The buffer allocation problem in production lines is an NP-hard combinatorial optimisation prob-lem. This paper proposes a new hybrid optimisation approach (using simulation) relying on geneticalgorithm (GA) and finite perturbation analysis (FPA). Unlike the infinitesimal perturbation analy-sis, which deals with small (infinitesimal variation) perturbations for estimating gradients of theperformance measure, FPA deals with larger (finite) or more lasting perturbations. It is an exten-sion specifically dedicated to discrete decision variables and applicable to most discrete-eventdynamic systems. The proposed method allows a global search using GA, with refinement in spe-cific solution-space regions using FPA. The main objective is to maximise the average productionrate of a production line with unreliable machines, by allocating the total buffer capacity in locationsbetween machines. Extensive numerical experiments show that: (1) the proposed hybrid GA-FPAmethod clearly outperforms the state-of-the-art methods from the literature; (2) combining FPA andGA is beneficial when compared to employing GA or FPA independent