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A PERFORMANCE ANALYSIS MODEL OF ORDER PICKING WAREHOUSE DESIGN

for TRANSPORTERS

Kainan University

黃 興 錫 (Heung Suk Hwang)Department of Business Management ,

Kainan University, Taiwan e-mail : hshwang@mail.knu.edu.tw

2005. 10. 29.

2005’ 倉儲系統與物料搬運研討會逢甲大學工業工程與系統管理學系

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Contents

1. INTRODUCTION

2. ORDER PICKING WAREHOUSE SYSTEM

3. SIMULATION MODEL FOR ORDER PICKING

WAREHOUSE SYSTEM ANALYIS

4. SUMMARY AND CONCLUSIONS

☞ Demonstrate a Hyundai W-Car ProblemKainan University

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1. Introduction☞ Developed a performance evaluation model for order picking warehouse in supply center(SC) by reducing the travel distance of transporters

☞ We developed a two-step approach : - a mathematical model - a simulation model using AutoMod simulator

☞ Also we developed computer program and demonstrated the pro posed methods,

☞ Then we carryout numerical studies to compare the system performance improvement over the number of transporter in order picking warehouse.  Kainan University

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☞ The major functions of the freight terminal system are :

1) Pickup and arrival,

2) Auto-sensing the freight information,

3) Auto-sorting, and

4) Delivery.

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15%

55%

15%12%

0%

10%

20%

30%

40%

50%

60%

Retrievaling Picking Storaging Arrivaling

Function

The

Ra

tio o

f A

nnua

l Ma

inte

rna

ce C

ost

Figure 1. Operating Cost Ratio of . General Warehouse

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Step 1. Design the Order Picking Warehouse- Design Parameters- System Configuration

Step 2. Analysis the Transporters Performance- Traveling Time in DC- Stop time at the SKU- Picking Time at Picking Area- Number of Upper Items Retrieved

by Transport

Step 3. Layout Design using AutoMod- Performance of Transport- Throughput and Performance of System

Mathematical Model

Simulation Model

Step 1. Design the Order Picking Warehouse- Design Parameters- System Configuration

Step 2. Analysis the Transporters Performance- Traveling Time in DC- Stop time at the SKU- Picking Time at Picking Area- Number of Upper Items Retrieved

by Transport

Step 3. Layout Design using AutoMod- Performance of Transport- Throughput and Performance of System

Mathematical Model

Simulation Model

Figure 2. Two-Step Approach of Order Picking Warehouse System

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2. Order Picking Warehouse System

Getting the Informationof Goods

Arriving(Strip Door)

Delivering(Stack Door)

Distribution

Getting the Informationof Goods

Arriving(Strip Door)

Delivering(Stack Door)

Distribution

Order picking warehouse

Getting the Informationof Goods

Arriving(Strip Door)

Delivering(Stack Door)

Distribution

- Information System - Pickup, sort, and delivery * Transfers the product to customers

Getting the Informationof Goods

Arriving(Strip Door)

Delivering(Stack Door)

Order pickingTransport/Sorting

Distribution

Figure 1. Freight Flow in Freight Terminal

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Dock

Transport

I/O

PickingPoint

Path

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Figure 4. General Layout of Picking Warehouse

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2.1 Probabilistic Picking in Warehouse

-We assumed that an item found in the i th aisle has the probability, This is proportional to the average of the turn over rate of all items found in a aisle or the number or racks for an item.

Notations used : M : number of freight of an item, : number of item stored in the ware house : probability of picking item m : number of item stored in the ware house = number of item 1

n : number of picking of order or : number of picking of each items per an order picking,

ip

imip

1m

1 2 km m m M

1 1, , , kn n n

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Prob ( picking n items in the warehouse where stored k items)

=

(1)

( , (1 ))N np np pk

i

i=1

( / ) (or ( ) )1 M

i

i

Nnn

i i

k mm M p

i

where, means the probability of picking item in a picking.ip i

All the cases of picking of item k when a transporter repeats n times of picking

with the probability , is given by,

( 2)

( 1,2, , )ip i k

1 2 !1

i

k

i

n nkn n n

ni

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The expected number of picking by a transporter :

(3)Pr( ( )) ! ( )

1 1 !

ini

i ii

k k pN n n

i i n

1

(or ( ) )i

kn

i ii

n p

-By the assuming that the probability that a pick comes from a randomly selected zone is 1/p where p is number of transporters or number of zones.

-Thus the expected number of picks in pf a transporter or zone during a

particular time period can be approximated using the binomial distribution

-The upper limit of picking UL(the number of items retrieved by a transporter) can be determined by using the normal distribution to approximate the binomial distribution. as followingThe binomial distribution B(n, p) can be approximate as N(np, np(1-p)) Kainan University

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( ) [ ](1 )

UL npP UL P

np p

[ ]( )(1 )

k

k k

UL P nP

P n P

Thus,

=

[ (1 ( ) 1] ! ( )1 1! !

i in ni i

i i

k kp pUL Z n

i in n

! ( )1 !

[ ]

! ( )(1 ( ))1 ! 1

i

i

i

ni

i

nni

ii

k pUL n

i nP Z

k kpn p

i n i

[ ! ( )(1 ( ))] ! ( )1 1 1! !

i i

i

n nni i

ii i

k k kp pUL Z n p n

i i in n

[ (1 ( ) 1] ! ( )1 1! !

i in ni i

i i

k kp pUL Z n

i in n

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2.2 Optimal Size of Unit RackNotations : AW : width of unit aisle(ft) AL : length of unit aisle(ft) LW : width of unit rack(ft) LL : length of unit aisle(ft) LH : width of unit aisle(ft) WM : number of aisle R : required through put( unit/hr or day) C : total length of rack(ft) TA : available space of system, VHV: horizontal speed of transporter(ft/hr) VVV : vertical speed of transporter(ft/hr) T : scale parameter of unit rack T: LL/VHV= LH/VVV

(0 1)TA

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We formulate this problem as following :

Min. WM St 2·LW·LH·WM = C (1) (AW + AL) ·((LW + LL) · WM + 1) = TAwhere, TU is given by following Eq. (2) (2)By Eq. 1 and 2, (3)

and by Eq, 2 and 3,

where,

/[ ( ( ) / ) / ]TU P P f n n T k n

( ) 0.38532 0.07333 2 /( 1)f n n n

/ / , ( / )T LL vhv LH vvv LH vvv vhv LL

60 [ ( ) / ]WM WM Rt WM R f n n 1/ 2[ /(2 )]c vvv vhv ( / )t p k n

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The algorithm to find WM is given by following 5 steps :

step 1 :

step 2 : if , go to step -4

Otherwise, go to step-3

step-3 : , go to step-2

step-4 : stop ,

WM = minimum number of aisle,

[( ) / 60]WM R t

(60 ) [ ( ) / ]WM WM Rt R f n n

1WM WM

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We could find optimal size of aisle and the system performance as following :- number of aisle : WM

- height of rack :

- length of rack :

- expected travel time(min) :

- system utilization rate(%):

utilization rate

1/ 2[( ) /(2 )]LH c vvv WM vhv

( / )LL vhv vvv LH ( )TL f n T pn k

(%) [( ) /(60 )] 100R TL WM n

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Numerical example to find WM and system utilization rate : 

S = , R = 294 picksn = 5 picks/trip, p = 0.25 Min/pickhv = 150 m/min, vv = 30 m/mink = 1.25 min/trip Number of aisle = 3Height of rack = 4.1mLength of rack = 20.6mExpected Travel Time = 2.83System Performance = 92.52%

2539m

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2.3 Travel Time Analysis Assumptions :- one picker in each zone,- each type of item in stored in one location,- sufficient supply of items in at each location,- items are picked along one side of an aisle at a time,- there are two sides to each aisle , - transporters travels through all the aisles, - items are randomly assigned to storage location within a facility,

The total processing time : 1) The picking time is given by following equation :

where, TN : number of transporter, : time for a transporter to pickup an item

: number of all the items picked up by transporter,

2 ijpt i

nT t

TN

itk

iji j

n

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2) Traveling time :

( )ttT f n T p n k

2 ( )tt

WM AL LWT

TN VHV VHV

3) Stop time for picking :

1

! ( )!

[ ] [1 [1 ]]

k nii

ii

pn n

n

jk

M WM TNE E

TN M WN

1

! ( )!

[ ] [1 [1 ]]

k nii

ii

pn n

n

jk ust ust

M WM TNE E t t

TN M WN

stt

Total process time per travel of transporter) = (picking time) + (traveling time) + (Stop time for each SHU

tps st tt ptT T T T 1

! ( )!

2( ( ) ) [1 [1 ]]

k nii

ii

pn

n

TN TTNtps ij i ust

M WM TNT WM AL LW n t t

TM TN M WN

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4) Determining of the optimal number of transporters - dependent on total process time, number of aisle, its length and number of required amount to be retrieved. - It is very complicated problem

Thus, we used a simulation method based on AutoMod simulator.

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3. Simulation Model for Order Picking Warehouse System Analysis

- We modeled the same order picking warehouse system using AutoMod simulator.

-We have run the simulation for 1000hours with following design parameters : Number of aisle = 3, height of rack = 4.1m, length of rack = 20.6m, C = 539 m2 , R = 294 picks, n = 5 picks/trip, p = 0.25 Min/pick, vhv = 150 m/min, vvv = 30 m/min, k = 1.25 min/trip

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Case 1 : Number Transporter = 1

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Case 2 : Number Transporter = 2

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Alter. ofTrans

Delivering RetrievingParking

Per. of Total time

Trips Made

Average timesec/trip

Per. of total time

Trips made

Av.time/trip

Per. of Total time

1 50.0% 34.65 52.2 50% 34.65 52.2 0

2 53.5% 31.34 61.8 46.5% 31.34 53.4 0

3 60.9% 26.27 83.4 39.1% 26.27 53.4 0

4 66.4% 19.61 121.8 33.6% 19.61 61.8 0

5 28.1% 28.82 350.4 71.9% 28.84 893.4 0

6 34.7% 5.85 2139.6 65.3% 5.88 4008 0

Table 1. Transporter Performance

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Table 2. Material handling flows(Amount of throughput)

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Alter. of Transporter(No. of Transporter)

Total Throughput Warehouse Utilization (%)

1 138.3 55.2

2 250.3 59

3 311.8 61.3

4 311.1 61.2

5 57.1 52.4

6 13.7 50.1

27

0

50

100

150

200

250

300

350

1 2 3 4 5 6

Alter. of Transport

Tota

l Thr

ough

put

Figure 4. Total Throughput per Alternative of Transporter

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Sample problem of order picking systems

- The picking utilization obtained from mathematical model is a little greater than that from simulation (92.52 > 61.3) - the optimal number of transporter : 3 - total throughput : 311.8.- There should be a minimum two line spaces between tables and - text.

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4. Conclusion - In this paper, we have presented an analysis for order picking systems by two-step approaches in this paper, mathematical and simulation model using AutoMod. - An algorithm for end-of-aisle is developed. - We have developed a computer program for the analytical method. - Computational results are presented on the relative performance of each type of methods. - These approaches have been compared with each other in terms of utilization of pickers, total throughput and handling time.

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Kainan University, Taiwan

Prof. Heung-Suk Hwnag

Thank You

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