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- 1. ByChetan 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
- 4. Concerned with unit load warehouse i.e. items are stored andretrieved in pallet quantities Dual command Cycle- a worker first stores and then picks thepallet Flow through process The angle of inclination of the cross aisles to be 45 degrees
- 5. The goal is to compare the average distances travelled by aworker from selected input and selected output in X layout withrespect to the traditional layout.
- 6. 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))
- 7. 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 eachhorizontal zone. Perzone_V-Number of sub aisles / picking aisle in each verticalzone.
- 8. Finding the intersection points of the picking aisle line with thecross 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
- 9. Calculate the total number of aisles i.e. sum of horizontal andvertical aisles. We number the aisles from zone 1 to zone 8 in anti clockwisedirection 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 numberlie the aisle number is converted into the local aisle number. This isformulated as below for zone 2 : LocalAisle = aisle - (zone-1)*perZone_H;
- 10. The point of intersection of this randomly generated aisle and crossaisle 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 liketossing the coin). Now ,we know that a random number on this aisle should betweenthe two known points .
- 11. 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 thevertical zones the random point varies along the X-axis. After generating two random points and two random aisle number wecan calculate the total travel distance from entry to point 1 to point 2and 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);
- 12. The X-layout model is programmed in matlab and run for 500different points by fixing 3 different input and 3 different out putpoints i.e.11,22,23.
- 13. sub aisle width"b"Cross aislewidth "a"Entry 1 Exit 1 -avg distEntry 2 Exit 2-avg distEntry 2 Exit 3-avg dist2 4 436.8473627 412.359603 469.96210783 6 458.9083926 421.9085264 440.20559964 8 438.8048983 403.970392 444.63491165 10 464.4144204 413.390739 472.15341356 12 438.0494148 431.7415695 485.23149067 14 459.9804163 436.8815879 466.5468598 16 479.5830189 429.3905281 481.52698189 18 467.6955873 414.8935882 424.159999310 20 488.820164 445.4807398 488.8825158
- 14. 02004006008001000120014001 2 3 4 5 6 7bDistance
- 15. 02004006008001000120014001 2 3 4 5 6 7bDistance
- 16. The average distance is low for the entry 2 and exit 2 comparedto the other input and output points as the b is varied The average distance decreases as we increase the dimensionsof the layout In a traditional layout, the average distance increases as the b isvaried Also, the average distance increases with the increase in thedimensions of the x Comparing the two layouts, the X layout would be much betterwhen the length of the warehouse is more and also the averagetravel distances are low for X compared to the traditional layout
- 17. The X layout can be extended by increasing the X’s appropriatelywith respect to the length of the warehouse , I/O points and thestorage space Finding an optimal angle of inclination for X Finding optimal number of inputs and output points at properlocation

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