What is the optimal order quantity Q$*?$

What is the optimal Re$-$order point R$?$

What is the optimal fill$-$rate service level $($with two decimal places$)?$

The backorder cost $($p$)$ is unreliable and should not be used.$$ Rework the model using a $97\%,$ in$-$stock service level requirement,$$What is the$$revised$$order quantity, Q$?$

The backorder cost $($p$)$ is unreliable and should not be used.$$ Rework the model using a $97\%,$ fill rate service level requirement,$$What is the$$revised$$order quantity, Q$?$

The backorder cost $($p$)$ is unreliable and should not be used.$$ Rework the model using a $97\%,$ fill rate service level requirement, How has the annual cost of backorders changed?

The backorder cost $($p$)$ is unreliable and should not be used.$$ Rework the model using a $97\%($or $99\%),$ fill rate service level requirement, What is the revised type $1$ service level $($ with two decimal places$)?$

Finally, the management team would like to do some sensitivity analysis on the type $2$ service level. $$By how much does Total Relevant Cost increase as the type $2$ service level is changed from $97\%$ to $99\%?$

At the $99\%$ type $2$ service level, what is the average inventory level?

Order Quantity Q units

USE FOLLOWING DATA

Annual demand D $110,000$ units per year

Standard deviation of annual demand sD $26,000$ units per year

Mean lead time L $0\mathrm{.}08$ years

Standard deviation of lead time sL $0\mathrm{.}04$ years

Type $1$ Service Level alpha

Inventory holding cost factor $($annual$)$ w $26\%$ per year

Unit purchase cost v $$495$ per unit

Holding cost per unit per year h per unit per year

Backordering cost per unit p $$82$ per unit backordered

Ordering cost per order A $$1,380$ per order

Std$.$ deviation of demand during the lead time s units per lead time

Mean demand during the lead time LTD units per lead time

Standard normal variate z

Safety Stock SS units

Expected units out of stock during the lead time nR $-$ units per cycle

Type $2$ Service Level b

Reorder point R units

Annual Cost of Cycle Stock GCC per year

Annual Cost of Safety Stock GSS per year

Annual Ordering Cost GOC per year

Annual Backordering Cost GBC per year

Annual Total Relevant Cost GQR per year