Q6 – Demand aggregation: heterogeneous demand The company has three distribution
ID: 434206 • Letter: Q
Question
Q6 – Demand aggregation: heterogeneous demand
The company has three distribution centers, DC1, DC2, and DC3 for tennis rackets. Mean and standard deviation of daily demand and lead time at each DC are not identical and are summarized in Table 8. The company uses continuous-review replenishment policy and targets CSL of 99%. Demands at the distribution centers are independent.
Table 8: Demand and lead time
DC1
DC2
DC3
Mean of daily demand (units per day)
D = 50
D = 100
D = 150
Standard deviation of daily demand
?D = 10
?D = 50
?D = 90
Lead time (days)
L = 4
L = 4
L = 4
(1) The company is considering a central distribution center (CDC) for tennis rackets to aggregate demands. The company targets CSL of 99%. Lead time is 4 days (L = 4) and there is no uncertainty of lead time. Calculate daily demand and standard deviation of the daily demand for tennis rackets at CDC. Enter the answers in the table below.
Answers
Daily demand at CDC
Standard deviation of daily demand at CDC
(2) Calculate safety inventory for tennis rackets at CDC. Enter the answer in the table below.
Answer
Safety inventory at CDC
DC1
DC2
DC3
Mean of daily demand (units per day)
D = 50
D = 100
D = 150
Standard deviation of daily demand
?D = 10
?D = 50
?D = 90
Lead time (days)
L = 4
L = 4
L = 4
Explanation / Answer
Re order point = avg demand x lead time + z x s.d. of demand x ( lead time)1/2
ROP for DC 1 = 50x4+ 2.33 x10x2
ROP for DC 2 =100x4 + 2.33 x50x 2
ROP for DC3 = 150x4+ 2.33 x90x2
Collective mean demand at the centralised warehouse = 200+400+600 =1200
Variance of collective demand = Var (1) +Var (2) + Va (3) + 2 Cov ( 1,2)+ 2 Cov ( 2,3) + 2 Cov ( 1,3)
= (10)2+ (50)2+( 90)1/2 + 0 = 100+2500+8100
= 10700
SD of the new sample= (Var )1/2 = 103.44
Safety stock = z x103.44 x (4)1/2 =2.33x103.44x2 = 482
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.