a$.$ Calculate the optimal review interval, T$*,$ at a warehouse. $(3$ points$)$

b$.$ Calculate order$-$up$-$to level, M$.(3$ points$)$

c$.$ Calculate the average inventory level, AIL $(2$ points$)$

d$.$ Calculate the total cost, TC$,$ per month $(3$ points$)$

e$.$ Calculate the total cost and AIL of FOUR branches assuming that the demand is

identically and independently distributed $($use the same $90\%$ CSL$).(3$ points$)$

f$.$ When the company consolidates the inventory at these warehouses into a single

warehouse, the company would like to improve the customer service level to $99\%.$

Given this scenario,

I. Calculate the optimal review interval, T$*,$ at a warehouse. $(3$ points$)$

II$.$ Calculate order$-$up$-$to level, AIL. $(3$ points$)$

III. Calculate the average inventory level, AIL$(3$ points$)$

IV$.$ Calculate the total cost, TC$,$ per month $(3$ points$)$

V$.$ Expected percentage AIL saving four warehouse case $(2$ points$)$

VI$.$ Expected percentage TC saving compared to four warehouse case $(2$ points$)$