The problem of efficiently cutting smaller two-dimensional pieces from a larger surface is recurrent in several manufacturing settings. This problem belongs to the domain of cutting and packing (C&P) problems. This study approached a category of C&P problems called the minimum time cut path (MTCP) problem, which aims to identify a sequence of cutting and sliding movements for the head device to minimize manufacturing time. Both cutting and slide speeds (just moving the head) vary according to equipment, despite their relevance in real-world scenarios. This study applied the MTCP problem on the practical scope and presents two metaheuristics for tackling more significant instances that resemble real-world requirements. The experiments presented in this study utilized parameter values from typical laser cutting machines to assess the feasibility of the proposed methods compared to existing commercial software. The results show that metaheuristic-based solutions are competitive when addressing practical problems, achieving increased performance regarding the processing time for 94% of the instances.
