Question $3(35\%)$

Kromo is an Indian retail chain for consumer electronics. The company currently has $25$ stores

located in major metropolitan areas. Weekly demand for smartphones at each store is normally

distributed, with a mean of $300$ and a standard deviation of $250.$ The supplier currently takes four

weeks to fulfill a replenishment order submitted periodically, which is placed separately by each

store. Kromo practices $3$ Sigma in managing its stockout rate $($i$.$e$.,z=3).$

Kromo has a holding cost of $25$ per cent. Each time when Kromo submits an order, the vendor

charges a fixed ordering cost, regardless of the order quantity of $$1,000.$ The cost of the smartphone

is $$200$ per unit.

$($a$)$ Suggest an optimal periodic review period $T$ for each product $($assuming each year has $52$

weeks$).(10$ marks$)$

For simplicity, for the following questions we assume that the periodic review period $T=3$ weeks.

$($b$)$ Obtain the overall annual holding costs of the safety stocks at all $25$ retailers. $(10$ marks$)$

$($c$)$ Kromo is considering moving smartphones to the online channel, where they would be stocked

in a single national warehouse. Assume that Kromo can move smartphones to the online

channel without losing demand $($the online demand is the sum of demand at each retail store$).$

How much saving in safety inventory can Kromo expect from going online if demand across

stores is independent? $(15$ marks$)$