The irregular strip packing problem (ISPP) is a combinatorial optimisation problem that has applicability in several industrial processes since it aims for the efficient use of material. Most of the techniques reported in the literature for solving the ISPP employ metaheuristics as they can cope with complex requirements that prevent the use of exact model formulations. This paper presents a biased random-key genetic algorithm (BRKGA) that uses the dotted board model to compute the fitnesses of candidate solutions aiming for the minimisation of the height of the large object. The algorithm allows the pieces to rotate in order to achieve better layouts. Computational experiments using instances from the literature were conducted to demonstrate the efficiency of the proposed method, with promising results.