1. The replenishment lead time (L) = 1week.
Problem 7.8
# of warehouses = 4
R/week at each warehouse
= 10,000/wk or 500,000 yr
R = N(10,000, 2,000)
H=.25(10) = 2.5 /yr
S = 1000
L = 1 week
SL = .95
Decentralized Policy
=20000
The replenishment lead time (L) = 1week.
Standard deviation of demand during lead time at each store
σ = 2,000.
Safety stock at each store for 95% level of service
Is= 1.65 x 2,000 = 3,300.
ROP = LTD + Is =
10, ,300 = 13,300.
=13300
=4(13300) = 53200
Average time unit spends in store (T) = Id / (4R) =
53,200/40,000 = 1.33 weeks.

2. Total Cost
We do not consider RC because it does not depend on the inventory policy. But you can always add it.
Inventory system cost for one warehouse
Inventory system cost for four warehouses = 4(58,250)
Inventory system cost for four warehouses = 233,000

3. b. Centralized Policy
R/week in each warehouse follows Normal distribution with mean of 10,000, and Standard deviation of 2,000
When combining all in a central warehouse
Mean (central) = 4(10000) = 40000
=40000
Variance (central) = 4(variance at each warehouse)
Variance at each warehouse = (2000)2 = 4,000,000
Variance (central) = 4(4,000,000) = 16,000,000
Standard deviation (central) = 4,000
R (central) = Normal(40,000, 4000)

4. Centralized Policy
The replenishment lead time (L) = 1week.
Standard deviation of demand during lead time in the centralized system is
σ (central) = 4,000.
Safety stock at each store for 95% level of service
Is (central) = 1.65 x 4,000 = 6,600.
=26600
=26600
53200
Average time unit spends in store (T) = / =
= .67 weeks.

5. Total Cost
We do not consider RC because it does not depend on the inventory policy. But you can always add it.
Inventory system cost for four warehouse in centralized system
Inventory system cost for four warehouses in decentralized system