Question

A regional grocery chain is deciding whether to store packaged goods at each of its 16 stores or at a centralized warehouse. Weekly demand at each store is N(400, 100). The safety stock is set to twice the standard deviation of average weekly demand to ensure about a 98% fill rate. How much inventory can be saved if they pool the safety stock and keep it at the warehouse instead of individual stores?

Answer 1

page-01 we Safely stock and keep at at the wore house instead random variable Xili=1,2,...16) Answery How much inventory common be saved if they place the individual stoles string at individual stories: According to the to the given problem have to suppose , denotes stock in -i-th store. .: X;NN (4-400, V=100) we have plzc2)x0.98 =) P ( xi-4 xi-4 <2) 40.98 -> p ( *i-,400 <2)*0.98 -> p (xic 400+2 *10)~0.98 - P(xi < 42040.98 Therefore Total size of stock in 16 stores is = 420 x16 = 6720. 16 ΣΧΗ Staring at the centralized warehouse :- we have to define, Y ::ECY) = E :) HE i=1 E Elxi)

16 I 400 page:02 i 6400 i vor (y) = Vour (Ž :) V 16 ç Vor (x;) izl 16 lor yor » Y - My <2) 20.9 Y-6400 22) $0.98 .: Y~N ( My = 6400, y = you) have PCż<2)~0.98 Y P ( ay % P ( > PCY 26400+2x40) 20.98 rip CY_6480) 20.98 conclusion: If they pool the safety stock and keep centralized warehouse instead of indivi- dual stores, the amount of inventory that can be saved 6480 it at the is 6720 = 240