1. By
Chetan Reddy Mitta

2.  Order picking is the most time consuming operation
 It accounts for 55% of the warehouse operating costs

3.  Cross Aisle Structure
 Input and output points
 Number of aisles
 Length of the aisles
 Dimensions of the warehouse

5.  Concerned with unit load warehouse i.e. items are stored and
retrieved in pallet quantities
 Dual command Cycle- a worker first stores and then picks the
pallet
 Flow through process
 The angle of inclination of the cross aisles to be 45 degrees

6. The goal is to compare the average distances travelled by a
worker from selected input and selected output in X layout with
respect to the traditional layout.

7.  Y-height of the warehouse
 X-Width of the warehouse
 a-cross aisle width
 b-sub aisle width/ picking aisle width
 Theta – angle of inclination
 x 1-X coordinate of intersection point of the sub aisle with the cross aisle
 y 1-Y coordinate of intersection point of the sub aisle with the cross aisle
 Entry i-Input i i={1,2,3}
 Exit i-Output I i={1,2,3}
 (Entry,Exit)=(coordinate x, coordinate y):
 ( 1,1)=((0,0),(0,Y)),(2,2)=((X/2,0),(X/2,Y)),(2,3)=((X/2,0),(X,Y))

8.  H-total number of aisles along horizontal
 V-Total number of aisles along the vertical
 Aisle offset_H-Aisle offset along horizontal
 Aisle offset_V-Aisle offset along vertical.
 I_x1,I_y1-x,y coordinates of point of intersection of first x .
 I_x2,I_y2-x,y coordinates of point of intersection of first x .
 Zone-1,2….8,9..12
 Perzone_H-Number of sub aisles / picking aisles in each
horizontal zone.
 Perzone_V-Number of sub aisles / picking aisle in each vertical
zone.

12.  Finding the intersection points of the picking aisle line with the
cross aisle line by using simple coordinate structure.
For e.g.: If we consider
 Zone 2 :
 LocalAisle = aisle - (zone-1)*perZone_H;
 x_1 = AisleOffset_H+(zone-1)*perZone_H*b+ LocalAisle*b;
 ymax = Y - AisleOffset_H + (-m)*x_1;
 ymax = Y - m*(x_1 -AisleOffset_H);
 perzone _H=X-4*Aisle offset_H*a/8*b
 perzone_V=Y-a-2*a*aisleoffset_V/4*b

13.  Calculate the total number of aisles i.e. sum of horizontal and
vertical aisles.
 We number the aisles from zone 1 to zone 8 in anti clockwise
direction and the zone 9 to 12 for vertical aisles .
 We generate two random aisle number s .
 Then we identify the zone in which the two random aisle number
lie
 the aisle number is converted into the local aisle number. This is
formulated as below for zone 2 :
 LocalAisle = aisle - (zone-1)*perZone_H;

14.  The point of intersection of this randomly generated aisle and cross
aisle is found.
 LocalAisle = aisle - (zone-1)*perZone_H;
 x_1 = AisleOffset_H+(zone-1)*perZone_H*b+ LocalAisle*b;
 ymax = Y - AisleOffset_H + (-m)*x_1;------------1
 ymax = Y - m*(x_1 -AisleOffset_H);-----------2
 It can lie in any of the two coordinates.
 We assumed a variable to take value between (0,1).
 So, if the value is < 0.5 takes one side or else the other (Just like
tossing the coin).
 Now ,we know that a random number on this aisle should between
the two known points .

15.  y_1 = ymax+ rand(1,1)*(Y/2-a/2-ymax);
 The same methodology is used for the zones 2,3,6,7.And for the
vertical zones the random point varies along the X-axis.
 After generating two random points and two random aisle number we
can calculate the total travel distance from entry to point 1 to point 2
and then to exit.
 E.g.: Entry 1 exit 1 and the two zones are 1 and 3 .
 Pick1_dist = distance(Pick1_x,Pick1_y,Pick1_x,Pick1_ymax);-
 Pick2_dist = distance(Pick2_x,Pick2_y,Pick2_x,Pick2_ymax);
 Travel_dist =
A1+A8+2*A9+2*Pick1_dist+2*Pick2_dist+2*distance(I2_x,I2_y,Pick2_
x,Pick2_ymax);

16.  The X-layout model is programmed in matlab and run for 500
different points by fixing 3 different input and 3 different out put
points i.e.11,22,23.

17. sub aisle width
"b"
Cross aisle
width "a"
Entry 1 Exit 1 -
avg dist
Entry 2 Exit 2-
avg dist
Entry 2 Exit 3-
avg dist
2 4 436.8473627 412.359603 469.9621078
3 6 458.9083926 421.9085264 440.2055996
4 8 438.8048983 403.970392 444.6349116
5 10 464.4144204 413.390739 472.1534135
6 12 438.0494148 431.7415695 485.2314906
7 14 459.9804163 436.8815879 466.546859
8 16 479.5830189 429.3905281 481.5269818
9 18 467.6955873 414.8935882 424.1599993
10 20 488.820164 445.4807398 488.8825158

23. 0
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1 2 3 4 5 6 7
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24. 0
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25.  The average distance is low for the entry 2 and exit 2 compared
to the other input and output points as the b is varied
 The average distance decreases as we increase the dimensions
of the layout
 In a traditional layout, the average distance increases as the b is
varied
 Also, the average distance increases with the increase in the
dimensions of the x
 Comparing the two layouts, the X layout would be much better
when the length of the warehouse is more and also the average
travel distances are low for X compared to the traditional layout

26.  The X layout can be extended by increasing the X’s appropriately
with respect to the length of the warehouse , I/O points and the
storage space
 Finding an optimal angle of inclination for X
 Finding optimal number of inputs and output points at proper
location