Using a computerized Inventory Management System, a Paint Supply Store franchise continuously monitors the inventory of all the paint located at each of their $15$ stores and their distribution warehouse. The Paint Supply Store franchise sells an average of $64$ gallons of Green Paint every week $($for $52$ weeks per year, Standard Deviation of the Demand $=7$ gallons$).$ They purchase Green Paint from their supplier at a price of $$3\mathrm{.}50$ per gallon. It takes $2\mathrm{.}25$ weeks to receive an order from the supplier.

Administrative costs for Ordering paint have been estimated to be $$30$ per order.

Holding Costs $=35\%$ of the purchase price per gallon per year.

How much Safety Stock should the company hold to have a Service Level of $95\mathrm{.}0\%?$

Reorder Point, ROP $=dL+SS$

$d=$ Average Demand Rate per Time Period

$D=$ Demand Rate per Year

$L=$ Average Lead time $($time periods$)$

$SS=$ Safety Stock $=z{}_{dL}$

${}_{dL}=\sqrt[\phantom{2}]{L{}_d^2}$

$\backslash$table$[[$Service Level,$z$ Value$],[99\mathrm{.}99\%,3\mathrm{.}719],[99\mathrm{.}90\%,3\mathrm{.}090],[99\mathrm{.}00\%,2\mathrm{.}326],[95\mathrm{.}00\%,1\mathrm{.}645],[90\mathrm{.}00\%,1\mathrm{.}282],[85\mathrm{.}00\%,1\mathrm{.}036],[80\mathrm{.}00\%,0\mathrm{.}842]]$

$($Assuming Lead Time is constant as in Periodic review$)$

${}_d=$ Standard Deviation of the demand

$z=$ Number of Standard deviations corresponding to a service level

$Q=$ order Quantity

Average Inventory Level $=\frac{Q}{2}+SS$

$H=$ Holding Cost Per Year Per Unit

$s=$ Ordering$/$Setup Cost Per Order

Total Annual Inventory Cost $=(\frac{Q}{2})H+(\frac{D}{Q})S+H(SS)$

Economic Order Quantity, EOQ $=\sqrt[\phantom{2}]{\frac{2DS}{H}}$ Time Between