1) Joe has a mail order business where he sells skateboards directly to consumer

Question

1)      Joe has a mail order business where he sells skateboards directly to consumers. Joe currently uses 4 warehouses and always ships to customers from their nearest warehouse. Each warehouse experiences demand that is independent and normally distributed with a mean weekly demand of 5,000 skateboards and a standard deviation of 1,000. Joe replenishes the warehouses weekly to ensure each warehouse maintains a 99% Type 2 Service Level.

a.       How much total safety stock should Joe carry across the 4 warehouses?

b.      What would Joe’s inventory reduction be if he consolidated to 1 single distribution warehouse?

Explanation / Answer

Safety stock = Z × LT

Z=99% service level = 2.33 ( Z score from normal distribution table)

LT= Lead time std deviation =1,000

Davg= Demand average =5000/7=715

So safety stock = 2.33*1000 =2,330.

For Four warehouse = 2,330*4=9,320

So Safety stock + Demand = total stock = 2,330+715=3045 per WH.

For 1 Warehouse consolidation. : 715*4 +2,330=5190

Total reduction inventory = (9320-5190)/9320=44% reduction.

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