Which requires less inventory? What$$s the cost difference?

Product costs $$2,500$ Annual holding cost of $35\%.$

Desired service level is $98\%$ Continuous Review $($no review period$)$

Mean demand at each DC $=100/$day Standard Deviation $($SD$)$ of demand $=20$

Except DC $5$ which has mean demand $200/$day and Standard Deviation of $30$

Except DC $6$ which has mean demand $300/$day and Standard Deviation of $35$

All demands are independent

Top scenario transit is uncertain: Mean $=3$ days, SD $=1$ day; $1$ factory serves six DCs

Bottom scenario transit has no uncertainty: always $1$ day; each factory services two DCs

Case

Facts:

or

FGI

Dist. Center

FactorySuppliers

Factory $3$

Suppliers Factory $2$

Factory $1$

$100$ units mean

demand, SD $=203$ day mean

replenishment

time, SD $=1$ day

Always

$1$ day

Always

$1$ day

$200$ units mean

demand, SD $=30$

$100$ demand

SD $=20$

$100$ demand

SD $=20$

$100$ demand

SD $=20$

Big

FGI

Dist. Center

$300$ units mean

demand, SD $=35$

Big