Now we no longer assume the size of the forward pick area to be fixed. Specifically, you are considering 10 possible sizes for the forward pick area: from 1,000 to 10,000 ft3 , in increments of 1,000 ft3 . As the size of the forward pick area increases, the cost of each pick from the forward pick area also increases because order pickers 1 OPRE 4330 HW 4: Warehousing must walk farther on average. Specifically, the cost per pick from the forward pick area is governed by the function f(x), where x is the size (in ft3 ) of the forward pick area:

f(x) = 2.1 + .0001x.

So, for example, if the forward pick area is 1,000 ft3 , then each pick costs $2.20 (as in the previous question); if it is 3,000 ft3 , then each pick costs $2.40, etc. Note that for this question you will need to change the cell containing the forward area cost per pick (cell B5 on the Parameters and Calculations sheet) from a static value to a formula based on f(x).

(a) (2 points) Report the optimal net benefit and the optimal number of SKUs to include in the forward pick area for each possible size as the area increases in size in increments of 1,000 ft3 , up to 10,000 ft3 (i.e., the net benefit and optimal number of SKUs when it is 1,000, 2,000, 3,000, . . ., 10,000 ft3 ).

(b) (4 points) What is the optimal size for the forward pick area, how many (and which) SKUs should optimally be stored there, and how much space should be allocated to each item?

Parameter	Value
Size of Forward Pick Area	1000
Cost per Replenishment	300
Cost per Pick from Reserve	6.7
Cost per Pick from Forward Pick Area	2.2
SKUs in Forward Area	30