Table of Contents
The optimization of a picker to product Order Picking System:
a supporting decision tool based on a multi-parametric simulation approach
Eniilio Ferari, Mauro Gambari, Riccardo Mancini (4), Arrigo Pareschi,
Alessandro Persona (*) and Alberto Regaitieri
Department of Mechanical Engineering (Plant Section), University of Bologna, Italy
(*) Department of Management and Engineating, University of Padova, Italy
(4) comesponding author vie Risorgimento 2, 40136 Bologna, Italy
Abstract
Modem fulfilment centers need to process a far higher volume of smaller odes with increasing
Picking costs. These picking costs can be up to 60% of total warehousing costs. Order picking is a
yuocess of gathering requested stock keeping units one order at a time, while picking operations
involve a lot of lage and medium-sized companies which belong to many incistia and savice
sectors. A significant example is now represented by the recent growth of ecommerce companies,
which operate in growing global and extended markets. This study shows and measures the impact
of altemative policies and configurations of manual picker to part order picking systems, with the
aim of designing and optimizing robust fatilities minimizing goba cots and maximizing thar
perfonmances in terms of efficiency and customer service quality. The impact of the most citical
and decisive parametass is quantified by a dynamic mullti-parametic modding of warehousing
system and by using an integrated approach. Contpared to the studies in the literature this approach
is imovative The amlysis is based on modding of thousands of whetif soemarios, which
interactively support the management decision making process. The effectiveness of simulation as a
supporting decision tool is justified by the computational complexity of the whole design problen
and by asset of innovative and practical results useful to system designer and controller.
Keywords
Order picking, picker to product, simulation, design and control optimization, class based storage.
1. Introduction
New, global and extended markets have to process and manage increasingly differentiated products
with shorter life cycles, low volumes and reducing customer deivey times. To survive in today's
global marketphoe, companies need to be able to ddiver products on time, maintain market
credibility and introduce new products and services faster than competitors. Recent growth and
strength devdopment of ecommerve has brought a new focus on warehousing facilities and in
particular on the design and management of Order Picking Systems (OPS).
The advanced technology can shrink geographical distance and restructure supply chains, enhancing
industial alliances and enabling efficent timely exchange of infomation between purchases and
suppliers, but needs to be integrated with efficient mamufactming and logistic operating policies.
These policies could efficiently support physical and dectronic information flows, and drastically
reduce global system costs. Ecommerce fulfilment centers need to process a far higher volume of
smaller ordes with increased picking oosts. Modem companies attempt to achieve high-volume
Foduction and distibution using minimal inventories throughout the logistic chan and aoconing
to shorter response time (van dm Bag 1999). They ae replacing sved rdaivedy small
distibution centers with a small mumber of lager ones, coveiing more extensive networks and
involving a lage mumber of system entities as confirmed by the study by Simpson and Eranguc
(2001). In warehouse and distribution centres products have to be picked from a set of specific
storage locations by an ordeypicking (OP) process driven by customer ores. Each ordedine
represents one product or artide code in a certain quantity, which has to be shipped to a specific
customer (Gray et al. 1992, Koster et al. 1999).
Existing paradigms conceming logistics facilities ae strongly influenced by these reasons, but in
the light of recent changes it is now reasonable to study and devdop new solutions on the integrated
management of physical and electronic infonvation flows (Fenai e@ al. 2002). Van den Berg (1999)
recognizes that these new market forces and fast technological devdopments in both material
handling and in information systems affect warehouse management and control tremendously.
The aim of this study is to show and measure the impact of altemative policies and configurations
of manual OPSs in order to design robust systems, minimizing global costs and maxinizing ther
performances in terms of efficiency and cstomer savice quality. The object of the dynamic
approach adopted is to model OPS by considering all the most ciitical and decisive parameters
involved, so that it is possible to represent altemative operating scenarios and optimize system
design and contol. The research approach is based on the integration of planing and oonbol
qtocesses, without neglecting intenelationships between all the system factors and paramdas
involved. According to a dynamic multt-paramettic modeling of the generic picker to part OPS, a
data bese interactive tool to support management optimizing decisionmaking process is developed.
Thanks to a set of thousands of simulation mums, the best values can be chosen for a set of free
system factors which respect a pool of physical and managing system oonstaints (unfree
parameters). As far as possible the optimizing approach is standard and systematic, in agreement
with the great number of parameters involved. As demonstrated by research in the liteaire, this
integrated approach is new. Picking operations involve a lot of lage and medium sized companies
belonging to many industrial and service sectors, such as the apparel industry, the food sector, wood
fumiture production and logistic outsourcing providers.
The remainder of the paper is divided into 6 sections. After the introduction, section 2 defines and
describes the generic problem of design and contol of a manual OPS. After an overview, Section 3
presents the approach to solving the optimization problen and a demonstration of its computational
complexity. Then section 4 describes the multi parametric dynamic moda. Section 5 summarizes
the principal results of research involved And finally section 6 discusses condusions and further
research.
2. Picker to part OPS
Van den Berg (1999) defines OP as a process of gathering stock keeping units (SKU) that have
been requested an order at a time He classifies management decisions concaming warehousing
systems into two principal families:
1. planning decisions, which refer to an intermediate term and to policies that are developed at
the tactical level. They principally concam fulfilment activity;
2. control decisions, which affect the short tam and operational decisions. They refer to
touting, sequencing, scheduling and orderbatching problems.
This study is interested in devdoping an interactive tool, which supports the planning, and contol
decisions in OPSs.
OPSs can be classified as picker to part (or product) systems when the picker is tavdling to
Picking locations, and part (or product) to picker if materials are brought to the picker The first
picker to part situation is generally identified by manval OP labd: pickers ride in vehides picking
along physical dots. Known examples of part to picker systems are Automated Storage and
Retieval System (AS/RS), miniload and carousd. These are not object of this study.
For many industrial applications aionetic solutions, such as ASRS and Automated Guided
Vehide Systems (AGVS), are inconvenient for several reasons, such as great number of items code,
yesence of heterogenous shapes of products, building’s physical constraints and specific activities
required. Of these aspects the present research confines itself to the study of manual OPSs, whose
in-depth and integrated-base studies are not, as yet, devedoped, as is clearly demonstrated in the
literate. It is very important to undedine that these warehouses ae widdy found in industial
conoems for stocks of raw materials, components, spare parts and finished goods.
4
Refening to the retrieval approach, there are two principal macro classes of OPS:
¢ unit load systems. Materials are moved and stored by devices capable of moving and storing
only asingle- unithandling load;
« less than unit load systems with multiple stops per trip. Vehicles are capable of handling
multiple unit loads simultaneously: orderpickes, which could be identified with operators
aboard retrieval machines, retrieve ses of items or multiple handling units of the same item
on a single OP cyde They visit different slots of warehouse facility before reuming to
input/output (1/0) or depot areas. Each picker is responsible for picking a complete customer
pool of orders during a mission (Caron et al. 2000).
This study deals with the second dass of design problems, and indudes OP optimization in unit
load system because it is a particular case of Jess than unit load systems in which each picking cycle
is mack of only one stop within the warehouse facility.
The adopted and most diffused system layout configuration, which is based on orientation of
Ficking aisle is lengthwise (or longitudinal): stocking padlld aises nm papendaiar to the
warehouse front-end with a central depot, as shown in Figure 1.
TRAVERSAL. RETURN
YO] [_] Casc vo
Figure 1. Traversal and retum policies.
Roodbergen and de Koster (2001) call this configuration basic warehouse layout. Moving pickers
are able to change aisles at the front and rear of the warehouse (two cross aisles). The storage area
system known as forward-reserve or low-level picker to part (Caron et al. 2000) is adopted: lower
levds of storage rack ae used for mamel OP (forward area), while higher levds contain bulk
storage (reserve area). Therefore the generic facility object of this dudy is a two-cioss, forward
reserve and less than unit load picker to product OPS
Interesting surveys, frameworks and classifications on warehousing problem and OPS are presented
by Gray et al. (1992), Larson et al (1997), van den Bey and Zijm (1999), Rouwenhorst (2000) and
Kim ef al. (2002). It emerges that stock area design process, which is the specific object of this
study, has crucial intereationships with other design steps involving receiving docks, packing area
and shipping docks. Simpson and Eranguc (2001) moda OP function within a supply chain system
in tens of fixed costs, inventory costs and deterministic demand A numerical case study of an
OPS besed on a cognitive design procedure is presented by Yoon and Sharp (1995). They show a
great deal of intenelationships between all involved decisions. Kim e@& al (2002) mode attities
(goods and parts) and resources (order pickers) as agents of a co- operative process.
2.1, Costs of an OPS
Direct labor costs in an OPS can be up to 60% of total warehousing costs (de Koster ef al. 1999, Lin
and Lu 1999, Simpson and Eranguc 2001). OP accounts for over 65% of total operating costs for a
typical warehouse, while travel time accounts for about 50% of all OP activity (Tompkins e@ al.
1996, van den Berg and Zijm 1999, Vaughan and Petersen 1999).
Caron et al. (2000) list the principal contributions to total picking cycle time:
¢ administrative time at the //O point at the start and end of the tour
* processing time (spent time extracting items and documenting the picking activity);
« travel time between pick locations. It could reach 60% of global order picker's time
(Brynzer and Johansson).
The importance of reducing picking variable travelling cyde time emages, which is a monotone
increesing function of the traveled distance. For this reason the perfonmance of the generic OPS is a
measure of the distance travded in a picking cycle which can be considered to be equal to the OP
cyde time when picker moves within each aisle at average velocity.
3. Solving approach to support OPS design and control.
As Yoon and Sharp (1996), Vaughan and Petersen (1999) and Malmborg and Al-Tassan (2000)
demonstrate, the decisions on design and control of an OPS involve a great deal of interdependent
rdationships between a vatiey of factors. Rouwenhorst e@ al. (2000) present a hiearchical
framework for the design of an OPS. It is based on a set of clusters of relevant problems to be
solved simultaneously. An integrated approach is necessary, but current and traditional arelysis has
oriented research towards isolated subpoblems, as the cument literature shows. The adopted
simulative tool is an effectiveness instument effective in supporting decisions about dynamic
systems (Bechtel and Jayaram 1997, Kosfeld 1998, Helo 2000, Riddals et al. 2000, Fenai & al
2002), expecially when taking the computational complexity of the generic optimization problen
into consideration The OPS optimization problem, named Order Picking Problem (OPP), bdongs
to the NP-hardness class of decision problems as defined by Operations Research (Papacimitiiou
and Steiglitz 1982, Lawler et al. 1998). It is configurable as a routing instance, which can be traced
to the wel known Traveling Salesman Problen (Lawler & al. 1985, Ddl’Amico @& al. 1997). In
Patticular, the generic OPP is configurable as a Vehide Routing Problem (VRP), which consists of
constructing a set of at most m vehide routes of least total duration, according to a portfolio of
capacity and time constraints, and in order to simultaneously satisfy a group of retieval requests.
Batching too is an NP-hard problem (Pan and Liu 1995, Ddl’Amioo e& al 1997). A genetic NP-
hardness problen is not solvable in reasonable (polynomial) time: for this reason the approach
based and developed on dynamic simulation modding is justified The am of this study is to
ywovide a computational bese tool for OPS plaming and management which could be used by
decisionmakers to explore a wide range of opadiing configurations in omer to investigate al
potential impacts of itical factors and to optimize system pefonmances. In particular this
optimization approach is necessary to support decisions on flexible systems, which opade in
strongly evolving markets.
4, Parametric modeling of the OPS
Malmborg and AlTassan (2000) describe four basic types of system parameters which influence
operating performances of a generic OPS:
1. item features items space requirements (Kosfeld 1998), product structure and conelation
(Brynzer and Johansson 1996, van den Bey 1999), transaction demand levels, packaging
and related packing and cutting problems (Dell’ Amico et al. 1997).
2. Functional specifications of storage equipment concaming meeial handing systers
pattems, such as automated (or product to picker) warehousing facilities, for which the
literature referred to is wide (Rosenblatt et al. 1993, Pan and Liu 1995, Sharker and Babu
1995, van den Bey and Zijm 1999, Dallati et al. 2000, Malmbory 2000, Malmborg and Al-
Tassan 2000, van den Berg and Gademann 2000), manual system etc.
3. System operating rules. Main operating policies are (Caron et al. 1998):
* batching policy, which deteminates the pools of single-ordes and the manner in
which they are combined for a simultaneous picking in each tip of an OP cyck, as
described from literature by Elsayed and Stem (1983), Gibson and Sharp (1992),
Gray & al. (1992), Brynzer and Johansson (1995), Pan and Liu (1995), Tang and
Chew (1997), Hwang et al. (1998), de Koster et al. (1999);
* routing and sequencing, which determine the sequence in which storage and retrieval
requests are execufed. Literate on routing procedures: Ralliff and Rosenthal
(1983), Hwang et al. (1988), Petersen (1997), de Koster et al. (1998), Goetschalckx
and Railiff (1998), Chew and Tang (1999), Vaughan and Petersen (1999), van den
Bey and Gademann (2000), Dallari & al. (2000), Caron et al. (1998 and 2000),
Roodberyen and de Koster (2001);
* storage location assignment and fulfilment policies. Altemative physical storage
policies and operating rdated miles ae the foo of a lage mimber of shades
(Malmboryg and Krishnakumar 1989, Park and Webster 1989, Francis et al. 1992,
Brynzer and Johansson 1995, Larson et al. 1997, Caron et al. 1998, van den Bag
1999a, Caron et al. 2000, Dallari et al. 200, Malmborg and Al-Tassan 2000, van
den Berg and Gademann 2000, Ferrari et al. 2002).
4. Physical configuration of storage area and unit load size. The ile of system layout
configuration on warehousing optimization process is described by Gibson and Shap
(1992), Caron et al. (2000), Roodbergen and de Koster (2001)
The besic approach of this research is to quantify principal relationships between these decision
levds, thereby presenting an integrated approach to solving global optimization of planning and
contol processes rather than the iterative procedures which have been developed in a few of the
efforts to be found in the literahre.
4.1 Multi-parametric model of the OPS
Figure 2 shows a visual interactive dynamic model of the parametric OPS. The longitudinal storage
system consists of multiple paralld aisles with two high bay pallet racks alongside each aisle Two
sided and single-deep shelving is adopted. Materials enter and exit the warehouse at a single
input/output (I/O) area.
[mal | Lull . 1:30.00
Figure 2. Dynamic model of the OPS.
Fach configuration object of a specific simulation nm comesponds to a special parametization of
the system and to a related choice of values, which ae assigned to all modded factors. The
following compose the set of factors, which are the object of the modeling process, and it is this set
of names which is used in subsequent sections and figures.
1) Shape (ratio p&q). The layout of inventory area is rectangular. Different values of ratio
between the two dimensions (respectivey frortal p and longitudinal q) ae associated with
this factor. Values range between 4&1 to 1&1, where p&q notation indicates the ratio
between frontal and longitudinal dimensions.
2) Curve The adopted storage location assignment policy is known as class based storage. It
partitions all products between a number of classes and resaves a physical warehouse
portion for each class, where items are located randomly. This policy is generally managed
according to a famous dispatching rule based on Cube per Order Index (COI) introduced by
10
3)
Haskett (1963). It is defined as the ratio of the number of storage addresses allocated to an
item, to the mumber of transaction per period: the mle is applied by routing incoming items
with lowest values to the most aovessible storage addresses of a facility (near the I/O point).
The CL-K notation denotes the number of dasses with K. Studies on class based storage
assignment policy by Kallina and Lymn 1976, Frazdle 1980, Pak and Webster 1999,
Francis et al. 1992, Gibson and Sharp 1992, Caron et al. 2000, Dallari et al. 2000, van den
Beg and Gademann 2000, show that better results are achievable with three classes.
Aovording to the implementation of a three classes (A, B and C) storage assignment (CL; 3),
the analysis could be effectively based on a COI - Pareto ABC auve that is related to
Physical stocks and movement frequencies. This is given the name of Cube per Order Index
curve (COFamve). An example of COLauve is illustated in gue 3 whee cumulated
values are reported on two axes. Through an analysis of different real cases, it emerges that
generally there are many items with srell index of rotation only a small portion of stock is
moved with high rotation values. For this reason some values which have been associafed
with ouve factor are 20/95, 20/90, 20/80 etc. whee notation x/y indicates that x% of
cumulated storage commits y% of material movements.
Class. In dass based storage assignment policy a critical choice on warehouse design is
represented by calculation of physical dimension and shape of each class (Fava et al.
2002). Class factor could belong to a set of many values, whose examples are 20/50/30,
5/45/55. The notation a/b’c and a, b, c values indicate the portion of total volume (in
percentage), which is associated to classes A, B and C respectively.
dd.
Cube per Order Index
cumulated frequencies
cumulated storage
Figure 3. Example of a COI-curve.
4) Policy. Different values could be travesal or raum acooding to figwe 1 and to the
following meanings:
1. traversal policy (TR): the picker enters at one end of an axle containing at least one
pick and exits at the other end;
2. Returm policy (RN): the picker enters and exits at the same end of the aisle.
5) Dimlist. This is the number of lines of a picking list and it is associafed with a mission of a
retrieval vehicle The generic picker begins and finishes his or her mission at the I/O zone,
when he or she reaches the end of the list.
6) Ratio. This factor relates the capacity of picking machine to the number of items which are
picked at each stop during a vehicle tip. It represents the average number of stops per route.
The number of times the I/O zone is visited during a picking cycle (equal to the number of routes
for a picking list) depends upon the values associated with DimList and Ratio parameters: every
time a vehicle is saturated or finishes its mission, it reaches this point The adopted order batching
procedure is First Come-First Served (FCFS): orders, and related requests and locations, ae
12
generated randomly, according to a COl-curve and Class factor value, and they are grouped in pools
of DimList parametric size. The adopted order routing policy is associated to the FCFS sequencing
of retrieval requests and to the calculation and choice of the Shortest Path (SP) between two generic
and consecutive slots to be visited (Papadimitriou and Steiglitz 1982).
A significant study on the optimization of automatic and parametric OPS based on four factors is
ywesented by Dallari & al. (2000). Caron et al. (2000) present a parametric analysis, related to a
Picker to part OPS, based on analytical modding and few factors, such as storage capacity of
picking system, number of pick stops per tour and shape of CO-based ABC curve. The present
research is a new oonbibution on mamel OPS planning and contol besed on an integrated,
dynamic and interactive process. It involves 6 factors for laye sds of values and diffeaent
‘warehousing system configurations, and these are not the object of in-depth and integrated approach
to be found in the cunent literature.
5. Results
The principal aim of the present research is to plan and develop a parametic simulative model of
OP warehousing systems, which are described above This section provides some guidelines for
choosing the best picking strategy for a given subset of system parameters. A set of more than
50000 simulation runs were executed in order to suudy the impact of physical and managing
parameters on the optimization of pickers’ horizzontal movements and according to the following
hypothesis and ranges of data:
¢ mumberof pickers stops = 200;
¢ dimlist =5, 10, 15, 20, 25, 30;
¢ ratio=1, 2,3, 4,5, 6, 7,8, 9, 10, 11, 12, 13;
* policies =traversal (TR), retum (RN);
¢ shape: 1&1, 2&1, 4&1;
13)
* curve: 60/20, 70/20, 80/20, 90/20, 95/20;
¢ classes: random, 5/40/55, 10/50/30, 20/30/50, 20/50/30.
In order to support management optimizing decisions in design and contol of real warehousing
facilities, the choice of these ranges of values is based on a study of the most widespread OPS
configurations.
The global number of simulated soenarios equals 11700; for each one five diffeent nms wee
executed in order to obtain a set of average performance data. The output of every mn is the global
picking cycle time. The number of stops bdonging to a single 1m has been optimized on the basis
of the calculus of the acceptable percentage exor and by a dedicated MSPE (Mean Square Pure
Eno) analysis. It represents the assessment of the exor variance when it is distributed acoording to
a nome distibution with average value equal to zav. If a single smulation nm of at least 200
stops is made, the enors are less then 0.3%. All results are in seconds and nonmelized in respect of
the maxinumrecorded mun time value so as to be able to compare very different soenarios easily.
These nomrelized values are the same as those obtained when considering travdled distance as an
output run value because of the existence of a direct proportionality between times and rdated
travelled distances. Following figures present graphs where Performance ratio on ordinate axis is
the ratio between the genetic picking cycle time and the maximum: recorded one.
6.1 Innovative guidelines to the design
Now a list of principal innovative results obtained is presented in order to offer a set of useful,
Practical and optimizing guidelines to the warehousing system designer and controller.
The first relevant deduction of note to emage is the little relevance of the single picking list
dimension (DimList) as the graph of Figure 4 Clearly illustrates. Figure 4 compares the effect of six
dimensions of a hypothetical picking list in tems of performance, considering a system Shape equal
to 4&1, a 80/20 Curve, a RN routing Policy and different values of Ratio parameter. For each value
14
of DimList paramefer a specula trend of system perfonmance emerges according to the 13 ratio
values, which have a measurable impact on cyde picking time because they impact on the
saturation of picking machines. Best performance system values comespond to the lower OP cyde
time and lower nonmalized values, which can be seen in the following graphs.
Curve 80/20; shape 4&1; policy RN
Ratio values Ratio
35
DimList
Figure 4. Impact of DimList parameter on system performance. Curve 80/20.Shape 4&1.Policy RN.
In omer to study the importance of ratio value and its rdationships with the rest of the system
design parameters, the graph in Figure 5 compares two routing polices and Ratio values by
considering a 80/20 Curve, a Shape equal to 4&1, and different values for Class parameter. First of
all, it emerges that Ratio acts independently from routing policies. Secondly, its effect is rdevant
when considering values of Ratio lower than 3, and thirdly it is reduced and has a constant tend for
Qreater ratios. Lower values ask for greater numbers of visits to the I/O because of the saturation of
Picking machines. In Figure 6, which is associated to 60/20 Curve, it emerges that Ratio always has
the same effect on system perfomance, but the adopted picking policy importance grows a great
deal. RN policy offas an aveage saving of about 10% compared to TR policy. Although
considering a breadthwise picking system (whee stocking aisles nm either padld to the
‘warehouse front-end), this conclusion confirms what Caron et al. (1998) demonstrate.
15
Curve 80/20; shape 481; policies RN andTR
1,00
0,90
0,80
0,70 ¥
0.60 TR Class values
f 0.50
£0.40
B 0,30
0,20
0,10
0,00
1 2 3 4 5 6 7 8 9 10 11 12 13
Figure 5. Impact of Ratio parameter on system performance. Curve 80/20. Shape 4&1.
Curve 60/20; shape 481; policies RN andTR
Figure 6. Impact of Ratio parameter on system performance Curve 60/20. Shape 4&1.
Random; shape 4&1; policies RN and TR
DimList values
——
a
Figure 7. Impact of Ratio parameter on system performance in random storage location policy.
Shape 4&1.
16
When considering a random storage location assignment Poicy, it was found that when the system
shape is constant (Figure 7), Ratio factor behaves as in previously described soenarios. The TR
Policy generates picking cycle times about 13% higger than RN values. This conclusion is different
from studies in the literature on breadthwise OPS where TR always performs equal to or better than
RN Policy (Goetschalckx and Ralliff 1988, Hall 1998, Caron et al. 1998). As a sat, Figures 5 to 10
describe the effect of warehouse Shape changing when global available plane area is constant. In
paticula, figwe 8, 9 and 10 ae in relationship with 5, 6, and 7 respectively. The influence of
picking area layout is consistent with Caron et al. (2000). Figure 8 shows that, when Shape is
quadratic (1&1) and Curve 80/20, Ratio has a greater impact in TR than in RN souting Policy: RN
policy is decisively more advantageous and offers savings greater than 30% in picking of vay
voluminous items. These results do not change significantly if diffeent kinds of COkcmves ae
considered: the graph in figure 9, which is based on a 60/20 cave, demonstrates that RN policy
guarantees almost 25% minimal savings. The comparison between Figure 6 and 9 shows the
quadratic as being the optimal Shape in RN Policy adoption, especially with lower Ratio values.
The opposite results are obtained with TR policy: the best peformance belongs to the “most
rectangular” system (Shape factor 4&1) and savings are about 10% for every Curve.
Figure 10 presents the effects of a random allocation policy in a quadratic system: comparison with
graph 7 shows that Shape factor does not affect the RN policy, while performances deteriorate in
TR xoutings. After the analysis of principal implications of Dimlist and Ratio factors, it is useful to
study the impact of different class based storage location assignments on picking cyde times
Figures 11, 12, 13 and 14 show picking system performances when the ordedlist dimension is 20
and Ratio value is 5. The lowest value of Shape factor on X-axis represents the quadratic
warehousing system: according to previous analysis RN is the best routing policy and offas
relevant savings. In rectangular systems based on Shape ratio value over 3, the best routing policy
and Class factor need to be chosen together and according to the specific COI curve of products.
17
Curve 80/20; shape 1&1;policies RN and TR
LN
Ae NX Class values
pos Law —
Fo Se ee ererere'
Figure 8. Impact of Ratio parameter on system performance. Curve 80/20. Shape 1&1.
Curve 60/20; shape 1&1; policies RN and TR
1
ag q Chass values
a ¢
———————-—-_——
Ratio,
1 2 3 4 5 6 7 8 9 10 nN WR 13
Figure 9. Impact of Ratio parameter on system performance. Curve 60/20. Shape 1&1.
random; shape 1&1;policies RN and TR
DimListvalues
1 2 3 4 Ly 6 7 8 9 10 ll 12 13
Ratio
Figure 10. Impact of Ratio parameter on system performance in random storage location policy.
Shape 1&1.
18
Passing from a 60/20 to a 90/20 curve OPS performance can change a great deal (between 10% to
25-30%), while system sub-optimizations based on Class factor choice does not impact more than
5%. This is worst if class based storage location policy is not adopted and products are randomly
allocated.
i
Og SeeeernN 1 a e0-RN
O8 j—e—70-RN |] | 29
a lees ra
fos | — s—90-RN
bs] fe Lae
Ie -a-sore | [foe eSauth
20.2 2 70-TR | Eg 2 —o—70-TR
oa —+—80-7R | | 02 80-TR
met ster =|
1 2 4 = 1 2 4 See |___90-TR
:
a Soa] | 0} ar
08 pa-7o-an| |go8 _w_70-RN
fe — ——s0-rn] |Eoe ——00-RN
fos —s0-an|] |fos 4 90-88
_—— ——— re meee Eon
[es |= 70-12 | |*5'3 2 70-TR
;
eet | ae Sart | so-re
1 2 4 “pe 1 2 4 “re
Figure 11, 12, 13, 14. Impact of Shape and Curve factors on system performance with traversal and
retum routing policies.
By compating Figure 15, which refas to a random dlocation, with previous graphs, patticilaly
‘with Figure 5, it can be seen that the dlasses optimization offers average savings in the order of 20%
compared to random allocation Policy. Best savings belong to a quadratic system with RN logic and
to rectangular systems based on TR routings. Figures 16 & 17 confirm what wes just explained: for
2 different system Shape they illustate system pefonmances according to diffaent dasses
configuration and random location policy separately. The advantages gained from the adoption of
COE based storage compared to random storage are generally greater with retum policy as Caron et
al. (1998) demonstrated when considering a breadthwise system, but they depend on Shape factor.
For this reason is not possible to extract the best routing policy, not as some of the studies in the
literature declare.
19
Dimlist 20; ratio 5; random; policies RN and TR
1,00
0,90
0,80
0,70
0,60
—+—random-TR
150
140 —————— —m_random-RN
0
0
0,30
0
0
0
120
+10
00
1 2 4 Shape
Figure 15. System performance in random storage location policy. DimList 20. Ratio 5.
Dimlist 20; ratio 5; shape 1&1
—e—RN G0
0,7
—m—TR 60
gos 4 — RN 70
4
0,5 TR70
0,4 vo a —K-RN 80
By — —e_TR 80
‘ =
i — Class| | 8 99
=_TR90
105040 203050 205030 54055 random
Figure 16. Routing policies effects in class based storage and random location policies. DimList 20.
Ratio 5. Shape 1621.
Dimlist 20; ratio 5; shape 4&1
0.8
—~_RN 60
0,7
F =_RN70
g
Hee gt. RN 80
Bos ————— RN 9O
PS Sean er
03 —e_TR 70
—4_TR 80
0.2 : : : : Chass
—=TR 90
105040 203050 205030 54055 random
Figure 17. Ettects of Routing policies in class based storage and random location policies. DimList
20. Ratio 5. Shape 4&1.
20
6. Conclusions and further research
A supporting decisionmaking database wes created: it picks up a set of more than 50000 simulative
quns in agrearent with different system soenarios so for a given pool of system input constraints it
reuums the optimizing values to be assigned to free parameters as output: Some brief concusions
may be drawn from the results of the simulation experiments:
1. in oer to involve all cucial and interelated parameters, the design optimization of an OPS
needs to be integrated: system performance depends on the combination of all these values;
2. the dimension of picking list is not as ctucial as Policy, Ratio, Shape and Curve factors. In
particular Policy and Ratio seem to be the most relevant parameters with respect to OPS
performance.
3. Lower Ratio values are more crucial to system optimization than bigger values.
4. COFbesed storage policies always yidd travd times significantly shorter than the shared
storage policy, agreeing with many other studies on manual and not mana OPS in the
literature; nevertheless Class factor plays only a secondary role on system optimization;
5. If operating policies and factors are ill defined or may vary over time, intermediate solutions
have to be configured through an economic amalysis of convenience. They could be the
object for further interesting studies on OPS and preferably canied out acooring to a
sensitivity analysis, such as a DOE (Design of Experiment), of system performance relative
to all the principal system parameters involved This is a good way to weigh the influence of
factors and their combinations;
6. best savings belong to quadratic system based on RN Policy, and to rectangular system
besed on TR routings.
21
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