Suppose you have pallets of size 42\" X 42\". You wish to load cartons of toolbo

Question

Suppose you have pallets of size 42" X 42". You wish to load cartons of toolboxes of dimensions 8" x 8" X 8 respectively. If the maximum height o each pallet is 48" 1. a) What is the maximum number of toolboxes each pallet can take so as t b) Suppose the company desires to store a 30-day supply of toolboxes att c) maximize the unit load? rate of 2,000 units per day, how many pallets would be needed? If the pallets are to be stored in a warehouse that allows for the loaded pallets to be stacked threg high, how much space (ft) would hold all the pallets for a 30-day supply? Assume aisle space of 30% of total area. be needed

Explanation / Answer

a) the dimension of each pallet is 42" x 42"

the area of pallet = 42 x 42 = 1764 sq.inches

Now, toolboxes can be arranged in two ways

case (i) : area covering = 18" x 8" = 144 sq.inches

total number of toolboxes can be fitted in one line = 1764 / 144 = 12.25

rounding it down we get number of toolboxes in one line = 12

height of each toolbox = 8"  

Total height of the pallet (i.e., max ) = 48"

therefore, the total number of toolboxes that can be fitted in one pallet = (48/8)* 12 = 72

case (ii): area covering = 8" x 8" = 64 sq.inches

total number of toolboxes can be fitted in one line = 1764 / 64 = 27.5625

rounding it down we get number of toolboxes in one line = 27

height of each toolbox = 18"  

Total height of the pallet (i.e., max ) = 48"

maximum number of layers = 48/18 = 2.66 ; rounding it down = 2

therefore, the total number of toolboxes that can be fitted in one pallet = 2* 27 = 54

so, we can conclude that the maximum number of toolboxes each pallet can take is 72

b) number of units required per day = 2000

total units for 30 days = 2000*30 = 60000

If each pallet can take 72 toolboxes then a total of (60000/72) = 833.33 rounding it up we get 834 pallets required .

c) given only 3 high the pallets can be stored . This says each layer has 834/3 = 278 pallets

area occupied by 278 pallets = 278 x 42" x 42" = 490392 sq.inches

and also a 30% of aisle space is required

Total area = 490392/(1-0.3) = 700560 sq.inches

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