Large Language Models (LLMs) are deep learning models designed to generate text based on textual input. Although researchers have been developing these models for more complex tasks such as code generation and general reasoning, few efforts have explored how LLMs can be applied to combinatorial problems. In this research, we investigate the potential of LLMs to solve the Travelling Salesman Problem (TSP). Utilizing GPT-3.5 Turbo, we conducted experiments employing various approaches, including zero-shot in-context learning, few-shot in-context learning, and chain-of-thoughts (CoT). Consequently, we fine-tuned GPT-3.5 Turbo to solve a specific problem size and tested it using a set of various instance sizes. The fine-tuned models demonstrated promising performance on problems identical in size to the training instances and generalized well to larger problems. Furthermore, to improve the performance of the fine-tuned model without incurring additional training costs, we adopted a self-ensemble approach to improve the quality of the solutions.

In the era of digital commerce, the surge in online shopping and the expectation for rapid delivery have placed unprecedented demands on warehouse operations. The traditional method of order fulfilment, where human order pickers traverse large storage areas to pick items, has become a bottleneck, consuming valuable time and resources. Robotic Mobile Fulfilment Systems (RMFS) offer a solution by using robots to transport storage racks directly to human-operated picking stations, eliminating the need for pickers to travel. This paper introduces'combi-stations'--a novel type of station that enables both item picking and replenishment, as opposed to traditional separate stations. We analyse the efficiency of combi-stations using queueing theory and demonstrate their potential to streamline warehouse operations. Our results suggest that combi-stations can reduce the number of robots required for stability and significantly reduce order turnover time, indicating a promising direction for future warehouse automation.

Robotic mobile fulfillment systems (RMFSs) are a new type of warehousing system, which has received more attention recently, due to increasing growth in the e-commerce sector. Instead of sending pickers to the inventory area to search for and pick the ordered items, robots carry shelves (called "pods") including ordered items from the inventory area to picking stations. In the picking stations, human pickers put ordered items into totes; then these items are transported by a conveyor to the packing stations. This type of warehousing system relieves the human pickers and improves the picking process. In this paper, we concentrate on decisions about the assignment of pods to stations and orders to stations to fulfill picking for each incoming customer's order. In previous research for an RMFS with multiple picking stations, these decisions are made sequentially. Instead, we present a new integrated model. To improve the system performance even more, we extend our model by splitting orders. This means parts of an order are allowed to be picked at different stations. To the best of the authors' knowledge, this is the first publication on split orders in an RMFS. We analyze different performance metrics, such as pile-on, pod-station visits, robot moving distance and order turn-over time. We compare the results of our models in different instances with the sequential method in our open-source simulation framework RAWSim-O.