Optimal Policy Based on the Continuous Review Model

The parameter of the problem:

Expected Annual Demand Rate $=D=2,400$ Units$/$year Normal distribution of $ML=200$

St$.$ Dev. $=30$

Service Level $)=(1\mathrm{.}65$

Purchasing Cost $=C=$$$\frac{45}{?}$ unit

Holding cost $=Ch=$$$\frac{9}{?}$ unit $\frac{?}{?}$ year

Ordering cost $Co=$$$300$

Optimal Order Quantity

$Q^{**}\frac{?}{S}=QRT(\frac{2**CoD}{C}H)=400$ Units

Optimal Cycle Length

$T^{**}=\frac{Q^{**}}{D}=0\mathrm{.}167(2$ months$)$

Number of Orders Per Year

$N^{**}=\frac{D}{Q^{**}}=6$ Orders per year

Reorder point

$R=ML+Z**$ St$.$Dev $=249\mathrm{.}5($round to $250)$

Safety Stock

$SS=R-ML=49\mathrm{.}5(roundto50)$

Minimum Total Inventory Cost per Unit Time

TCU$(Q^{**})=C^{**}D+Co\frac{D}{Q^{**}}+Ch\frac{Q^{**}}{2}+SS**Ch=$$$112,050$

Managerial Interpretation: