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A Survey on ASRS

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European Journal of Operational Research 194 (2009) 343–362

Invited Review

A survey of literature on automated storage and retrieval systems
Kees Jan Roodbergen a,*, Iris F.A. Vis b,1

RSM Erasmus University, P.O. box 1738, 3000 DR Rotterdam, The Netherlands
VU University Amsterdam, Faculty of Economics and Business Administration, De Boelelaan 1105, Room 3A-31,
1081 HV Amsterdam, The Netherlands

Received 27 June 2006; accepted 22 January 2008
Available online 5 February 2008

Automated Storage and Retrieval Systems (AS/RSs) are warehousing systems that are used for the storage and retrieval of products
in both distribution and production environments. This paper provides an overview of literature from the past 30 years. A comprehensive
explanation of the current state of the art in AS/RS design is provided for a range of issues such as system configuration, travel time
estimation, storage assignment, dwell-point location, and request sequencing. The majority of the reviewed models and solution methods
are applicable to static scheduling and design problems only. Requirements for AS/RSs are, however, increasingly of a more dynamic
nature for which new models will need to be developed to overcome large computation times and finite planning horizons, and to
improve system performance. Several other avenues for future research in the design and control of AS/RSs are also specified.
Ó 2008 Elsevier B.V. All rights reserved.
Keywords: Logistics; Automated Storage and Retrieval Systems; Warehouse; System design; Control policies

1. Introduction
Automated storage and retrieval systems have been
widely used in distribution and production environments
since their introduction in the 1950s. An automated storage
and retrieval system (AS/RS) usually consists of racks
served by cranes running through aisles between the racks.
An AS/RS is capable of handling pallets without the interference of an operator, thus the system is fully automated.
Both in production and distribution environments AS/RSs
are used for putting products (e.g., raw materials or (semi-)
finished products) in storage and for retrieving those products from storage to fulfill an order. Between 1994 and
2004, there has been a significant increase in the number
of AS/RSs used in distribution environments in the United
States (Automated Storage Retrieval Systems Production
Section of the Material Handling Industry of America,

Corresponding author. Tel.: +31 10 4088723; fax: +31 10 4089014.
E-mail addresses: [email protected] (K.J. Roodbergen),
[email protected] (I.F.A. Vis).
Tel.: +31 20 5986067; fax: +31 20 5986005.
0377-2217/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved.

2005). The usage of AS/RSs has several advantages over
non-automated systems. Examples are savings in labour
costs and floor space, increased reliability and reduced
error rates. Apparent disadvantages are high investments
costs (approximately $634,000 for a single aisle AS/RS,
Zollinger, 1999), less flexibility and higher investments in
control systems (about $103,000, Zollinger, 1999).
In designing an AS/RS, many physical design and control issues have to be addressed in the right way to fully
take advantage of all its pros. This paper intends to present
a critical overview of all important issues concerning AS/
RS design and control in both production and distribution
environments while studying recent and past literature.
Previously, several overview papers have been published
that discuss part of the AS/RS literature. Almost all of
these overview papers, however, have a focus different from
AS/RSs, for example, general warehouse design. Because
of this, only a limited number of aspects of AS/RSs and
a limited number of references with respect to AS/RSs
are presented in those papers. Matson and White (1982)
review a number of material handling research areas one
of which is concerned with AS/RSs. Kusiak (1985)


K.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362

describes design and operational decision problems for
flexible manufacturing systems with a focus on automated
guided vehicles and AS/RSs. The author discusses design,
storage and batching (i.e., consolidation of orders) policies
for AS/RSs. Johnson and Brandeau (1996) discuss stochastic models for the design and control of automated guided
vehicles and AS/RSs. Manda and Palekar (1997) discuss
some papers on travel time estimation for AS/RSs and
storage assignment rules.
General overviews of warehouse design and control
include Cormier and Gunn (1992), Van den Berg
(1999),Rouwenhorst et al. (2000), De Koster et al. (2007)
and Gu et al. (2007). Due to their broad scope, these five
papers only discuss a fraction of the AS/RS issues and literature. To our knowledge, Sarker and Babu (1995) is the
only paper discussing exclusively AS/RSs, however, this
paper only reviews some design aspects of AS/RSs while
focussing on travel time models. We conclude that our
paper seems to be the first overview paper in over 10 years
devoted exclusively to AS/RSs, and the first ever to give a
broad overview of all design and control issues in AS/RSs.
The main structure of the paper can be described as follows. First, we present a general description of AS/RSs and
a classification of related design and control issues. The
main body of the paper consists of an overview of literature
discussing solution methods for these design and control
problems. At the end, we indicate relevant open research
questions. In more detail, Section 2 defines various types
of AS/RSs and describes some important technical characteristics. Section 3 presents a classification of both physical
design and control issues. This broad introduction will be
followed in Section 4 by a more detailed description of
methods that support each of the discussed physical design
issues. Papers addressing individual control policies for
storage assignment (Section 5), batching (Section 6), parking of idle AS/RSs (Section 7) and sequencing (Section 8)
will be discussed in subsequent sections. Travel time estimates and other performance measures will be treated in
Section 9. Section 10 presents conclusions and issues for
further research.
2. AS/RS types
An AS/RS system is defined as a storage system that
uses fixed-path storage and retrieval machines running on
one or more rails between fixed arrays of storage racks
(Automated Storage Retrieval Systems Production Section
of the Material Handling Industry of America (2005)). AS/
RSs are used to store and retrieve loads in various settings.
The main components of an AS/RS are racks, cranes,
aisles, I/O-points, and pick positions. Racks are typically
metal structures with locations that can accommodate
loads (e.g., pallets) that need to be stored. Cranes are the
fully automated storage and retrieval machines that can
autonomously move, pick up and drop off loads. Aisles
are formed by the empty spaces between the racks, where
the cranes can move. An input/output point (I/O-point) is

a location where retrieved loads are dropped off, and where
incoming loads are picked up for storage. Pick positions (if
any) are places where people are working to remove individual items from a retrieved load before the load is sent
back into the system.
A large number of system options exist for AS/RSs. The
most basic version of an AS/RS has in each aisle one crane,
which cannot leave its designated aisle (aisle-captive) and
which can transport only one unit-load at a time (single
shuttle). Product handling in this case is by unit-load
(e.g., full pallet quantities) only; no people are involved
to handle individual products. The racks in the basic version are stationary and single-deep, which means that every
load is directly accessible by the crane. This AS/RS type is
referred to as a single unit-load aisle-captive AS/RS.
Numerous variations exist of this basic AS/RS. An overview of the main options is presented in Fig. 1. We will
briefly discuss some of the options below.
One possible variation of the basic AS/RS is when
cranes are capable of changing aisles. In this case, it is possible to have fewer cranes than aisles in the system. This
may be useful if the amount of requests does not justify
the purchase of a crane for each aisle. To overcome the
restriction of the crane’s unit-load capacity, multi-shuttle
cranes exist. Such a crane can transport two or more loads
at a time. Cranes which can transport two loads are also
referred to as dual-shuttle cranes; cranes capable of transporting more than two loads are still rarely seen. The
increased transport capacity enables a crane, for example,
to first retrieve one load and then store another load in
the same location without having to go to the I/O-point
in between.
Often an AS/RS is installed for handling unit-loads only
(typically, pallets). Unit-loads arrive at the I/O-point of the
AS/RS from other parts of the warehouse by means of, for
example, automated guided vehicles, conveyors, or forklift
trucks. The unit-loads are stored in the AS/RS and after a
period of time they are retrieved again, for example, to be
shipped to a customer. In many cases, however, only part
of the unit-load may be needed to fulfill a customer’s order.
This can be resolved by having a separate picking area in
the warehouse; in which case the AS/RS serves to replenish
the picking area. Alternatively, the picking operation can
be integrated with the AS/RS. One option is to design
the crane such that a person can ride along (person-onboard). Instead of retrieving a full pallet automatically
from the location, the person can pick one item from the
location. A more common option to integrate item picking
is when the AS/RS drops off the retrieved unit loads at a
workstation. A picker at this workstation takes the
required amount of products from the unit-load after
which the AS/RS moves the remainder of the load back
into the storage rack. This system is often referred to as
an end-of-aisle system. If the unit-loads are bins, then the
system is generally called a miniload AS/RS.
Storage in the racks may occur single or double deep. In
a double-deep rack, each rack location has space for two

K.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362










Stationary racks







Movable racks


Mobile racks
(on rails)


Unit load


Rotating racks






Fig. 1. Classification of various AS/RS system options.

unit-loads; one load is stored in front of the other load. A
load can only be put into or retrieved from the second position if there is no load in the first position. Double-deep
storage might be beneficial if the variety of loads is relatively low and the turnover rate of these loads is high
(Tompkins et al., 2003). Modifications to the crane may
be required to be able to store and retrieve loads from both
positions. Carousel systems (horizontal or vertical, single or
double) are suitable for storing small and medium-sized
products at different levels. A crane is used to store and
retrieve items from the rotating carousel. The lower and
upper part of a double carousel can rotate independently
of each other.
Finally, worthy of mentioning is a special type of AS/
RSs called autonomous vehicle storage and retrieval systems.
This system separates horizontal and vertical travel. Vehicles travel horizontally over rails through aisles, while lifts
are used to transfer loads vertically.

AS/RS Design
Physical Design


Performance measurement



Dwell point

3. Overview of design decisions
It is crucial to design an AS/RS in such a way that it can
efficiently handle current and future demand requirements
while avoiding bottlenecks and overcapacity. Due to the
inflexibility of the physical layout and the equipment, it is
essential to design it right at once. In Fig. 2 a schematic
view of design issues and their interdependence is
It is important to realise that the AS/RS is usually just
one of many systems to be found in a warehouse. The true
performance of the AS/RS is typically influenced by the
other systems as are the other systems’ performances
influenced by the AS/RS. This is most visible at, but not
restricted to, the interplay of systems at the AS/RS’
I/O-points. Loads are picked up and dropped off at an
I/O-point by the AS/RS. It is the task of, for example, a
conveyor system or a set of vehicles to make the connection

Design of other material handling
systems in the facility
Fig. 2. Design of an AS/RS system.

from the I/O-point to the rest of the warehouse. Delays in
one system can cause delays in the other system. Thus,
when deciding on the number of I/O-points, their location
and their buffer capacity it may be necessary to also look at
the other systems’ characteristics.
Furthermore, the requirements for the AS/RS may
depend on the general environment of the system. In manufacturing environments the AS/RS primarily needs to
provide all required materials in time to make sure that
production can continue. Production is leading and should
never be halted to wait for the AS/RS. In distribution envi-


K.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362

ronments, the AS/RS performs or supports the order
retrieval process, to make sure that customers’ orders leave
the facility in time.
Part of the actual design of an AS/RS consists obviously
of determining its physical appearance. The physical design
consists of two aspects which together determine the physical manifestation of the system. First, we have the choice
of the AS/RS type (system choice). Second, the chosen system must be configured, for example, by deciding on the
number of aisles and the rack dimensions (system configuration). These interrelated choices can be made based on,
among others, historical and forecasted data, product
characteristics, the available budget, required throughput,
required storage space and available land space. Various
options for AS/RS types are displayed in Fig. 1, however,
little research is available to select the best type of system
from the available options. A more elaborate overview of
various AS/RS types along with selection criteria can be
found in Allen (1992).
A list of configuration decisions for any given type of
AS/RS is displayed in Table 1. For a typical design problem, total capacity is given beforehand. This essentially
means that the mathematical product of the number of
aisles, rack height, and rack length is constant. Increasing
the number of aisles thus implies reducing rack length
and/or height to maintain the desired storage capacity.
Because of this relation, having more aisles indirectly
results in shorter response times, due to the decreased rack
length and height. Furthermore, design changes often have
an impact in multiple ways at the same time. In a standard
system with one crane per aisle, having more aisles also
means having more cranes, which in turn results in a higher
throughput and higher investment costs.

Table 1
Overview of design decisions for AS/RSs
Class of problems

Storage assignment




Decisions to be made

Number of aisles
Height of the storage racks
Length of the aisles
Equally sized or modular storage locations
Number and location of the I/O-points
Buffer capacity at the I/O-points
Number of cranes per aisle
Number of order pickers per aisle (if any)
Storage assignment method
Number of storage classes
Positioning of the storage classes
Type of batching (static or dynamic)
Batch size (capacity or time based)
Selection rule for assignment of orders to
Sequencing restrictions (e.g., due dates)
Type of operation (single or dual command)
Scheduling approach (block or dynamic)
Sequencing method
Type of positioning (static or dynamic)
Location where idle cranes will be placed.

Even when the number of aisles is given, there is still a
trade-off between rack height and length. Since cranes
can travel vertically and horizontally simultaneously, the
actual travel time equals the maximum of the horizontal
and vertical travel time (Chebyshev distance metric). Horizontal travel speeds are typically up to 3 m2 compared to
vertical travel speeds of up to 0.75 m2 (Tompkins et al.,
2003). A good balance between rack height and length
can help to reduce travel times. A common, yet not necessarily optimal, configuration is one where the racks are
square-in-time, which means that the time needed to reach
the highest row equals the time needed to reach the farthest
column. Any rack that is not square-in-time is called
Often racks have equally sized storage locations. However, to meet highly varying customers’ demand, it is also
interesting to allow the storage of different shaped loads
within a single rack. Also, an AS/RS may have more than
one I/O-point per aisle. Instead of only placing an I/Opoint at the front of an aisle, another one might be located
at the middle and/or rear of the aisle. In that way, for
example, flows of incoming and outgoing loads can easily
be separated. Research in the field of physical design will
be treated in Section 4.
Just as important as the physical design are the software
controls needed to get the AS/RS operational (see e.g.,
Fohn et al., 1994; Terry et al., 1988). A good design procedure should simultaneously address both physical design
and control issues of the system. Regardless of the actual
optimisation procedure, a system of performance measurement is needed to evaluate the overall performance of the
resulting system at every stage. This underlines the importance of performance measurement in the field. Many publications have appeared on performance measurement,
which will be discussed in Section 9.
Control policies are methods which determine the
actions performed by the AS/RS. Typically, the operation
of an AS/RS is governed by a coherent set of such control
policies, which each take care of a specific subset of the
activities. A storage assignment policy serves to determine
which products are assigned to which locations. The position where an idle crane (i.e., a crane that has no jobs to
perform) waits is determined by a dwell-point policy. The
dwell-point is best chosen to minimise the expected time
to travel to the next (still unknown) request.
A unit-load AS/RS can operate in two ways, namely in a
single command cycle or in a dual command cycle. In a single command cycle the crane performs either a single storage or a single retrieval request. The storage cycle time
then is equal to the sum of the time to pick-up a load at
the input station, the time to travel to the storage location,
the time to place the load in the rack and the time to return
to the input station. The retrieval cycle time can be defined
similarly. If an AS/RS performs both a storage and a
retrieval request in a single cycle, we call this a dual command cycle. In this case, the cycle time is defined as the
sum of the time to pick-up the load, the time to travel to

K.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362

the storage location and store the load, the empty travel
time (interleaving time) from the storage location to the
retrieval location and the time to pick the unit-load and
transport it to the output station. Clearly, the total time
to perform all storage and retrieval requests reduces if dual
commands are performed. A tour of an AS/RS consists of a
sequence of single or dual command cycles, starting at the
origin of the first request and ending at the destination of
the last request. Sequencing rules can be used to create
tours such that the total time to handle all request is minimised or the due times are least violated.
As a final control policy, batching considers how one can
combine different customer orders into a single tour of the
crane (mainly applicable to person-on-board AS/RS).
Table 1 provides an overview of all control decision problems that may need to be selected. From literature it is
known that certain combinations of control policies work
better than other combinations. In Sections 5–8 we present
an extensive discussion of all AS/RS control policies that
have been treated in literature.
4. Physical design
Only a few papers address the design of AS/RSs in combination with the design of other material handling systems
in the facility. Most of these papers consider manufacturing environments. Chincholkar and Krishnaiah Chetty,
1996 use approaches as Petri Nets and the Taguchi method
to simultaneously address the scheduling of jobs to an
AS/RS system and the scheduling of jobs to machines in
a flexible manufacturing system. The AS/RS is both
responsible for storing and retrieving loads and for transferring them between machines. Inman (2003) studies the
usage of AS/RSs in the automotive industry. The function
of the AS/RS is to restore the sequence in which jobs are
handled at the various processes in the facility. A model
is proposed to determine the capacity of the AS/RS based
on the number of jobs that need to be rescheduled. As a
result, the design of the AS/RS is completely subordinate
to the assembling processes in the facility.
Hwang et al. (2002) consider the design of miniload
AS/RSs in combination with Automated Guided Vehicles.
Both a non-linear model and heuristics have been proposed
to determine the optimal number of loads to be transferred
by each AGV to machines in combination with an optimal
design of the AS/RS. Park and Webster (1989a) address the
design of warehouses by proposing an approach that simultaneously selects the used storage equipment, that might be
an AS/RS, and the overall size and shape of the storage
In order to deal with one or more design issues for AS/
RSs, methods ranging from simulation, analytical models,
artificial intelligent approaches (e.g., Knapp and Wang,
1992; Chincholkar et al., 1994; Hsieh et al., 1998) to experimental approaches (e.g., Lim et al., 1996) have been proposed in the literature. We will use the classification as
indicated in Table 1 in our discussion on solution proce-


dures that assist in decision making for one or multiple
physical design issues in combination with one or more
control issues. Table 2 presents an overview of papers
and indicates which issues the authors address. Note that
we do not mark a control policy if it is only used as a fixed
input factor to the model. Only decision variables are
marked. Furthermore, papers that only focus on control
issues, but not on physical design, have been excluded since
they will be discussed in one of the subsequent sections.
For all simulation models, we can conclude that they
only address some of the physical design aspects and that
configurability of control policies is very limited. Furthermore, only few configurations and types of AS/RSs have
been tested in combination with fixed values for various
input factors. In this way, it can never be guaranteed that
a (near-) optimal design has been found. Randhawa and
Shroff (1995) have been performing the most extensive simulation study. These authors examine the effect of different
sequencing rules on six layout configurations (with a varying I/O-point, item distribution over racks, rack configuration and rack dimensions). Based on a limited number of
experiments the authors conclude, among other things,
that locating the I/O-point at the middle of the aisle,
instead of at the end of the aisle, results in a higher
In our opinion, in general the strength of simulation
could be better exploited in AS/RS research to compare
numerous designs, while taking into account more design
aspects, especially in combination with control policies.
Also, sensitivity analyses on input factors should be performed such that a design can be obtained which can perform well in all applicable scenarios. As a result more
general information could be obtained on good design
Rosenblatt et al. (1993) already tried to overcome this
drawback of existing simulation models by alternatingly
using optimisation and simulation in order to reach the
best design given a certain service level. From several
experiments the authors conclude that an optimal design
requires fewer cranes than aisles. Hwang and Ko (1988)
use their travel time model for a crane operating in multiple
aisles to conclude that multiple-aisles AS/RSs might be
interesting if the number of storage and retrieval requests
are low. Contrary to these results, most other analytical
models included in Table 2 assume exactly one crane per
aisle. Mathematical programming models, queueing theory
and heuristics have been mostly used in developing analytical design models. From the overview in Table 2 we conclude that all models address some, but certainly not all
physical design aspects. None of the physical analytical
design models includes any of the mentioned control decisions problems.
Summarising, most research is performed on determining the layout of a single storage rack. In this context, no
attention has been paid to the storage capacity (single or
multiple deep) of the storage locations themselves. Furthermore, hardly any attention has been paid to the location


Table 2
Overview of research in design models that can assist in decision making for physical design in combination with control issues


Ashayeri et al.
Houshyar and
Chung (1991)
Taboun and
Bhole (1993)
Randhawa and
Shroff (1995)
Lee et al. (1996)
Potrcˇ et al.

Type of AS/

System configuration


of cranes

Number of aisles
and their length









Unit-load and


Karasawa et al.
Zollinger (1982)
Ashayeri et al.
Azadivar (1987)
Bozer and White
Van Oudheusden
and Zhu (1992)
Bozer and White
Chang and Wen
Hwang and Ko
Park et al. (1999)





vehicle S/R



Rosenblatt et al.

Lee et al. (2005)

Number of



Malmborg (2002,
Koh et al. (2005)

Number of I/Opoints and

K.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362


K.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362

and the number of I/O-points. In some types of distribution centres (e.g., cross-docking areas), it might, for example, be interesting to locate I/O-points at both ends of a
storage rack. Also, only little research has been performed
on the configuration of multi-shuttle AS/RSs, which
already have been proven to be efficient in terms of
throughput. From the literature studied, it can be concluded that most authors combine only one or a few control rules with their physical design research. Batching
and dwell-point locations have not been considered in
physical design. Thus, despite the fact that decisions in
both categories (physical design and control rules) are
highly interrelated, they are usually addressed separately.
In the next sections we discuss papers that propose policies
for the various control issues indicated in Table 2.
5. Storage assignment
Several methods exist for assigning products to storage
locations in the racks. Five often used storage assignment
policies for AS/RSs are described here in more detail (see
e.g., Hausman et al., 1976 or Graves et al., 1977). These
rules are:

dedicated storage assignment
random storage assignment
closest open location storage assignment
full-turnover-based storage assignment
class-based storage assignment

For the dedicated storage method each product type is
assigned to a fixed location. Replenishments of that product always occur at this same location. The main disadvantage of dedicated storage are its high space requirements
and consequent low space utilisation. This is due to the fact
that locations are reserved even for products that are out of
stock. Furthermore, for each product type sufficient space
must be reserved to accommodate the maximum inventory
level that may occur. Most advantages of dedicated storage, such as locating heavy products at the bottom or
matching the layout of stores, are related to non-automated order-picking areas and are not as interesting for
AS/RSs. For random storage all empty locations have an
equal probability of having an incoming load assigned to
it. If the closest open location storage is applied, the first
empty location that is encountered will be used to store
the products. This typically leads to an AS/RS where racks
are full around the I/O-points and gradually more empty
towards the back (if there is excess capacity).
The full-turnover storage policy determines storage locations for loads based on their demand frequency. Frequently requested products get the easiest accessible
locations, usually near the I/O-points. Slow-moving products are located farther away from the I/O-point. An
important assumption for this rule is that the turnover frequencies need to be known beforehand. Heskett (1963,
1964) presents the cube-per-order index (COI) rule, which


is a form of full-turnover storage. The COI of a load is
defined as the ratio of the load’s required storage space
to the number of request for this product per period. The
COI rule assigns loads with the lowest COI to the locations
closest to the I/O-point. Malmborg and Bhaskaran (1990)
give a proof of optimality for this rule while taking into
account the non-uniqueness of the COI layout if dual command scheduling is used. Malmborg and Krishnakumar
(1989) show that the COI-rule is optimal for person-aboard
AS/RSs with respect to order-picking costs if there are
fixed inventory levels and a fixed balanced assignment of
order pickers to items. However, according to Lee (1992)
the COI-rule cannot be applied for person-on-board systems due to the fact that an order usually consists of more
than two independent items at different locations. Therefore, the author develops a new heuristic that outperforms
the COI-rule.
For practical purposes it is easiest if a full-turnover policy is combined with dedicated storage. The problem is that
demand frequencies change constantly and also the product
assortment is usually far from constant. Any change in frequency and any addition of a new product to the system
may require a large amount of repositioning of loads to
bring it back in line with the full-turnover rule. To prevent
excessive repositioning, a new storage allocation is in practice typically calculated once per period. To reduce space
requirements and periodic repositioning while maintaining
most of the efficiency gains, class-based storage can be used,
which will be discussed next.
5.1. Class-based storage
This storage assignment method divides the available
warehouse space into a number of areas. Each item is subsequently assigned to one of the areas, based on the item’s
demand frequency. Random storage is applied within an
area. Actually, the full-turnover storage policy can be seen
as a class-based policy with only one item per class. Often
class-based storage with three classes is referred to as ABC
storage. This reflects the common practice to call the fastest-moving items the A-items, the next fastest-moving items
the B-items, and so on. The main advantage of class-based
storage is an increased efficiency due to storing the fastmoving items near the I/O-point, while at the same time
the low storage space requirements and flexibility of the
random storage method apply.
A designer faces three major decisions when implementing class-based storage in an AS/RS.
1. Zone divisioning (i.e., determining number of classes).
2. Zone sizing (i.e., number of products to be assigned to
each zone).
3. Zone positioning (i.e., where to locate each of the
From Table 3 it can be seen that several types of zone sizing procedures have been developed to derive boundaries

Kouvelis and Papanicolaou (1995) suggest to use their formulas in
combination with the recursive procedure of Eynan and Rosenblatt
(1993) for this problem

No paper is specifically written about this; problem
can be solved using n = 3 in solution approaches for n
Recursive procedure (Rosenblatt and Eynan, 1989)
or Dynamic programming (Van den Berg, 1996)
Numerical procedure (Hausman et al., 1976)

No paper is specifically written about this; problem can
be solved using solution approaches for rectangular

Formula (Kouvelis and Papanicolaou, 1995)
Numerical procedure (Hausman et al., 1976)

No paper is specifically written about this; problem can be solved using
n = 3 in solution approaches for n classes

Single command
Rectangular racks
Single command
Square-in-time racks

for each of the classes. For dual command scheduling,
research has mainly focused on rectangular racks. Clearly,
the resulting procedures can also be used in square-in-time
racks which are a special case of rectangular racks. Both
Rosenblatt and Eynan (1989) and Eynan and Rosenblatt
(1994) conclude that a relatively small number of classes,
usually less than 10, is to be preferred to obtain most of
the potential savings in travel times as compared to fullturnover storage. In practice, often the number of classes
is restricted to three. Van den Berg (1996) proposes a
dynamic programming algorithm that assigns both locations and products to classes.
Several strategies exist for zone positioning, varying
from optimal solutions for single command scheduling to
rules of thumb for dual command scheduling. Hausman
et al. (1976) prove that a L-shaped configuration with
square-in-time boundaries for classes A, B and C is optimal
when single command scheduling is applied in square-intime racks. Graves et al. (1977) demonstrate through simulation that this L -shaped configuration is close to optimal
for dual command scheduling in square-in-time racks.
Guenov and Raeside (1992) also study dual command
scheduling and compare three different zone shapes. Their
conclusion is that the performance of each of the proposed
shapes depends on the location of the I/O-point and that
none is superior to the others. Eynan and Rosenblatt
(1994) present a layout for n classes in rectangular racks
while single command scheduling is used. This layout combines n  2L-shaped zones, a transient region for class
n  1 and a rectangular zone for class n. Fig. 3 presents
examples of zone shapes for both types of racks for three
Some variations of the class-based storage policy have
been studied. Park and Webster (1989b) propose a classbased storage method in a three-dimensional system which
minimises total travel times. Hsieh and Tsai (2001) suggest
a class-based method for production facilities based on the
bill of materials. Thonemann and Brandeau (1998) alter the
algorithms of Hausman et al. (1976) such that they can be






n Classes


Table 3
Solution procedures to derive optimal boundaries for zone sizing decisions in class-based storage

Search procedure (Kouvelis and Papanicolaou, 1995)

K.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362

Dual command
Rectangular racks


Fig. 3. Typical zone positioning for three classes in respectively square-intime (upper part) and rectangular racks (lower part).

K.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362

used in an environment with stochastic demand. Several
authors (e.g., Hwang and Ha, 1994; Vickson and Fujimoto,
1996; Vickson and Lu, 1998) examine class-based policies
for carousels. The racks in the carousel are partitioned into
two regions with an appropriate boundary shape (above or
next to each other). Bengu¨ (1995) studies an organ pipe
arrangement for carousels in which the items with the highest access probability are located in the middle and the rest
is positioned at the left or right side according to a decreasing access probability.
5.2. Performance of storage assignment rules
Travel time estimates (see Section 9) for both single and
dual command scheduling in different types of AS/RS configurations are an appropriate analytical tool for comparing control rules (e.g., Hausman et al., 1976; Graves
et al., 1977). With simulation more extensive experiments
under stochastic conditions can be performed (e.g., Schwarz et al., 1978; Kaylan and Medeiros, 1988; Kulturel
et al., 1999; Van den Berg and Gademann, 2000). Malmborg (1996) and Malmborg and Altassan (1998) develop
a storage policy trade-off for respectively unit-load and
small systems to roughly compare different policies in a
short time prior to a simulation study.
Results from both analytical and simulation studies
show that full-turnover-based and class-based storage
assignment outperform random storage. Kulturel et al.
(1999) compare a three class-based policy with a duration
of stay policy, which was originally introduced by Goetschalckx and Ratliff (1990). While applying the duration
of stay policy, products with the shortest duration in the
warehouses are assigned to storage locations closest to
the I/O-point. The three-class-based policy only outperforms the duration of stay policy if the number of product
types is small. Methods as Petri Nets (e.g., Lin and Wang,
1995) are able to update the system to cope with rapidly
changing dynamic environments and to compare different
Updating, reshuffling of items in idle periods of the AS/
RS and reconsidering storage assignment decisions can be
vital in current dynamic environments to maintain the
desired performance level (e.g., Muralidharan et al., 1995;
Jaikumar and Solomon, 1990). The COI policy is usually
well applicable in static environments with independent
demand of products. Moon and Kim (2001) show by
means of a simulation study that re-location of items is
required if the production quantity of each item changes
over time. Sadiq et al. (1996) propose a dynamic storage
assignment policy to reassign items to storage locations
in systems with a rapidly changing product mix and short
product life cycles. By using predicted future product
mix, correlated demand of products and demand forecasts,
the dynamic policy intends to minimise total order processing times, which consist of order-picking times and relocating times. It is shown that this dynamic policy outperforms
the static COI rule.


Summarising, in literature various storage assignment
policies have been developed and were compared both
through simulation and analytical methods. Most authors
address single aisle AS/RSs with one I/O-point. Storage
assignment policies for other types of configurations (e.g.,
multiple I/O-points) or other types of AS/RSs (e.g., multiple shuttle AS/RSs) hardly have been formulated.
6. Batching
Suppose we have a number of orders that need to be
retrieved from storage in a person-on-board item-picking
AS/RS. We could retrieve the orders one at a time or we
could try to combine several orders in a single tour of the
crane. The latter approach is called batching. Batching
problems for person-on-board AS/RSs are quite similar
to batching problems for order pickers in warehouses.
For a detailed review of this type of research, refer to De
Koster et al. (2007). In this section, we will only focus on
papers that deal with batching problems for AS/RSs with
cranes that operate in a single aisle.
An advantage of batching is that the length of a tour for
a batch of orders is shorter than the sum of the individual
orders’ tour lengths. However, more effort is needed to
keep track of which item belongs to which order or to sort
items later on. A limit on the size of a batch is usually
determined by the capacity of the crane or an upper limit
on the required response time. As a result, an important
decision problem in batching is the determination of the
size of each batch in combination with the assignment of
orders to these batches such that travel times are minimised. One of the first papers referring to batching of
orders for person-on-board AS/RSs is Barrett (1977).
Elsayed (1981) concludes that this problem, that can be
formulated as a mixed integer programming model (Armstrong et al., 1979) is NP-hard.
To obtain solutions for large problems in acceptable
computation times, numerous heuristics have been developed. As presented in Fig. 4, most heuristic batching methods basically follow the same three steps: a method of
initiating batches by selecting a seed, a method of allocating orders to batches, and a stopping rule to determine
when a batch has been completed. An important assumption in all heuristics is the fact that a single order cannot
be split over various batches, but needs to be picked as a
whole. Table 4 indicates several seed selection, order addition rules and stopping rules.
Contrary to a single seeding rule a cumulative seeding
rule (e.g., Elsayed and Stern, 1983) uses all orders that
are already in the batch as the seed. Hwang et al. (1988)
and Hwang and Lee (1988) develop heuristics based on
cluster analysis. As common in cluster analysis, both attribute vectors related to storage locations of an order and
similarity measures, based on, for example, the boundaries
of the area in which the crane needs to travel to reach all
locations of an order, are used in formulating heuristics.
A seed order will be selected and the most similar order will


K.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362

more difficult when orders arrive on-line (see e.g., Bhaskaran and Malmborg, 1989). This is due to the fact that there
is a trade-off for on-line arrivals between reducing waiting
times (by calculating batches frequently based on few available orders) and reducing travel times (by calculating
batches less frequently to obtain more possibilities for efficient combinations).

Initiate batch by selecting a first
order (i.e. seed) based on a
seed selection rule
cluster method

Allocate orders to batches by using
an order addition rule

7. Dwell-point location
Yes, start
a new batch

Decide if batch is complete
by using a stopping rule

Fig. 4. Common structure for batching heuristics.

be added. These two orders can be merged and can be used
as a new seed in the next step. This process will be repeated
until a cluster of orders has been obtained.
Pan and Liu (1995) perform a comparative analysis of
batching heuristics based on average travel times. In the
experiments the shape and the capacity of the cranes as well
as the storage assignment policies have been varied. The
authors conclude that only the storage capacity of a crane
highly impacts the choice for a certain rule. Based on the
results of 42 experiments with each 30 orders, the authors
advice to use the heuristic of Hwang and Lee (1988).
The methods included in Table 4 do not address time
constraints on retrievals. Both Elsayed et al. (1993) and
Elsayed and Lee (1996) discuss the batching problem with
due dates in combination with the scheduling problem of
orders. A penalty function has been introduced which measures both the earliness and tardiness of orders. Furthermore, all mentioned papers assume that the arrival
patterns of orders are known before the start of the operations. However, in many warehouses there is a batch-arrival component (for example, orders left from the
previous day that did not make the departure time) and
an on-line component. It is known that batching becomes

Several methods have been proposed to deal with the
decision where to position an idle crane, i.e., how to determine the crane’s dwell-point. Bozer and White (1984) introduced four simple static dwell-point strategies. Table 5
summarises these rules and indicates the resulting onedimensional parking location. Park (1991) showed that
the input station rule returns an optimal dwell-point if
the probability, that the first request after an idle period
is a storage request, is at least 1/2.
Egbelu (1991) proposes linear programming models that
are capable of responding to fluctuations in types of
requests. A two-dimensional dwell-point location (including the height in the rack) can be determined such that
the response time to the location of need is minimised.
Important drawbacks of this dynamic approach are the
facts that LP solution techniques need to be implemented
in the AS/RS control system and that computation times
may be too high to be of practical value. Hwang and
Lim (1993) propose an efficient algorithm for the minimum
expected travel time model of Egbelu (1991) by transforming it into a single facility location model.
Egbelu and Wu (1993) compare the four rules of Bozer
and White (1984) and the two dynamic rules of Egbelu
(1991) by means of a simulation study. A ranking of the
alternatives is difficult to make due to the fact that the rules
are compared with a small number of replications for just
one layout with five different arrival rates of requests under
random and dedicated storage policies.
Several static approaches have been proposed for other
types of unit-load AS/RSs. Chang and Egbelu (1997) consider a single crane serving multiple aisles. A mathematical

Table 4
Overview of seed selection, order addition and stopping rules for batching
Type of rule



Seed selection

Order with largest number of locations to be visited
Order with smallest number of locations to be visited
Order with largest volume
Order with smallest volume
Order with highest percentage of capacity of crane
Cumulative rule
Clustering rule

Elsayed (1981)
Elsayed (1981)
Elsayed (1981)
Elsayed (1981)
Elsayed and Unal (1989)
Elsayed and Stern (1983)
Hwang et al. (1988) and Hwang and Lee (1988)

Order addition

Largest number of common locations
Geometric similarities

Egbelu (1991)
Hwang and Lee (1988)

Stopping rules

Capacity constraint
Time constraint
All orders are completed


K.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362

programming model has been developed to determine a
dwell-point from a three-dimensional point of view. Except
for the location and height, the exact aisle also needs to be
specified. Peters et al. (1996) developed closed-form analytical models to determine dwell-points in continuous
square-in-time and rectangular racks under random storage based on the travel time estimations of Bozer and
White (1984). Park (1999) developed an optimal dwellpoint policy for square-in-time racks under dedicated storage. Park (2001) shows that for rectangular racks under
random storage the dwell-point location can be determined
in terms of the probability of occurrence of a certain type
of request. Van den Berg (2002) presents analytical expressions for determining dwell-points under randomised and
class-based storage policies. Contrary to Peters et al.
(1996), these methods can be used for various AS/RS configurations with varying locations of the I/O-point instead
of situating it at the lower corners of the rack.
Summarising, simple rules of thumb, closed-form
analytical expressions and mathematical programming
approaches have been formulated to position idle AS/RS
cranes at a dwell-point in various AS/RS configurations.
Most approaches address static positioning of single unitload capacity AS/RSs and do not study other types of
AS/RSs. So far, no extensive and statistically sound simulation study has been performed on dwell-point policies in
combination with other physical design and control issues
(see also Table 2) which makes it difficult to provide designers with an advice when to use which policy.
8. Sequencing of storage and retrieval requests
Storage requests in distribution or production environments are usually not time-critical. The exact point in time
at which loads are stored is not of much importance for the
performance of the system. Therefore, storage requests are
usually stored according to the first-come-first-served principle. In sequencing retrievals usually due times of retrievals should be met, which makes it necessary to look
beyond simple first-come-first-served. Furthermore, by
sequencing the retrievals in a smart way, improvements
in the overall throughput of the AS/RS can be obtained.
The list of retrievals is continuously changing over time.
Performed retrievals are deleted from the list and new
retrieval jobs are added. Han et al. (1987) suggest two ways
to deal with this dynamic problem. Firstly, select a block of
the most urgent storage and retrieval requests, sequence


them and when they are completed select the next block,
and so on. This is called block sequencing. Secondly, we
can resequence the whole list of requests every time a
new request is added and use due times or priorities. We
refer to this kind of sequencing as dynamic sequencing.
The performance of both approaches differs per situation.
For example, Eben-Chaime (1992) concludes that in a specified non-deterministic environment, the block sequencing
strategy might be inappropriate. However, a block
sequencing approach is more transparent and simpler with
respect to implementation.
Various algorithms and heuristics can be used to schedule storage and retrieval requests within a block. The
main objectives in those approaches are to minimise total
travel times or total travel distances. Most literature
focuses on single and dual command scheduling of unit
load AS/RSs with one input/output station and one crane
per aisle. Therefore, we first discuss sequencing methods
for this basic sequencing problem. In Section 8.2, we discuss extensions of the basic sequencing problem. The
sequencing problem of other types of AS/RSs is treated
in Section 8.3.
8.1. The basic sequencing problem
For the sequencing problem of unit-load AS/RSs, the
two common types of cycles to be addressed are single
command and dual command cycles (see also Section 3).
In a single command cycle only one unit-load is moved
(either a storage or a retrieval) before the crane returns
to the I/O-point. A dual command cycle consists of two
moves, one storage and one retrieval. The possibility of
performing dual command cycles depends on the availability of storage and retrieval requests. If both types of
requests are available, dual command cycles give advantages with respect to travel times (Graves et al., 1977).
An alternative might be to perform dual commands
whenever possible and single commands otherwise. EbenChaime and Pliskin (1996, 1997) show that systems that
operate under this more hybrid mode might achieve more
stable waiting lines and can use less cranes. Some warehouses, however, have patterns in arriving and leaving
loads. For example, trucks with incoming loads arrive in
the morning and trucks transporting outgoing loads arrive
in the evening. In this case, cranes might perform single
command cycles. If arriving and leaving trucks overlap in
time, dual command cycles can be performed.

Table 5
Static dwell-point rules for unit-load AS/RS (Bozer and White, 1984)


Input station

Always at
Always at
If a single
If a single
If a single
If a single

Last location

input station
midpoint location of racks
command storage request has been performed then
command retrieval request or a dual command has
command storage request has been performed then
command retrieval request or a dual command has

positioning at input station
been performed then positioning at output station
positioning at last storage location
been performed then positioning at output station


K.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362

Table 6
Solvable special cases of the basic sequencing problem for unit-load AS/RS
Characteristics of case

Steps of solution method


 Non-dedicated storage
 The number of storages equals the number of
 A single I/O point

1. Solve assignment problem to combine storage (with location) with
retrieval requests
2. Apply Murthy’s ranking algorithm (Murthy, 1968) to search assignment solutions
3. The optimal solution equals the first assignment solution where no load
needs to be stored in a non-empty location (this may occur when the
location will be empty at a later time due to a retrieval)

Lee and Schaefer

 Dedicated storage
 The number of storages is smaller then or equal
to the number of retrievals
 A single I/O-point

Can be translated into an assignment problem

Lee and Schaefer

 Dedicated storage
 Any number of storage and retrieval requests
 A separate input and a separate output point
that might be positioned at different locations
of the rack

Transportation problem that combines departure positions of empty trips
(end of loaded trip) with arrival positions of empty trips (start of loaded
trip) such that total empty travel distances are minimised

Van den Berg and
Gademann (1999)

Bozer et al. (1990) explain that the dual command
scheduling of AS/RSs can be formulated as a Chebyshev
travelling salesman problem, which is known to be NPcomplete. Han et al. (1987) indicate that in general the
problem of optimally sequencing a given list of requests
is NP-hard. One of the reasons for this complexity is
the fact that the set of locations available for storage
depends on where previous loads are stored and which
retrievals have already been performed. However, some
special cases of the sequencing problem can be solved in
polynomial time. A summary of these results is shown
in Table 6. Computation times are high for solving the
problem in which non-dedicated storage is used (Lee
and Schaefer, 1996).
For the dynamic sequencing problem various methods,
as summarised in Table 7 have been formulated. Several
studies, including simulation studies, have been performed
to compare the performance of these heuristics in combination with several storage assignment policies (see, e.g., Linn
and Wysk, 1987). Han et al. (1987) show that the nearestneighbour heuristic can provide a lower average cycle time
than the first come first served rule. Furthermore, it is
shown that the nearest-neighbour heuristic has a better performance than the shortest leg heuristic over the long run
due to the fact that the storage locations close to the input
station are filled up first and, thereafter, only locations far
from the input station remain open.

Eynan and Rosenblatt (1993) conclude that quite significant savings in interleaving times can be obtained by combining nearest-neighbour scheduling with class based
storage assignment. Schwarz et al. (1978) investigate the
performance and predictions of previously developed
deterministic models in a stochastic environment. It is
found that the results of the models hold in this environment. However, the predictions in improvements are generally larger than the actual improvements.
Other approaches to find solutions to the sequencing
problem include neural networks (e.g., Wang and Yih,
1997), expert systems (e.g., Linn and Wysk, 1990a,b), artificial intelligence (e.g., Seidmann, 1988), genetic algorithms
(e.g., Krishnaiah Chetty and Sarveswar Reddy, 2003) and
the Taguchi method (e.g., Lim et al., 1996). These methods
can be applied in situations with high uncertainty and little
information. Furthermore, these methods are capable of
learning and adapting to changes in the environment, such
as fluctuations in demand. The output can consist of combinations of storage assignment, retrieval location selection, queue selection and job sequencing.
8.2. Extensions of the basic sequencing problem
An extension of the previously described basic scheduling problem is the problem in which storage and retrieval
requests with release and due times need to be scheduled.

Table 7
Methods for dynamic sequencing of unit-load AS/RS


Shortest completion time
Nearest-neighbour (Han et al., 1987)

Retrieval requests will be scheduled in order of appearance
Retrieval request with shortest completion time will be served first
Pairs of storage and retrieval requests are chosen such that the distance from the storage to the retrieval location
is minimal
Storage locations are selected such that the least extra distance needs to be travelled to perform the storage
request while travelling to the retrieval location
Approach includes heuristics and an optimal branch-and-bound method to determine sequences for all known

Shortest leg (Han et al., 1987)
On-line asymmetric TSP (Ascheuer
et al., 1999)

K.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362

Models and heuristics have been proposed that intend to
minimise the sum of earliness and tardiness penalties in
the case that all requests or a group of requests have one
common due time (e.g., Lee and Kim, 1995; Elsayed and
Lee, 1996; Elsayed et al., 1993; Linn and Xie, 1993).
Other configurations of an AS/RS such as multiple
I/O-points per aisle might require new solution approaches.
Randhawa et al. (1991) use simulation to evaluate various
scheduling rules for systems with one input/output station
at each aisle and systems with two input/output stations
at each aisle. It is shown that reductions in expected crane
round trip times and in throughput times can be obtained
for systems with two input/output stations.
Kanet and Ramirez (1986) add location selection to the
scheduling problem in case products are stored at multiple
locations. This decision is incorporated in the integer programming model by including costs per retrieval operation
and costs to separate items at a location into different parts
related to different retrieval orders. Jaikumar and Solomon
(1990) study the prepositioning of pallets in periods the
AS/RS would otherwise be idle. By positioning loads that
are expected to be needed in the next time period, closer
to the I/O-point it is possible to reduce travel times during
the actual handling of retrieval requests.
8.3. Sequencing for other types of AS/RSs
Some research has been done to the scheduling of
storage and retrieval requests for other types of AS/RSs.
Several authors address the problem of sequencing storage
and retrieval requests in a twin-shuttle AS/RS. Due to the
double capacity of the crane, more routing options emerge
since cycles can be performed in which at most four locations are visited before returning to the I/O-point. Simple
nearest-neighbour heuristics (Sarker et al., 1991, 1994)
and a minimum perimeter heuristic (Keserla and Peters,
1994) have been developed.
In a miniload AS/RS current retrieval requests become
future storage requests, since loads are returned into the system after items have been picked. Therefore, the problem can
be reformulated such that only a queue of retrieval requests
exists, which result in a less complicated problem. The picker
at the end of the aisle also needs to be incorporated in the
model. Retrieval requests are rearranged such that successive requests are located close to each other. Storages and retrievals which are close to each other can be paired by a
nearest-neighbour heuristic (Mahajan et al., 1998).
Van Oudheusden et al. (1988), Goetschalckx and Ratliff
(1988) and Hwang and Song (1993) propose heuristics for
the sequencing problem in person-on-board AS/RSs.
Abdel-Malek and Tang (1994) and Hwang et al. (1999)
study the sequencing problem for automated single and
double shuttle carrousel storage and retrieval systems.
Summarising, various methods are described in the literature to schedule storage and retrieval requests such that
the total (empty) distance travelled is minimised. The situation considered in the majority of the literature concerns


an unit-load AS/RS working in one aisle with one input/
output station. For some specific instances optimal
sequencing methods exist. However, the general dynamic
sequencing problem is hard to solve and, therefore, heuristics have been developed to find feasible schedules. Hardly
any attention has been paid to methods for the scheduling
of storage and retrieval requests when each aisle has two or
more input/output stations or when a single crane operates
in multiple aisles. Although multi-shuttle cranes have proven to be successful, only a few heuristics have been developed for quadruple (or more) command scheduling.
9. Performance measurement
In evaluating the design and control rules of an AS/RS
several performance measures can be used. Based on the
literature overview presented in this paper, we can at least
consider the following performance measures:
 travel time per request,
 number of requests handled per time period (e.g., Azadivar, 1986; Foley et al., 2002),
 total time required to handle a certain number of
 waiting times of cranes of the AS/RS,
 waiting times of products to be stored/retrieved,
 number of requests waiting to be stored/retrieved (e.g.,
Hur et al., 2004).
Lee (1997), Malmborg and Altassan (1997) and Bozer
and Cho (2005) propose throughput performance models.
The models of Lee (1997) and Malmborg and Altassan
(1997) are similar but published independently in the same
year (Eldemir et al., 2003). Eldemir et al. (2003) concludes
that the more time-efficient model of Bozer and Cho (2005)
slightly overestimates the throughput and that the other
model slightly underestimates the throughput. Eldemir
et al. (2004) propose more time-efficient throughput models
which can be used to estimate space requirements for both
random and class-based dedicated storage.
Clearly, throughput estimates are the inverse of the
expected travel times of an AS/RS. As a result, estimating
travel times is very important in designing AS/RSs.
Numerous research has been done in this area. Sarker
and Babu (1995) presented a short review of travel time
models for AS/RSs. Here we extend this overview and present a categorisation of all literature in Table 8 by discussing
the main characteristics of each paper. We discuss some of
these papers in more detail to provide a rough line of
research in this area. First we discuss travel time models
for single unit-load aisle-captive AS/RSs. Thereafter, we
discuss relevant literature for other types of AS/RSs.
9.1. Travel time models for single-shuttle unit-load AS/RSs
Hausman et al. (1976) were one of the first to present
travel time models for single-shuttle unit-load AS/RSs.

Sarker et al.
Keserla and
Peters (1994)
Meller and



Hausman et al.
Graves et al.
Bozer and White
Han et al. (1987)
Hwang and Ko
Rosenblatt and
Eynan (1989)
Kim and
Seidmann (1990)
Hwang and Lee
Eynan and
Eynan and
Chang et al.
Kouvelis and
Pan and Wang
Mansuri (1997)
Thonemann and
Brandeau (1998)
Lee et al. (1999)
Wen et al. (2001)
Ashayeri et al.
Eldemir et al.



Continuous Discrete Unequal

Single Multiple Square- Non
in-time squarein-time




Single I/O at
location various

I/O point(s)











Multiple Random Dedicated Fullnlocations
turnover class













More than
command command dual


Table 8
Overview of research in travel time models for different types of AS/RS for different types of layouts, racks, location of I/O-points, storage assignment methods, scheduling approaches and operational characteristics



None (or Acceleration/ Maximum Stochastic
Dwellimplicitly) deceleration velocity
environment point

Operational characteristics

K.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362





For remark on classification see section 3.

Both single and double carousels are considered.


The authors also consider variance in travel times.

Travel time estimates to visit n locations.



Sari et al. (2005)

Gives an estimate for interleaving times.

Hu et al. (2005)





Foley and
Frazelle (1991)
Park et al.
Park et al. (2006)
Elsayed and
Unal (1989)
and Raeside
Chiang et al.
Hwang and Ha
Koh et al. (2002)







K.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362


The authors proposed estimates for single command scheduling in square-in-time continuous racks. Random, fullturnover, two- and three-class-based storage assignment
policies were considered. Graves et al. (1977) extended
those results by also considering interleaving times resulting from a first-come-first-served (FCFS) dual command
scheduling policy.
Bozer and White (1984) relaxed some of the assumptions by proposing travel time models for rectangular racks
with alternative single I/O-points. The authors considered
FCFS dual command scheduling and random storage as
control policies. The authors introduce b as the shape factor
of the rack to deal with rectangular racks. Here
b ¼ minðth =T ; tv =T Þ, where th indicates the horizontal travel time to the farthest column, tv the vertical travel time
to the farthest row and T ¼ maxðth ; tv Þ. Based on empirical
tests, the authors conclude that the model’s performance is
Other authors since then mainly continue the research of
Hausman et al. (1976), Graves et al. (1977) and Bozer and
White (1984) by studying different control policies, configurations of AS/RSs and/or operational characteristics.
Instead of a FCFS-policy a nearest-neighbour (NN) policy
can be used to schedule requests. Recursive procedures
(Rosenblatt and Eynan, 1989; Eynan and Rosenblatt,
1994) and closed-form expressions (Kim and Seidmann,
1990; Kouvelis and Papanicolaou, 1995) have been proposed for n-class based storage and full turnover storage.
From Table 8 it can be concluded that only a few papers
address dedicated storage as storage assignment policy
(Mansuri, 1997; Eldemir et al., 2004). Instead of addressing
discrete values in applying their control policies several
authors (Thonemann and Brandeau, 1998; Pan and Wang,
1996; Ashayeri et al., 2002) study stochastic environments
with varying demand.
Different configurations of single-shuttle unit-load AS/
RSs that have been studied include multi-aisle AS/RSs
(see Hwang and Ko, 1988) and racks with unequal sized
cells (see Lee et al., 1999). The results of the model of
Hwang and Ko (1988) can be used to determine the minimum number of cranes and number of aisles served by each
Almost all papers mentioned so far assumed that the
operational characteristics of an AS/RS could be ignored.
Hwang and Lee (1990) incorporate both the maximum
velocity of a crane and the time required to reach the peak
velocity or to come to a halt. Chang et al. (1995) extend the
work of Bozer and White (1984) by including acceleration
and deceleration rates instead of assuming constant speed.
Wen et al. (2001) extend the work of Chang et al. (1995) by
considering class-based and full-turnover-based storage
assignment policies.
9.2. Travel time models for other types of AS/RSs
New travel time estimates are required for multi-shuttle
AS/RSs to deal with quadruple and even sextuple (e.g.,


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Meller and Mungwattana, 1997) command scheduling.
Both the work of Bozer and White (1984) and Han et al.
(1987) have been extended by various authors (Sarker
et al., 1991; Keserla and Peters, 1994; Malmborg, 2000)
for multi-shuttle AS/RSs while examining different control
In miniload AS/RSs picker and crane are dependent on
each other; delays of one influence the performance of the
other. Foley and Frazelle (1991) consider a miniload
square-in-time AS/RS operating under a FCFS dual command scheduling policy and random storage. Also closedform travel time expressions for miniload AS/RSs with
one- and two-class-turnover based storage have been formulated (Park et al., 2003, 2006).
Person-on-board AS/RSs usually handle multiple locations in one tour. Authors (e.g., Elsayed and Unal, 1989;
Guenov and Raeside, 1992; Chiang et al., 1994) typically
derive expressions for upper and lower bounds for travel
times based on the number of locations to be visited given
a storage assignment and sequencing policy.
Hwang and Ha (1991) present travel time models for
single and double carousel systems. The authors investigate
the effects on performance of information availability of
upcoming orders. Clearly, an increase in throughput can
be obtained with this additional information, however,
the increase in throughput is lower than one might expect.
Finally, some authors present travel time estimates for
less frequently used types of AS/RSs, such as a rotating
tower cranes (Koh et al., 2002), heavy load platform based
AS/RSs (Hu et al., 2005) and flow-rack AS/RSs (Sari et al.,
Summarising, it can be concluded that travel time models for both square-in-time and rectangular racks have been
developed for unit-load AS/RSs operating under most
common storage assignment policies and two sequencing
heuristics derived from practice. So far no studies have
been performed that include dwell-point rules in travel time
estimates. Compared to unit-load AS/RSs, many issues,
such as N-class based storage or operational characteristics, have not been addressed in travel time models for
other types AS/RSs.
10. Conclusions and further research issues
In both manufacturing and distribution environments,
AS/RSs are used to store products and to retrieve products
from storage in response to production orders or customers’ orders. In designing an AS/RS, various physical design
problems and control problems need to be solved (see
Section 3). Literature related to the various interrelated
physical design and control problems, such as storage
assignment, batching, dwell-point location and request
scheduling was treated in Sections 4–8. To evaluate the performance of AS/RSs, we can use, for example, the travel
time estimates we discussed in Section 9.
From the literature survey, we conclude that most of the
literature addresses design and control problems in static

environments. However, in today’s world of rapidly changing customers’ demand, small internet orders, tight delivery
schedules, high competition and high service level requirements, it will be increasingly difficult to maintain a good
performance when using existing static solution techniques.
The research in the field of AS/RSs should now move
towards developing models, algorithms and heuristics that
include the dynamic and stochastic aspects of current business. In this context, one can think of self-adaptive storage
assignment methods, on-line-batching policies and dynamic
dwell-point rules. Also algorithms for physical design may
need to focus more on robustness of the design than on perfect optimality to ensure that the system will be capable of
remaining efficient in yet unknown future situations.
Furthermore, almost all existing papers just address one
or two decision problems simultaneously, instead of jointly
optimising a combination of physical design problems and
control problems (including batching, dwell-point rules
and I/O-point decisions). Obviously, it is not a simple exercise to include a multitude of design and control aspects in
one model. However, we would like to encourage the development of simulation models which compare numerous
designs while taking combinations of design aspects and
control policies into account.
Little attention has been paid so far to the relationship
between AS/RSs and other material handling systems in
production or distribution facilities. Especially in situations
where the AS/RS is just one of many systems, total warehouse performance cannot be assessed by simply adding
up performances of all individual systems. An integrated
approach would be desirable. Therefore, we advice – as a
first step – to develop approaches which simultaneously
optimise the design of an AS/RS and another material handling system. For example, by explicitly considering the
interface between an AS/RS and a conveyor system, or
by analysing the impact of replenishments by the AS/RS
to a separate order-picking area.
Except for those general issues, further detailed research
can also be advised for each of the following issues.
 Models to assist in AS/RS type selection.
 Analytical and simulation models for the design of nontraditional AS/RSs (e.g., multi-shuttle AS/RSs).
 Storage assignment policies for multi-shuttle AS/RSs.
 Storage assignment policies for AS/RSs working in multiple aisles and/or multiple I/O-points.
 Policies which simultaneously address storage assignment and batching of orders.
 Superior heuristics for batching that outperform all
existing rules in various settings.
 Dwell-point rules for non-traditional AS/RSs.
 Algorithms or heuristics to schedule AS/RSs in a single
aisle with multiple I/O-points.
 Travel-time models for AS/RSs operating in a single
aisle with multiple I/O-points.
 Travel-time models which incorporate operational characteristics of non-traditional AS/RSs.

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