Question

(a) A firm has two independent stores operating in two markets. Each store experiences daily demand that is normally distributed with mean = 10 and std = 1. Assuming service level of 90% (i.e., z=1.28) and a lead time of one, what is the safety stock kept at each store? What is the total reorder point for the two stores combined?

(b) Now, the firm decides to consolidate the two stores into its two branches of a single firm such that the warehouse storage is centralized. Assuming the demand random variables at the two branches are independent, what is the distribution of demand experienced by the firm? What are the firm’s total safety stock and the recorder point (assuming service level of 90% and a lead time of one)?

(c) Following part (b), if the lead time increases to 3 days, what are the firm’s total safety stock and the recorder point?

Answer 1

(a)

Mean demand, d = 10
Stdev, s = 1
Lead tme, L = 1

Safety stock in each store = z.s.sqrt(L) = 1.28*1*sqrt(1) = 1.28 units or 2 units if we round up.

Re-order point = d.L + SS = 10*1 + 2 = 12 units

Combined safety stock = 2*2 = 4 units

There is nothing called a combined reorder point. The reorder point means each store will place an order when the inventory level is 12 units. Adding the ROPs of the two stores does not give us any meaningful parameter.

(b)

Mean demand of two sores combined, d = 20
Variance of the two stores = 1^2 + 1^2 = 2
So, stdev of two stores combined, s = sqrt(2) = 1.414

Safety stock = z.s.sqrt(L) = 1.28*1.414*sqrt(1) = 1.81 units or 2 units if we round up.

Re-order point = d.L + SS = 20*1 + 2 = 22 units

So, safety stock of the single store is now 2 units only

(c)

d = 20
s = 1.414
L = 3

Safety stock = z.s.sqrt(L) = 1.28*1.414*sqrt(3) = 3.13 units or 4 units if we round up.

Re-order point = d.L + SS = 20*3 + 4 = 64 units