehouse, and the mathematical simulation used for validation didn't test the solution's scalability. Furthermore, while the method proved efficient for warehouses with crossovers only at the ends of aisles, the inclusion of additional crossovers within aisles introduced complications. These complexities increased the number of equivalence classes to consider, making the method potentially impractical for warehouses with more than two or three internal aisle crossovers. Looking ahead, future research could explore optimizing this algorithm for warehouses with multiple internal aisle crossovers and testing its practicality and scalability in more diverse and larger warehouse configurations. \begin{table}
\begin{tabular}{l l} \hline \hline
**Evaluation Method** & **Papers** \\ \hline Simulation & [PERSON] et al. [71] \\ \hline Laboratory testing & [PERSON] et al. [72] \\ \hline Real-world case & [PERSON] et al. [73] \\ \hline Benchmark & [PERSON] et al. [74] \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Summary of evaluation methods used in the papers on probabilistic methods. The research conducted by [PERSON] et al. [78] serves as a sanity check for the design of warehouse order picking optimization systems. Their work focuses on developing a system that enhances the efficiency of order picking processes for warehouse workers, with the basis rooted in a practical, real-world challenge. In the study, it came out that the layout of the warehouse had little effect on the paths of the workers.