Assembly refers both to the process of combining parts to create a structure and to the product resulting therefrom. The complexity of this process increases with the number of pieces in the assembly. This paper presents the assembly planning system design (APSD) program, a computer program developed based on a matrix-based approach and the discrete artificial bee colony (DABC) algorithm, which determines the optimum assembly sequence among numerous feasible assembly sequences (FAS). Specifically, the assembly sequences of three-dimensional (3D) parts prepared in the computer-aided design (CAD) software AutoCAD are first coded using the matrix-based methodology and the resulting FAS are assessed and the optimum assembly sequence is selected according to the assembly time optimisation criterion using DABC. The results of comparison of the performance of the proposed method with other methods proposed in the literature verify its superiority in finding the sequence with the lowest overall time. Further, examination of the results of application of APSD to assemblies consisting of parts in different numbers and shapes shows that it can select the optimum sequence from among hundreds of FAS.