A survey of literature on automated storage and retrieval systems [608690]

Invited Review
A survey of literature on automated storage and retrieval systems
Kees Jan Roodbergena,*, Iris F.A. Visb,1
aRSM Erasmus University, P.O. box 1738, 3000 DR Rotterdam, The Netherlands
bVU 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
Abstract
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 timeestimation, storage assignment, dwell-point location, and request sequencing. The majority of the reviewed models and solution methodsare 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./C2112008 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 inter-ference of an operator, thus the system is fully automated.Both in production and distribution environments AS/RSsare used for putting products (e.g., raw materials or (semi-)finished products) in storage and for retrieving those prod-ucts 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 UnitedStates ( Automated Storage Retrieval Systems Production
Section of the Material Handling Industry of America,2005). The usage of AS/RSs has several advantages over
non-automated systems. Examples are savings in labourcosts and floor space, increased reliability and reducederror rates. Apparent disadvantages are high investmentscosts (approximately $634,000 for a single aisle AS/RS,
Zollinger, 1999 ), less flexibility and higher investments in
control systems (about $103,000, Zollinger, 1999 ).
In designing an AS/RS, many physical design and con-
trol issues have to be addressed in the right way to fully
take advantage of all its pros. This paper intends to presenta critical overview of all important issues concerning AS/RS design and control in both production and distributionenvironments while studying recent and past literature.
Previously, several overview papers have been published
that discuss part of the AS/RS literature. Almost all ofthese overview papers, however, have a focus different fromAS/RSs, for example, general warehouse design. Becauseof this, only a limited number of aspects of AS/RSs anda limited number of references with respect to AS/RSsare presented in those papers. Matson and White (1982)
review a number of material handling research areas one
of which is concerned with AS/RSs. Kusiak (1985)
0377-2217/$ – see front matter /C2112008 Elsevier B.V. All rights reserved.
doi:10.1016/j.ejor.2008.01.038*Corresponding author. Tel.: +31 10 4088723; fax: +31 10 4089014.
E-mail addresses: kroodbergen@rsm.nl (K.J. Roodbergen),
ivis@feweb.vu.nl (I.F.A. Vis).
1Tel.: +31 20 5986067; fax: +31 20 5986005.www.elsevier.com/locate/ejorAvailable online at www.sciencedirect.com
European Journal of Operational Research 194 (2009) 343–362

describes design and operational decision problems for
flexible manufacturing systems with a focus on automatedguided vehicles and AS/RSs. The author discusses design,storage and batching (i.e., consolidation of orders) policiesfor AS/RSs. Johnson and Brandeau (1996) discuss stochas-
tic 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 lit-
erature. 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 whilefocussing on travel time models. We conclude that ourpaper seems to be the first overview paper in over 10 yearsdevoted exclusively to AS/RSs, and the first ever to give abroad overview of all design and control issues in AS/RSs.
The main structure of the paper can be described as fol-
lows. First, we present a general description of AS/RSs anda classification of related design and control issues. Themain body of the paper consists of an overview of literaturediscussing solution methods for these design and controlproblems. At the end, we indicate relevant open researchquestions. In more detail, Section 2defines various types
of AS/RSs and describes some important technical charac-teristics. Section 3presents a classification of both physical
design and control issues. This broad introduction will befollowed in Section 4by a more detailed description of
methods that support each of the discussed physical designissues. Papers addressing individual control policies forstorage assignment (Section 5), batching (Section 6), park-
ing of idle AS/RSs (Section 7) and sequencing (Section 8)
will be discussed in subsequent sections. Travel time esti-mates and other performance measures will be treated in
Section 9. Section 10presents 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 accommodateloads (e.g., pallets) that need to be stored. Cranes are the
fully automated storage and retrieval machines that canautonomously move, pick up and drop off loads. Aisles
are formed by the empty spaces between the racks, wherethe cranes can move. An input/output point ( I/O-point )i sa location where retrieved loads are dropped off, and whereincoming loads are picked up for storage. Pick positions (if
any) are places where people are working to remove indi-vidual items from a retrieved load before the load is sentback 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) andwhich can transport only one unit-load at a time (singleshuttle). Product handling in this case is by unit-load(e.g., full pallet quantities) only; no people are involvedto handle individual products. The racks in the basic ver-sion are stationary and single-deep, which means that everyload 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 over-
view of the main options is presented in Fig. 1 .W ew i l l
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 pos-sible to have fewer cranes than aisles in the system. Thismay 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 alsoreferred to as dual-shuttle cranes ; cranes capable of trans-
porting more than two loads are still rarely seen. Theincreased 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 theAS/RS from other parts of the warehouse by means of, forexample, automated guided vehicles, conveyors, or forklifttrucks. The unit-loads are stored in the AS/RS and after aperiod 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 inthe warehouse; in which case the AS/RS serves to replenishthe picking area. Alternatively, the picking operation canbe integrated with the AS/RS. One option is to designthe crane such that a person can ride along (person-on-board). 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 pickingis when the AS/RS drops off the retrieved unit loads at aworkstation. A picker at this workstation takes therequired amount of products from the unit-load afterwhich the AS/RS moves the remainder of the load backinto the storage rack. This system is often referred to asanend-of-aisle system. If the unit-loads are bins, then the
system is generally called a minilo ad
AS/RS .
Storage in the racks may occur single or double deep. In
adouble-deep rack , each rack location has space for two344 K.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362

unit-loads; one load is stored in front of the other load. A
load can only be put into or retrieved from the second posi-tion if there is no load in the first position. Double-deepstorage might be beneficial if the variety of loads is rela-tively 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 andretrieve items from the rotating carousel. The lower andupper part of a double carousel can rotate independentlyof 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. Vehi-cles travel horizontally over rails through aisles, while liftsare used to transfer loads vertically.
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 theinflexibility of the physical layout and the equipment, it isessential to design it right at once. In Fig. 2 a schematic
view of design issues and their interdependence is
presented.
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 theother systems as are the other systems’ performancesinfluenced by the AS/RS. This is most visible at, but notrestricted 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 connectionfrom the I/O-point to the rest of the warehouse. Delays inone system can cause delays in the other system. Thus,when deciding on the number of I/O-points, their locationand their buffer capacity it may be necessary to also look atthe other systems’ characteristics.
Furthermore, the requirements for the AS/RS may
depend on the general environment of the system. In man-ufacturing environments the AS/RS primarily needs toprovide all required materials in time to make sure thatproduction can continue. Production is leading and shouldnever be halted to wait for the AS/RS. In distribution envi-AS/RSs
Rack Crane Handling
Stationary racks
Rotating racks
(carousel)
Horizontal Vertical
Single DoubleSingledeep Doubledeep Aislecaptive Aislechanging
Picking
Person-on-board End-of-aisle Unit loadLoads
Pallets BinsMovement Shuttle
Single DualMovable racks
Mobile racks(on rails)
Fig. 1. Classification of various AS/RS system options.
System
choiceSystem
configurationPhysical DesignAS/RS Design
Control
Storage
assignment
Dwell pointBatching SequencingPerformance measurement
Design of other material handling
systems in the facility
Fig. 2. Design of an AS/RS system.K.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362 345

ronments, the AS/RS performs or supports the order
retrieval process, to make sure that customers’ orders leavethe facility in time.
Part of the actual design of an AS/RS consists obviously
of determining its physical appearance. The physical designconsists of two aspects which together determine the phys-
ical manifestation of the system. First, we have the choice
of the AS/RS type ( system choice ). Second, the chosen sys-
tem must be configured, for example, by deciding on thenumber of aisles and the rack dimensions ( system configu-
ration ). These interrelated choices can be made based on,
among others, historical and forecasted data, productcharacteristics, 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 ofvarious AS/RS types along with selection criteria can befound in Allen (1992) .
A list of configuration decisions for any given type of
AS/RS is displayed in Table 1 . For a typical design prob-
lem, total capacity is given beforehand. This essentially
means that the mathematical product of the number of
aisles, rack height, and rack length is constant. Increasingthe number of aisles thus implies reducing rack lengthand/or height to maintain the desired storage capacity.Because of this relation, having more aisles indirectlyresults in shorter response times, due to the decreased racklength and height. Furthermore, design changes often havean 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 higherthroughput and higher investment costs.Even when the number of aisles is given, there is still a
trade-off between rack height and length. Since cranescan travel vertically and horizontally simultaneously, theactual travel time equals the maximum of the horizontaland vertical travel time (Chebyshev distance metric). Hor-izontal travel speeds are typically up to 3 m
2compared 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 neces-sarily optimal, configuration is one where the racks aresquare-in-time , which means that the time needed to reach
the highest row equals the time needed to reach the farthestcolumn. Any rack that is not square-in-time is calledrectangular .
Often racks have equally sized storage locations. How-
ever, to meet highly varying customers’ demand, it is alsointeresting to allow the storage of different shaped loadswithin a single rack. Also, an AS/RS may have more thanone I/O-point per aisle. Instead of only placing an I/O-point at the front of an aisle, another one might be locatedat the middle and/or rear of the aisle. In that way, forexample, 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 proce-
dure should simultaneously address both physical designand control issues of the system. Regardless of the actualoptimisation procedure, a system of performance measure-
ment is needed to evaluate the overall performance of the
resulting system at every stage. This underlines the impor-tance of performance measurement in the field. Many pub-lications 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 operationof 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 posi-tion where an idle crane (i.e., a crane that has no jobs toperform) waits is determined by a dwell-point policy . The
dwell-point is best chosen to minimise the expected timeto 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 sin-
gle command cycle the crane performs either a single stor-
age or a single retrieval request. The storage cycle time
then is equal to the sum of the time to pick-up a load atthe input station, the time to travel to the storage location,the time to place the load in the rack and the time to returnto 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 com-
mand cycle . In this case, the cycle time is defined as the
sum of the time to pick-up the load, the time to travel toTable 1
Overview of design decisions for AS/RSs
Class of problems Decisions to be made
System
configuration/C15Number of aisles
/C15Height of the storage racks
/C15Length of the aisles
/C15Equally sized or modular storage locations
/C15Number and location of the I/O-points
/C15Buffer capacity at the I/O-points
/C15Number of cranes per aisle
/C15Number of order pickers per aisle (if any)
Storage assignment /C15Storage assignment method
/C15Number of storage classes
/C15Positioning of the storage classes
Batching /C15Type of batching (static or dynamic)
/C15Batch size (capacity or time based)
/C15Selection rule for assignment of orders to
batches
Sequencing /C15Sequencing restrictions (e.g., due dates)
/C15Type of operation (single or dual command)
/C15Scheduling approach (block or dynamic)
/C15Sequencing method
Dwell-point /C15Type of positioning (static or dynamic)
/C15Location where idle cranes will be placed.346 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 andtransport it to the output station. Clearly, the total timeto perform all storage and retrieval requests reduces if dualcommands are performed. A tourof an AS/RS consists of a
sequence of single or dual command cycles, starting at theorigin of the first request and ending at the destination ofthe last request. Sequencing rules can be used to create
tours such that the total time to handle all request is mini-mised 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 thecrane (mainly applicable to person-on-board AS/RS).
Table 1 provides an overview of all control decision prob-
lems that may need to be selected. From literature it is
known that certain combinations of control policies workbetter than other combinations. In Sections 5–8we present
an extensive discussion of all AS/RS control policies thathave been treated in literature.
4. Physical design
Only a few papers address the design of AS/RSs in com-
bination with the design of other material handling systems
in the facility. Most of these papers consider manufactur-ing environments. Chincholkar and Krishnaiah Chetty,
1996 use approaches as Petri Nets and the Taguchi method
to simultaneously address the scheduling of jobs to anAS/RS system and the scheduling of jobs to machines ina flexible manufacturing system. The AS/RS is both
responsible for storing and retrieving loads and for trans-
ferring them between machines. Inman (2003) studies the
usage of AS/RSs in the automotive industry. The functionof the AS/RS is to restore the sequence in which jobs arehandled at the various processes in the facility. A modelis proposed to determine the capacity of the AS/RS basedon the number of jobs that need to be rescheduled. As aresult, 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 proposedto determine the optimal number of loads to be transferredby each AGV to machines in combination with an optimaldesign of the AS/RS. Park and Webster (1989a) address the
design of warehouses by proposing an approach that simul-
taneously selects the used storage equipment, that might be
an AS/RS, and the overall size and shape of the storagearea.
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 exper-
imental approaches (e.g., Lim et al., 1996 ) have been pro-
posed in the literature. We will use the classification asindicated in Table 1 in our discussion on solution proce-dures that assist in decision making for one or multiplephysical design issues in combination with one or morecontrol issues. Table 2 presents an overview of papers
and indicates which issues the authors address. Note thatwe do not mark a control policy if it is only used as a fixedinput 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 sincethey 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 thatconfigurability of control policies is very limited. Further-more, only few configurations and types of AS/RSs havebeen 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 sim-
ulation study. These authors examine the effect of differentsequencing rules on six layout configurations (with a vary-ing I/O-point, item distribution over racks, rack configura-tion and rack dimensions). Based on a limited number ofexperiments 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 higherthroughput.
In our opinion, in general the strength of simulation
could be better exploited in AS/RS research to comparenumerous designs, while taking into account more designaspects, especially in combination with control policies.Also, sensitivity analyses on input factors should be per-
formed such that a design can be obtained which can per-
form well in all applicable scenarios. As a result moregeneral information could be obtained on good designpractices.
Rosenblatt et al. (1993) already tried to overcome this
drawback of existing simulation models by alternatinglyusing optimisation and simulation in order to reach thebest 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 multipleaisles to conclude that multiple-aisles AS/RSs might beinteresting if the number of storage and retrieval requestsare 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 analyt-
ical design models. From the overview in Table 2 we con-
clude that all models address some, but certainly not allphysical design aspects. None of the physical analyticaldesign models includes any of the mentioned control deci-sions problems.
Summarising, most research is performed on determin-
ing 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. Further-more, hardly any attention has been paid to the locationK.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362 347

Table 2
Overview of research in design models that can assist in decision making for physical design in combination with control issues
Solution
approachAuthors Type of AS/
RSSystem configuration Controls
Storage
racksStoragelocationsNumberof cranesNumber of aislesand their lengthNumber of I/O-points and
locationNumber of
order
pickersBuffer
capacityStorageassignmentDwell-pointBatching Sequencing
Simulation Ashayeri et al.
(1983)Unit-load
Houshyar andChung (1991)Unit-load /C2
Taboun andBhole (1993)Unit-load /C2/C2
Randhawa andShroff (1995)Unit-load /C2/C2 /C2 /C2
Lee et al. (1996) Unit-load /C2
Potrcˇet al.
(2004)Unit-load andmulti-shuttle/C2 /C2
Simulation
andanalyticalRosenblatt et al.(1993)Unit-load /C2/C2 /C2 /C2
Analytical Karasawa et al.(1980)Unit-load /C2/C2
Zollinger (1982) Unit-load /C2/C2
Ashayeri et al.(1985)Unit-load /C2
Azadivar (1987) Unit-load /C2
Bozer and White
(1990)End-of-aisleminiload/C2
Van Oudheusden
and Zhu (1992)Person-on-board/C2
Bozer and White(1996)End-of-aisleminiload/C2/C2
Chang and Wen(1997)Unit-load /C2
Hwang and Ko(1988)Unit-load /C2/C2
Park et al. (1999) End-of-aisleminiload/C2
M
almborg
(2001a)Unit-load /C2/C2
Malmborg(2001b)Multi-shuttle
Malmborg (2002,2003a)Autonomousvehicle S/R/C2/C2
Koh et al. (2005) End-of-aisle
miniload/C2
Lee et al. (2005) Unit-load /C2348 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 distribu-
tion centres (e.g., cross-docking areas), it might, for exam-ple, be interesting to locate I/O-points at both ends of astorage rack. Also, only little research has been performedon the configuration of multi-shuttle AS/RSs, whichalready have been proven to be efficient in terms of
throughput. From the literature studied, it can be con-
cluded that most authors combine only one or a few con-trol rules with their physical design research. Batchingand dwell-point locations have not been considered inphysical design. Thus, despite the fact that decisions inboth categories (physical design and control rules) arehighly 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 orGraves et al., 1977 ). These
rules are:
/C15dedicated storage assignment
/C15random storage assignment
/C15closest open location storage assignment
/C15full-turnover-based storage assignment
/C15class-based storage assignment
For the dedicated storage method each product type is
assigned to a fixed location. Replenishments of that prod-
uct always occur at this same location. The main disadvan-tage of dedicated storage are its high space requirementsand consequent low space utilisation. This is due to the factthat locations are reserved even for products that are out ofstock. Furthermore, for each product type sufficient spacemust be reserved to accommodate the maximum inventorylevel that may occur. Most advantages of dedicated stor-
age, such as locating heavy products at the bottom or
matching the layout of stores, are related to non-auto-mated order-picking areas and are not as interesting forAS/RSs. For random storage all empty locations have an
equal probability of having an incoming load assigned toit. If the closest open location storage is applied, the first
empty location that is encountered will be used to storethe 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).
Thefull-turnover storage policy determines storage loca-
tions for loads based on their demand frequency. Fre-quently requested products get the easiest accessiblelocations, usually near the I/O-points. Slow-moving prod-ucts are located farther away from the I/O-point. Animportant assumption for this rule is that the turnover fre-
quencies need to be known beforehand. Heskett (1963,
1964) presents the cube-per-order index (COI) rule, whichis a form of full-turnover storage. The COI of a load is
defined as the ratio of the load’s required storage spaceto the number of request for this product per period. TheCOI rule assigns loads with the lowest COI to the locationsclosest 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 com-
mand 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 arefixed inventory levels and a fixed balanced assignment oforder pickers to items. However, according to Lee (1992)
the COI-rule cannot be applied for person-on-board sys-tems due to the fact that an order usually consists of more
than two independent items at different locations. There-
fore, the author develops a new heuristic that outperformsthe COI-rule.
For practical purposes it is easiest if a full-turnover pol-
icy is combined with dedicated storage. The problem is thatdemand frequencies change constantly and also the productassortment is usually far from constant. Any change in fre-quency 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 preventexcessive repositioning, a new storage allocation is in prac-tice typically calculated once per period. To reduce spacerequirements and periodic repositioning while maintainingmost 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 sub-
sequently assigned to one of the areas, based on the item’sdemand frequency. Random storage is applied within anarea. Actually, the full-turnover storage policy can be seenas a class-based policy with only one item per class. Oftenclass-based storage with three classes is referred to as ABC
storage. This reflects the common practice to call the fast-
est-moving items the A-items, the next fastest-moving items
theB-items , and so on. The main advantage of class-based
storage is an increased efficiency due to storing the fast-moving items near the I/O-point, while at the same timethe low storage space requirements and flexibility of therandom storage method apply.
A designer faces three major decisions when implement-
ing 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
zones).
From Table 3 it can be seen that several types of zone siz-
ing procedures have been developed to derive boundariesK.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362 349

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-timeracks which are a special case of rectangular racks. BothRosenblatt 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 ofthe potential savings in travel times as compared to full-turnover storage. In practice, often the number of classesis restricted to three. Van den Berg (1996) proposes a
dynamic programming algorithm that assigns both loca-tions 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-in-time racks. Graves et al. (1977) demonstrate through sim-
ulation 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. Theirconclusion is that the performance of each of the proposedshapes depends on the location of the I/O-point and thatnone is superior to the others. Eynan and Rosenblatt
(1994) present a layout for nclasses in rectangular racks
while single command scheduling is used. This layout com-bines n/C02L-shaped zones, a transient region for class
n/C01 and a rectangular zone for class n.Fig. 3 presents
examples of zone shapes for both types of racks for threeclasses.
Some variations of the class-based storage policy have
been studied. Park and Webster (1989b) propose a class-
based storage method in a three-dimensional system whichminimises total travel times. Hsieh and Tsai (2001) suggest
a class-based method for production facilities based on thebill of materials. Thonemann and Brandeau (1998) alter the
algorithms of Hausman et al. (1976) such that they can beTable 3
Solution procedures to derive optimal boundaries for zone sizing decisions in class-based storage
Single command Single command Dual command
Square-in-time racks Rectangular racks Rectangular racks
Two
classesNumerical procedure ( Hausman et al., 1976 ) Formula ( Kouvelis and Papanicolaou, 1995 ) Search procedure ( Kouvelis and Papanicolaou, 1995 )
Three
classesNumerical procedure ( Hausman et al., 1976 ) No paper is specifically written about this; problemcan be solved using n = 3 in solution approaches for n
classesNo paper is specifically written about this; problem can be solved using
n = 3 in solution approaches for n classes
nClasses No paper is specifically written about this; problem canbe solved using solution approaches for rectangular
racksRecursive procedure ( Rosenblatt and Eynan, 1989 )
or Dynamic programming ( Van den Berg, 1996 )Kouvelis and Papanicolaou (1995) suggest to use their formulas in
combination with the recursive procedure of Eynan and Rosenblatt
(1993) for this problem
ABC
ABC
Fig. 3. Typical zone positioning for three classes in respectively square-in-
time (upper part) and rectangular racks (lower part).350 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
forcarousels . The racks in the carousel are partitioned into
two regions with an appropriate boundary shape (above ornext to each other). Bengu ¨(1995) studies an organ pipe
arrangement for carousels in which the items with the high-est access probability are located in the middle and the restis positioned at the left or right side according to a decreas-ing 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 con-
figurations are an appropriate analytical tool for compar-
ing 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., Sch-
warz et al., 1978; Kaylan and Medeiros, 1988; Kulturelet al., 1999; Van den Berg and Gademann, 2000 ).Malm-
borg (1996) and Malmborg and Altassan (1998) develop
a storage policy trade-off for respectively unit-load andsmall systems to roughly compare different policies in ashort time prior to a simulation study.
Results from both analytical and simulation studies
show that full-turnover-based and class-based storageassignment outperform random storage. Kulturel et al.
(1999) compare a three class-based policy with a duration
of stay policy , which was originally introduced by Goe-
tschalckx and Ratliff (1990) . While applying the duration
of stay policy, products with the shortest duration in thewarehouses are assigned to storage locations closest tothe I/O-point. The three-class-based policy only outper-forms the duration of stay policy if the number of producttypes 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
policies.
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 thedesired performance level (e.g., Muralidharan et al., 1995;
Jaikumar and Solomon, 1990 ). The COI policy is usually
well applicable in static environments with independentdemand of products. Moon and Kim (2001) show by
means of a simulation study that re-location of items isrequired if the production quantity of each item changesover time. Sadiq et al. (1996) propose a dynamic storage
assignment policy to reassign items to storage locationsin systems with a rapidly changing product mix and shortproduct life cycles. By using predicted future productmix, correlated demand of products and demand forecasts,the dynamic policy intends to minimise total order process-
ing times, which consist of order-picking times and relocat-
ing times. It is shown that this dynamic policy outperformsthe static COI rule.Summarising, in literature various storage assignment
policies have been developed and were compared boththrough simulation and analytical methods. Most authorsaddress single aisle AS/RSs with one I/O-point. Storageassignment policies for other types of configurations (e.g.,multiple I/O-points) or other types of AS/RSs (e.g., multi-
ple 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 wecould try to combine several orders in a single tour of thecrane. The latter approach is called batching . Batching
problems for person-on-board AS/RSs are quite similarto 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 withcranes 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 sortitems later on. A limit on the size of a batch is usuallydetermined by the capacity of the crane or an upper limiton the required response time. As a result, an importantdecision problem in batching is the determination of thesize of each batch in combination with the assignment oforders to these batches such that travel times are mini-
mised. 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 ( Arm-
strong et al., 1979 ) is NP-hard.
To obtain solutions for large problems in acceptable
computation times, numerous heuristics have been devel-oped. As presented in Fig. 4 , most heuristic batching meth-
odsbasica
lly follow the same three steps: a method of
initiating batches by selecting a seed, a method of allocat-
ing orders to batches, and a stopping rule to determinewhen a batch has been completed. An important assump-tion in all heuristics is the fact that a single order cannotbe split over various batches, but needs to be picked as awhole. Table 4 indicates several seed selection, order addi-
tion 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 attri-bute vectors related to storage locations of an order andsimilarity measures, based on, for example, the boundariesof 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 willK.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362 351

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 wellas the storage assignment policies have been varied. Theauthors conclude that only the storage capacity of a cranehighly impacts the choice for a certain rule. Based on theresults 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 mea-sures both the earliness and tardiness of orders. Further-more, all mentioned papers assume that the arrival
patterns of orders are known before the start of the opera-
tions. However, in many warehouses there is a batch-arri-val component (for example, orders left from theprevious day that did not make the departure time) andan on-line component. It is known that batching becomesmore difficult when orders arrive on-line (see e.g., Bhaska-
ran and Malmborg, 1989 ). This is due to the fact that there
is a trade-off for on-line arrivals between reducing waitingtimes (by calculating batches frequently based on few avail-able orders) and reducing travel times (by calculatingbatches less frequently to obtain more possibilities for effi-
cient combinations).
7. Dwell-point location
Several methods have been proposed to deal with the
decision where to position an idle crane, i.e., how to deter-
mine the crane’s dwell-point .Bozer and White (1984) intro-
duced four simple static dwell-point strategies. Table 5
summarises these rules and indicates the resulting one-
dimensional 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 periodis a storage request, is at least 1/2.
Egbelu (1991) proposes linear programming models that
are capable of responding to fluctuations in types ofrequests. A two-dimensional dwell-point location (includ-ing 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 thefacts that LP solution techniques need to be implementedin the AS/RS control system and that computation timesmay 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 transform-
ing 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 rulesare compared with a small number of replications for justone layout with five different arrival rates of requests underrandom and dedicated storage policies.
Several static approaches have been proposed for other
types of unit-load AS/RSs. Chang and Egbelu (1997) con-
sider a single crane serving multiple aisles. A mathematicalInitiate batch by selecting a first
order (i.e. seed) based on aseed selection rule
Allocate orders to batches by using anorder addition rule
Decide if batch is complete by using a stopping ruleNo Yes, start
a new batchcumulative/
cluster method
Fig. 4. Common structure for batching heuristics.
Table 4
Overview of seed selection, order addition and stopping rules for batching
Type of rule Rule Author
Seed selection Order with largest number of locations to be visited Elsayed (1981)
Order with smallest number of locations to be visited Elsayed (1981)
Order with largest volume Elsayed (1981)
Order with smallest volume Elsayed (1981)
Order with highest percentage of capacity of crane Elsayed and Unal (1989)
Cumulative rule Elsayed and Stern (1983)
Clustering rule Hwang et al. (1988) andHwang and Lee (1988)
Order addition Largest number of common locations Egbelu (1991)
Geometric similarities Hwang and Lee (1988)
Stopping rules Capacity constraint Several
Time constraint Several
All orders are completed Several352 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. Exceptfor the location and height, the exact aisle also needs to bespecified. Peters et al. (1996) developed closed-form analyt-
ical models to determine dwell-points in continuoussquare-in-time and rectangular racks under random stor-
age based on the travel time estimations of Bozer and
White (1984) .Park (1999) developed an optimal dwell-
point policy for square-in-time racks under dedicated stor-
age. Park (2001) shows that for rectangular racks under
random storage the dwell-point location can be determinedin terms of the probability of occurrence of a certain typeof request. Van den Berg (2002) presents analytical expres-
sions 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 con-
figurations 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 programmingapproaches have been formulated to position idle AS/RScranes at a dwell-point in various AS/RS configurations.
Most approaches address static positioning of single unit-
load capacity AS/RSs and do not study other types ofAS/RSs. So far, no extensive and statistically sound simu-lation study has been performed on dwell-point policies incombination with other physical design and control issues(see also Table 2 ) which makes it difficult to provide design-
ers with an advice when to use which policy.
8. Sequencing of storage and retrieval requests
Storage requests in distribution or production environ-
ments are usually not time-critical. The exact point in time
at which loads are stored is not of much importance for theperformance of the system. Therefore, storage requests are
usually stored according to the first-come-first-served prin-
ciple. In sequencing retrievals usually due times of retri-evals should be met, which makes it necessary to lookbeyond simple first-come-first-served. Furthermore, bysequencing the retrievals in a smart way, improvementsin 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, sequencethem 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 anew request is added and use due times or priorities. Werefer 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 spec-
ified non-deterministic environment, the block sequencing
strategy might be inappropriate. However, a blocksequencing approach is more transparent and simpler withrespect to implementation.
Various algorithms and heuristics can be used to sche-
dule storage and retrieval requests within a block. Themain objectives in those approaches are to minimise total
travel times or total travel distances. Most literature
focuses on single and dual command scheduling of unitload AS/RSs with one input/output station and one craneper aisle. Therefore, we first discuss sequencing methodsfor this basic sequencing problem. In Section 8.2, we dis-
cuss extensions of the basic sequencing problem. Thesequencing problem of other types of AS/RSs is treatedin 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 singlecommand 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 ofperforming dual command cycles depends on the availabil-ity of storage and retrieval requests. If both types ofrequests are available, dual command cycles give advanta-ges with respect to travel times ( Graves et al., 1977 ).
An alternative might be to perform dual commands
whenever possible and single commands otherwise. Eben-
Chaime and Pliskin (1996, 1997) show that systems that
operate under this more hybrid mode might achieve morestable waiting lines and can use less cranes. Some ware-houses, however, have patterns in arriving and leavingloads. For example, trucks with incoming loads arrive inthe morning and trucks transporting outgoing loads arrivein the evening. In this case, cranes might perform singlecommand 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 )
Rule Dwell-point
Input station Always at input station
Midpoint Always at midpoint location of racks
Input/output If a single command storage request has been performed then positioning at input station
If a single command retrieval request or a dual command has been performed then positioning at output station
Last location If a single command storage request has been performed then positioning at last storage locationIf a single command retrieval request or a dual command has been performed then positioning at output stationK.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362 353

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 NP-
complete. Han et al. (1987) indicate that in general the
problem of optimally sequencing a given list of requestsisNP-hard. One of the reasons for this complexity is
the fact that the set of locations available for storagedepends on where previous loads are stored and which
retrievals have already been performed. However, some
special cases of the sequencing problem can be solved inpolynomial time. A summary of these results is showninTable 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 performedto compare the performance of these heuristics in combina-tion with several storage assignment policies (see, e.g., Linn
and Wysk, 1987 ).Han et al. (1987) show that the nearest-
neighbour heuristic can provide a lower average cycle timethan the first come first served rule. Furthermore, it isshown that the nearest-neighbour heuristic has a better per-formance 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 farfrom the input station remain open.Eynan and Rosenblatt (1993) conclude that quite signif-
icant savings in interleaving times can be obtained by com-bining nearest-neighbour scheduling with class basedstorage assignment. Schwarz et al. (1978) investigate the
performance and predictions of previously developeddeterministic models in a stochastic environment. It isfound that the results of the models hold in this environ-ment. However, the predictions in improvements are gener-
ally 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), arti-
ficial intelligence (e.g., Seidmann, 1988 ), genetic algorithms
(e.g., Krishnaiah Chetty and Sarveswar Reddy, 2003 )a n d
the Taguchi method (e.g., Lim et al., 1996 ). These methods
can be applied in situations with high uncertainty and littleinformation. Furthermore, these methods are capable of
learning and adapting to changes in the environment, suchas fluctuations in demand. The output can consist of com-binations of storage assignment, retrieval location selec-tion, queue selection and job sequencing.
8.2. Extensions of the basic sequencing problem
An extension of the previously described basic schedul-
ing problem is the problem in which storage and retrieval
requests with release and due times need to be scheduled.Table 6
Solvable special cases of the basic sequencing problem for unit-load AS/RS
Characteristics of case Steps of solution method Authors
/C15Non-dedicated storage
/C15The number of storages equals the number of
retrievals
/C15A single I/O point1. Solve assignment problem to combine storage (with location) with
retrieval requests
2. Apply Murthy’s ranking algorithm ( Murthy, 1968 ) to search assign-
ment 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
(1996)
/C15Dedicated storage
/C15The number of storages is smaller then or equal
to the number of retrievals
/C15A single I/O-pointCan be translated into an assignment problem Lee and Schaefer
(1997)
/C15Dedicated storage
/C15Any number of storage and retrieval requests
/C15A separate input and a separate output pointthat might be positioned at different locationsof the rackTransportation 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 minimisedVan den Berg and
Gademann (1999)
Table 7
Methods for dynamic sequencing of unit-load AS/RS
Rule Description
First-come-first-served Retrieval requests will be scheduled in order of appearance
Shortest completion time Retrieval request with shortest completion time will be served first
Nearest-neighbour ( Han et al., 1987 ) Pairs of storage and retrieval requests are chosen such that the distance from the storage to the retrieval location
is minimal
Shortest leg ( Han et al., 1987 ) 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
On-line asymmetric TSP ( Ascheuer
et al., 1999 )Approach includes heuristics and an optimal branch-and-bound method to determine sequences for all known
loads354 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 inthe case that all requests or a group of requests have onecommon 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 stationat each aisle and systems with two input/output stationsat each aisle. It is shown that reductions in expected craneround trip times and in throughput times can be obtainedfor systems with two input/output stations.
Kanet and Ramirez (1986) add location selection to the
scheduling problem in case products are stored at multiplelocations. This decision is incorporated in the integer pro-gramming model by including costs per retrieval operationand costs to separate items at a location into different partsrelated 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 thatare 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 storageand 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 loca-tions are visited before returning to the I/O-point. Simplenearest-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 sys-
tem after items have been picked. Therefore, the problem can
be reformulated such that only a queue of retrieval requestsexists, which result in a less complicated problem. The pickerat the end of the aisle also needs to be incorporated in themodel. Retrieval requests are rearranged such that succes-sive requests are located close to each other. Storages and ret-rievals which are close to each other can be paired by anearest-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 anddouble shuttle carrousel storage and retrieval systems.
Summarising, various methods are described in the liter-
ature to schedule storage and retrieval requests such that
the total (empty) distance travelled is minimised. The situ-
ation considered in the majority of the literature concernsan unit-load AS/RS working in one aisle with one input/output station. For some specific instances optimalsequencing methods exist. However, the general dynamicsequencing problem is hard to solve and, therefore, heuris-tics have been developed to find feasible schedules. Hardlyany 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 operatesin multiple aisles. Although multi-shuttle cranes have pro-ven to be successful, only a few heuristics have been devel-oped 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 leastconsider the following performance measures:
/C15travel time per request,
/C15number of requests handled per time period (e.g., Azadi-
var, 1986; Foley et al., 2002 ),
/C15total time required to handle a certain number of
requests,
/C15waiting times of cranes of the AS/RS,
/C15waiting times of products to be stored/retrieved,
/C15number 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 othermodel 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 pres-ent a categorisation of all literature in Table 8 by discussing
the main characteristics of each paper. We discuss some ofthese papers in more detail to provide a rough line of
research in this area. First we discuss travel time models
forsingl
e 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.K.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362 355

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
AS/RS
characteristicsAuthors Layout Rack I/O point(s) Storage Scheduling Operational characteristics
SingleaisleMultipleaislesSquare-in-timeNonsquare-
in-timeContinuous Discrete Unequal
sizedcellsSingle
locationSingle I/O atvarious
locationsMultiple
locationsRandom Dedicated Full-
turnovern-
class
basedSingle
commandDualcommandMore thandual
commandNone (or
implicitly)Acceleration/decelerationMaximumvelocityStochasticenvironmentDwell-point
Unit-load Hausman et al.(1976)/C2/C2 /C2 /C2 /C2 /C2 2,3 /C2/C2
Graves et al.(1977)/C2/C2 /C2 /C2 /C2 x 2,3 /C2 FCFS /C2
Bozer and White(1984)/C2/C2 /C2 /C2 /C2 /C2 FCFS /C2
Han et al. (1987) /C2/C2 /C2 /C2 /C2 NN /C2
Hwang and Ko(1988)/C2/C2 /C2 /C2 /C2 /C2 /C2
Rosenblatt andEynan (1989)/C2/C2 /C2 /C2 N /C2/C2
Kim and
Seidmann (1990)/C2/C2 /C2 /C2 /C2 /C2 N /C2/C2 /C2
Hwang and Lee
(1990)/C2/C2 /C2 /C2 /C2 /C2 /C2 /C2 /C2
Eynan andRosenblatt
(1993)
a/C2/C2 /C2 /C2 NN N x
Eynan and
Rosenblatt(1994)/C2/C2 /C2 /C2 N /C2/C2
Chang et al.
(1995)/C2/C2 /C2 /C2 /C2 x /C2/C2
Kouvelis and
Papanicolaou(1995)/C2/C2 /C2 /C2 /C2 2 /C2 x /C2
Pan and Wang
(1996)/C2/C2 /C2 /C2 N FCFS /C2
Mansuri (1997) /C2/C2 /C2 /C2 /C2 /C2 /C2
Thonemann and
Brandeau (1998)/C2/C2 /C2 /C2 /C2 /C2 2,3 /C2 /C2
Lee et al. (1999) /C2/C2 /C2 /C2 /C2 /C2 /C2 x /C2
Wen et al. (2001) /C2/C2 /C2 /C2 /C2 /C2 /C2 /C2
Ashayeri et al.(2002)/C2/C2 /C2 /C2 /C2 /C2 FCFS
Eldemir et al.(2004)/C2/C2 /C2 /C2 /C2 /C2 /C2
Unit-load Sarker et al.(1991)/C2/C2 /C2 /C2 /C2 NN /C2
Multiple
shuttleKeserla and
Peters (1994)/C2/C2 /C2 x /C2/C2 NN /C2
Meller and
Mungwattana(1997)/C2/C2 /C2 /C2 /C2 /C2 x
Malmborg
(2000)/C2/C2 /C2/C2356 K.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362

The authors proposed estimates for single command sched-
uling in square-in-time continuous racks. Random, full-turnover, two- and three-class-based storage assignmentpolicies were considered. Graves et al. (1977) extended
those results by also considering interleaving times result-ing from a first-come-first-served (FCFS) dual command
scheduling policy.
Bozer and White (1984) relaxed some of the assump-
tions by proposing travel time models for rectangular racks
with alternative single I/O-points. The authors consideredFCFS dual command scheduling and random storage ascontrol policies. The authors introduce bas the shape factor
of the rack to deal with rectangular racks. Hereb¼minðt
h=T;tv=TȚ, where thindicates the horizontal tra-
vel time to the farthest column, tvthe vertical travel time
to the farthest row and T¼maxðth;tvȚ. Based on empirical
tests, the authors conclude that the model’s performance issatisfactory.
Other authors since then mainly continue the research of
Hausman et al. (1976), Graves et al. (1977) and Bozer andWhite (1984) by studying different control policies, config-
urations 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 pro-
posed 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(seeHwang 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 mini-
mum number of cranes and number of aisles served by eachcrane.
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 storageassignment 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.,Miniload Foley and
Frazelle (1991)/C2/C2 /C2 x FCFS /C2
Park et al.
(2003)b/C2/C2 /C2 /C2 /C2 /C2 /C2 /C2 x
Park et al. (2006) /C2/C2 /C2 /C2 2 FCFS /C2
Person-on-
boardElsayed and
Unal (1989)/C2/C2 /C2 /C2 x /C2
Multi-
commandcGuenov
and Raeside
(1992)/C2/C2 /C2 3
Chiang et al.(1994)
d/C2/C2 /C2 /C2 /C2 /C2
Carousel Hwang and Ha
(1991)e/C2/C2 x /C2/C2 /C2
Rotating
tower
craneKoh et al. (2002) /C2/C2 /C2 x /C2/C2
Platforms/
heavyloadsHu et al. (2005) /C2/C2 /C2 /C2 /C2 /C2
Flow-rack
AS/RSSari et al. (2005) /C2/C2 x /C2
aGives an estimate for interleaving times.
bThe authors also consider variance in travel times.
cTravel time estimates to visit nlocations.
dFor remark on classification see section 3.
eBoth single and double carousels are considered.K.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362 357

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
policies.
In miniload AS/RSs picker and crane are dependent on
each other; delays of one influence the performance of theother. Foley and Frazelle (1991) consider a miniload
square-in-time AS/RS operating under a FCFS dual com-mand scheduling policy and random storage. Also closed-form travel time expressions for miniload AS/RSs withone- and two-class-turnover based storage have been for-mulated ( Park et al., 2003, 2006 ).
Person-on-board AS/RSs usually handle multiple loca-
tions 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 traveltimes based on the number of locations to be visited givena 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 ofupcoming orders. Clearly, an increase in throughput canbe 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 rotatingtower cranes ( Koh et al., 2002 ), heavy load platform based
AS/RSs ( Hu et al., 2005 ) and flow-rack AS/RSs ( Sari et al.,
2005).
Summarising, it can be concluded that travel time mod-
els for both square-in-time and rectangular racks have beendeveloped for unit-load AS/RSs operating under mostcommon storage assignment policies and two sequencingheuristics derived from practice. So far no studies havebeen performed that include dwell-point rules in travel timeestimates. Compared to unit-load AS/RSs, many issues,
such as N-class based storage or operational characteris-
tics, 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 custom-
ers’ orders. In designing an AS/RS, various physical design
problems and control problems need to be solved (seeSection 3). Literature related to the various interrelated
physical design and control problems, such as storageassignment, batching, dwell-point location and requestscheduling was treated in Sections 4–8. To evaluate the per-
formance of AS/RSs, we can use, for example, the traveltime estimates we discussed in Section 9.
From the literature survey, we conclude that most of the
literature addresses design and control problems in staticenvironments. However, in today’s world of rapidly chang-ing customers’ demand, small internet orders, tight deliveryschedules, high competition and high service level require-ments, it will be increasingly difficult to maintain a goodperformance 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 busi-ness. In this context, one can think of self-adaptive storageassignment methods, on-line-batching policies and dynamicdwell-point rules. Also algorithms for physical design mayneed to focus more on robustness of the design than on per-fect optimality to ensure that the system will be capable ofremaining efficient in yet unknown future situations.
Furthermore, almost all existing papers just address one
or two decision problems simultaneously, instead of jointlyoptimising a combination of physical design problems andcontrol problems (including batching, dwell-point rulesand I/O-point decisions). Obviously, it is not a simple exer-cise to include a multitude of design and control aspects inone model. However, we would like to encourage the devel-opment 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 inproduction or distribution facilities. Especially in situationswhere the AS/RS is just one of many systems, total ware-house performance cannot be assessed by simply addingup performances of all individual systems. An integrated
approach would be desirable. Therefore, we advice – as a
first step – to develop approaches which simultaneouslyoptimise the design of an AS/RS and another material han-dling system. For example, by explicitly considering theinterface between an AS/RS and a conveyor system, orby analysing the impact of replenishments by the AS/RSto a separate order-picking area.
Except for those general issues, further detailed research
can also be advised for each of the following issues.
/C15Models to assist in AS/RS type selection.
/C15Analytical and simulation models for the design of non-traditional AS/RSs (e.g., multi-shuttle AS/RSs).
/C15Storage assignment policies for multi-shuttle AS/RSs.
/C15Storage assignment policies for AS/RSs working in mul-tiple aisles and/or multiple I/O-points.
/C15Policies which simultaneously address storage assign-ment and batching of orders.
/C15Superior heuristics for batching that outperform allexisting rules in various settings.
/C15Dwell-point rules for non-traditional AS/RSs.
/C15Algorithms or heuristics to schedule AS/RSs in a singleaisle with multiple I/O-points.
/C15Travel-time models for AS/RSs operating in a single
aisle with multiple I/O-points.
/C15Travel-time models which incorporate operational char-
acteristics of non-traditional AS/RSs.358 K.J. Roodbergen, I.F.A. Vis / European Journal of Operational Research 194 (2009) 343–362

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