Comparative Analysis of Optimized GCD and Hybrid LLM-GCD Approaches for Retail Shelf Space Allocation

To solve the retail shelf space allocation problem, we need methods that find a good balance between speed and quality. This paper looks at two different methods: an optimized dynamic programming algorithm that uses greatest common divisor (GCD) reduction and a hybrid method that combines Large Language Model (LLM) categorization with parallel GCD optimization. When testing mixed product datasets with 20, 50, and 100 items, it is clear there is a trade-off between speed and optimality. The optimized GCD method finds the best solutions while using the available space, but it takes longer to compute (2.49 ms to 75.74 ms). The hybrid approach shows better computational efficiency (1.89 ms to 10.68 ms) by using smart product grouping and parallel processing, and it uses 91%–98.9% of the space. The hybrid method gives up 3%–9% of possible profit, but it cuts computation time by 78%–85%, which makes it good for real-time retail applications where speed is very important.