$(25$ points$)$ Suppose you are laying out a floor stack area with an aisle $14$ feet $(4\mathrm{.}3$ meters$)$ wide to accommodate forklift trucks. All pallets are $48$ by $40$ inches $(1200$ by $1000$ mm$)$ and are stored with the $40-$inch side facing the aisle. Assume that each SKU experiences demand that is constant and is reordered once each inventory cycle as below.

SKU

Order quantity $($pallets$)$

Stack height $($pallets$)$

Order cycle $($weeks$)$

A

$20$

$2$

$4$

B

$24$

$3$

$3$

C

$12$

$1$

$6$

D

$4$

$3$

$2$

$(1)$ For each SKU, compute a space$-$efficient lane depth.

$(2)$ Compute a single, common lane depth that will be space$-$efficient for the set of SKUs.

$(25$ points$)$ Suppose you are laying out a floor stack area that will be a single pallet position deep. The aisle will be $2$ pallets wide. Assuming that demands are constant, which SKUs will give the best space utilization in this area?

$(25$ points$)$ 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?

$(25$ points$)$ Consider two SKUs moving through a unit$-$load warehouse. Every Monday morning $100$ pallets of SKU A are shipped out and in the afternoon $100$ new pallets of SKU A arrive. Every other Monday, $10$ pallets of SKU B are shipped out and in the afternoon $10$ pallets arrive. On average there are $500$ pallets of SKU A on$-$hand and $20$ pallets of SKU B$.$

$(1)$ Which SKU has priority for storage in the most convenient storage locations under FIFO?

$(2)$ How would your answer change if the FIFO requirement were dropped?