Performance Evaluation of Warehousing Units

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Performance Evaluation of Warehousing Units
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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

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An example applicationTravel-Time Models for
AS/RS(Y. Bozer and J. White, IIE Trans., pgs
329-338, 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

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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) ?_i1N t_oi
• E(DC) (2 / (N (N-1)))
• ?_i1N-1 ?_ji1N t_oi
  t_ij t_jo

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Bozer Whites approximating formulae
H
sv
L
sh
th L / sh tv H / sv
T maxth, tv b minth, tv/T
E(SC) (1/3)b21 E(DC) (4/3)
(1/2)b2-(1/30)b3
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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 852-866,
  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
  271-280, 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 273-281, 1991
• R. Foley, S. Hackman and B. C. Park, Back-of-the
  envelope miniload throughput bounds and
  approximations, working paper, ISyE, Georgia
  Tech, 2001