QUESTION $4$

An electronics store sells a personal desktop super$-$computer for $$2,575.$ The wholesale price is $$1,545.$ The store

estimates the weekly demand is Poisson distributed and average $0\mathrm{.}75$ units. The store's annual inventory holding cost

rate is $20\%.$ Assume orders are made weekly and the lead time to receive an order is $6$ weeks.

The Poisson Loss Function values are located on pages $481-482$ of your textbook.

What base stock level minimizes inventory while achieving a $99\%$ in$-$stock probability? $($Report your answer as an

integer.$)$

Suppose the base stock level is $S=9.$

a$.$ What is the average inventory held at the end of the week? $($Report your answer to two decimal places.$)$

What is the average on$-$order inventory? $($Report your answer to two decimal places.$)$

c$.$ What is the probability a stockout occurs during a week? $($Report your answer as a decimal to four decimal places.$)$

d$.$ What is the probability the store is out of stock at the end of a week? $($Report your answer as a decimal to four

decimal places.$)$

e$.$ What is the probability the store has two or more units of inventory at the end of a week? $($Report your answer as a

decimal to four decimal places.$)$

Suppose the store changes is considering a new replenishment policy in which an order is placed every $2$ weeks.

a$.$ What base stock level yields at least a $99\%$ in$-$stock probability while minimizing inventory? $($Report your answer as

an integer.$)$

b$.$ What is the average on$-$order inventory? $($Report your answer to two decimal places.$)$ Please provide complete working for each answer and excel working is require.