Performance Evaluation of Warehousing Units

Some general remarks In general, a difficult problem due the –large number of operational issues that must be introduced in the model –stochastic nature of the system operations –unique aspects of the various environments –etc. Therefore, simulation is the most extensively used tool Analytical models exist mainly for some automated modules, because –they present some better defined structure and behavior (therefore, easier to justify the modeling assumptions) –the need for good performance estimates for these modules is more critical, due to their high investment cost and inflexibility to modifications –modeling and analyzing automated (production) systems is a prevailing trend in the scientific community

An example application: “Travel-Time Models for AS/RS” (Y. Bozer and J. White, IIE Trans., pgs , 1984) Modeling assumptions: The S/R machine operates either on a single or a dual command basis. The S/R machine travels simultaneously in the horizontal and vertical directions with constant velocities. Pick-up and deposit times associated with load handling can be ignored. In general, this is a deterministic component of the overall cycle time which can be added to it at the end, if it is deemed significant. Randomized storage is used; thus, any location in the pick face is equally likely to be selected for storage or retrieval. Quantities to be evaluated: Expected cycle time and throughput, under SC and DC operation

A “brute force” calculation Assuming that: the total number of storage locations is N one-way travel time from I/O point to location i is t_oi = t_io one-way travel time between locations i and j is t_ij = t_ji we have: E(SC) = (2/N) *  _{i=1}^N t_oi E(DC) = (2 / (N * (N-1))) * *  _{i=1}^{N-1}  _{j=i+1}^N [t_oi+ t_ij + t_jo]

Bozer & White’s approximating formulae L H shsh svsv t h = L / s h t v = H / s v T = max{t h, t v } b = min{t h, t v }/T E(SC) = (1/3)b^2+1 E(DC) = (4/3) + (1/2)b^2-(1/30)b^3

Some interesting follow-up works Y. Bozer and J. White, “Design and Performance Models for End-of-Aisle order picking systems” Management Science, Vol. 36, No. 7, pgs , 1990 Y. Bozer and J. White, “A generalized design and performance analysis model for end-of-aisle order-picking systems”, IIE Trans., Vol. 28, pgs , 1996 R. Foley and E. Frazelle, “Analytical results for miniload throughput and the distribution of dual command travel time”, IIE Trans., Vol. 23, No. 3, pgs , 1991 R. Foley, S. Hackman and B. C. Park, “Back-of-the envelope miniload throughput bounds and approximations”, working paper, ISyE, Georgia Tech, 2001