DOI 10.1007/s00170-003-1932-3 ORIGINAL ARTICLE Int J Adv Manuf Technol (2005) 25: 979–987 Zaki Sari · Can Saygin · Noureddine Ghouali Travel-time models for ﬂow-rack automated storage and retrieval systems Received: 25 February 2003 / Accepted: 27 August 2003 / Published online: 20 February 2004  Springer-Verlag London Limited 2004 Abstract In this paper, closed-form travel-time expressions for ﬂow-rack automated storage and retrieval systems are developed. The expressions, which are based on a continuous approach, are compared for accuracy, via simulation, with exact models which are based on a discrete approach. There is no signiﬁcant difference between the results ob- tained from the continuous-approach-based closed-form expres- sions and the ones from the discrete-approach-based exact so- lutions. The closed-form expressions are easy to calculate due to their simplistic forms, even without a computer, while the exact solutions are extremely complex. On the basis of compu- tation time, the proposed closed-form expressions are extremely practical when compared with the discrete-approach-based ex- pressions, which require extensive computation time. The closed-form travel-time expressions developed in this study can be used to (1) establish performance standards for ex- isting AS/RS, (2) evaluate throughput performance for ﬂow-rack AS/RS alternative design conﬁgurations, and (3) compare dif- ferent storage techniques for improved system performance. Due to their simplistic, yet accurate, deﬁnitions, the closed-form ex- pressions, as well as the results of this study, are applicable to industry. Keywords Automated storage and retrieval systems (AS/RS) · Flow-Rack AS/RS · Inventory management Notations b: shape factor T : normalization factor E( SC): single-cycle expected travel time Z. Sari · N. Ghouali Universit´ e de Tlemcen, Laboratoire d’Automatique de Tlemcen, B.P. 119, 13000 Tlemcen, Algeria C. Saygin (✉) University of Missouri – Rolla, Engineering Management Department, 1870 Miner Circle, Rolla, MO 65409, USA E-mail: saygin@umr.edu E( DC): dual-cycle expected travel time E( RC): expected retrieval time E(V ): expected travel time between two points on rack face L , H, D: length, height and depth of the ﬂow-rack AS/RS rack l, h , d: length, height and depth of each ﬂow-rack AS/RS stor- age segment M: number of segments in a bin (i.e., number of layers in rack) m: layer rank N l : number of bins in each row N h : number of bins in each column t h : horizontal travel time from the pickup/drop-off point to the farthest column t ′ h : horizontal travel time between two consecutive bins t v : vertical travel time from the pickup/drop-off point to the farthest row t ′ v : vertical travel time between two consecutive bins V h , V v : horizontal and vertical speeds of storage/retrieval ma- chine ρ: load rate (x, y): bin position (x, y) d : dwell-point position 1 Introduction Automated storage and retrieval systems (AS/RS) have been widely used not only as alternatives to traditional warehouses but also as part of advanced manufacturing systems [1]. Improved inventory management and control, increased storage capacity to meet long-range plans, quick response to locate/store/retrieve items, and reduced labor cost due to automation are among the major advantages provided by AS/RS [2, 3]. A typical AS/RS is composed of storage racks, storage/retrieval (S/R) machines and pickup/drop-off (P/D) stations. Several types of AS/RS are distinguished based on size and the volume of inventory items. These different types include unit-load, mini-load, man- on-board, deep-lane, automated item-retrieval system and ﬂow- rack systems.