Question

Consider a collection of pallets of paint of various kinds. Each sku will be floor stacked 4 pallets high. Which skus are best stored in the area of the warehouse with lane depth of 3 pallet positions and an aisle 3 pallets wide?

Answer 1

Let Nx is the number of pallets of sku x and ‘x’ is the warehouse

‘r’ be the width of the aisle i.e. pallet positions = 3 (given in the problem)

Px is the height on which pallets are stacked (for sku x) = 4 (given in the problem)

Hence, the skus which should offer the best space utilization (considering depth of 3 pallet positions and an aisle 3 pallets wide) should fall in between the range of

=>           2.5 < Optimum lane depth < 3.5

=>           2.5 < (square root of ((r/2) * (Nx / Px)) < 3.5

=>           2.5 < (square root of ((3/2) * (Nx / 4)) < 3.5

=>           square of (2.5) < ((3 * Nx) / 8) < square of (3.5)

=>           6.25 < (3Nx / 8) < 12.25

Therefore, 16.7 < Nx < 32.7

Answer is the skus between the range of 17 to 33 pallets, are best stored in the area of the warehouse with lane depth of 3 pallet positions and aisle 3 pallets wide.