Safety Stock$]$

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.

What is the Total Annual Inventory Cost for the company's current policy?

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

Orders $=$TBO$=\frac{\text{E}\text{O}\text{Q}}{D}$

$$1153\mathrm{.}24$

$$241\mathrm{.}23$

$$794\mathrm{.}68$

$$4681\mathrm{.}95$

$$1116\mathrm{.}05$