Optimal dimensions minimizing expected travel time of a single machine flow rack AS/RS

In this paper, the aim is to determine the optimal dimensions of a flow rack automated storage and retrieval system (AS/RS) using a single machine for storage and retrieval operations. These optimal dimensions are evaluated for minimum expected travel times of the storage and retrieval machine. An enumeration technique is used on a large range of system configurations going from 100 to 20,000 storage segments. Initially, optimization is carried out on six travel time expressions dealing with single and dual cycle travel times considering two dwell point positions. The results are then studied to investigate the influence of travel time expressions on both optimal dimensions and the shape factor of the system rack. Secondly, a new generalized mathematical model was developed by introducing an occurrence proportion parameter, relative to dual cycles, in order to determine the influence of the system functioning (proportion of dual cycles and load rate) on optimal dimensions.