As a new generation of automated warehousing systems, 3D compact storage systems have been increasingly installed worldwide for handling inventory items in warehouses, distribution centres and manufacturing factories. Due to the problem complexity and system novelty, research investigating these systems, design models in particular, lags behind. This study, thus, addresses the design of 3D compact storage systems, where the I/O port is located at the lower mid-point of the storage rack, in attempting to assist practitioners in designing such systems that can achieve optimal performance while meeting system capacity requirements. In view of its importance in system design, we first derive the system expected travel time and subsequently optimise the three dimensions of the storage rack. We consider all the possible configurations of the three rack dimensions and develop closed form expressions for travel time derivation and rack dimension optimisation. We compare the result with an available design model, where the I/O port is located in the lower left-corner of the storage rack. The comparison shows that our model produces shorter system expected travel time, thus higher system throughput. We also elaborate several numerical examples to demonstrate how our model can be applied to design 3D compact storage systems in practice. Based on the numerical examples, we further provide several managerial implications, which are useful for practitioners to make suitable design decisions.