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?

(d) “In general term, while centralization has a downward pressure on the safety stock, it may actually raise the safety stock and reorder point.” Is this statement true? Explain.

Answer 1

a)

Mean demand, d = 10

std dev of demand, s = 1

Lead time, L = 1

z = 1.28 for 90% service level

Safety stock kept at each store = z*s*sqrt(L)

= 1.28*1*sqrt(1)

= 1.28

Reorder point of each store = d*L+safety stock

= 10*1+1.28

= 11.28

Total reorder point for the two stores = 11.28*2

= 22.56

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b)

Consolidated store

Mean demand, d = 2*10 = 20

Std dev of demand, s = 1*sqrt(2) = 1.414

Safety stock = z*s*sqrt(L)

= 1.28*1.414*sqrt(1)

= 1.81

Reorder point = 20*1+1.81

= 21.81

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c)

Total safety stock = 1.28*1.414*sqrt(3)

= 3.14

Reorder point = 20+3.14

= 23.14

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d)

Generally centralization decreases the safety stock. However, if centralization increases the lead time and/or fluctuation in supply, then it may actually raise the safety stock and reorder point, instead of decreasing it.