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Step 1: Economic Order Quantity (EOQ)

It is the bare minimum of an item that a corporation has on hand, such that when a stock falls below this level, the item must be reordered. During the replenishment lead period, it is normally approximated as the predicted usage plus safety stock. The EOQ (Economic Order Quantity) paradigm believed that there is no time lag between ordering and procuring suppliers.

Economic Order Quantity (EOQ) is a manufacturing formula that finds the most cost-effective number of items to acquire based on ordering and carrying expenses. In other words, it reflects the best amount of inventory that a firm should purchase each time to reduce the expenses associated with ordering and storing inventory.

Given,

Annual demand (A) = 2,400 books

Ordering cost per unit (S) = $5

Holding cost (H) = $4

Number of working days in a year = 365

Lead time (L) = 7 days

Standard deviation $\left({\mathrm{蟽}}_{\mathrm{D}}\right)$= 4 sets

$$\begin{gathered} \mathrm{EOQ}=\sqrt{\frac{2脳\mathrm{A}脳\mathrm{S}}{\mathrm{H}}} \\ \mathrm{Where}, \\ \mathrm{A}=\mathrm{Annual}\mathrm{Demand} \\ \mathrm{S}=\mathrm{Ordering}\mathrm{cost}\mathrm{per}\mathrm{unit} \\ \mathrm{H}=\mathrm{Carrying}\mathrm{cost}\mathrm{per}\mathrm{unit} \end{gathered}$$

$$\begin{gathered} \mathrm{EOQ}=\sqrt{\frac{2脳\mathrm{A}脳\mathrm{S}}{\mathrm{H}}} \\ =\sqrt{\frac{2脳2,400脳5}{4}} \\ =77.45\mathrm{or}78\mathrm{units} \end{gathered}$$

So, the Economic Order Quantity (EOQ) is 78 units.

Given,

Annual demand (A) = 2,400 books

Number of working days in a year = 365

$$\begin{gathered} \mathrm{Daily}\mathrm{demand}\left(\mathrm{d}\right)=\frac{\mathrm{Annual}\mathrm{Demand}}{\mathrm{No}.\mathrm{of}\mathrm{working}\mathrm{days}} \\ =\frac{2,400}{365} \\ =6.57\mathrm{or}7 \end{gathered}$$

So, the daily demand is 7 units.

Calculation of standard deviation during the lead time

Given,

Lead time (L) = 7 days

Standard deviation $\left({\mathrm{蟽}}_{\mathrm{D}}\right)$= 4 sets

role="math" localid="1650530972150" $$\begin{gathered} {\mathrm{蟽}}_{\mathrm{L}}=\sqrt{\underset{\mathrm{i}=1}{\overset{\mathrm{L}}{鈭�}}{\mathrm{蟽}}^2\mathrm{d}} \\ =\sqrt{7脳4^2} \\ =10.58\mathrm{sets} \end{gathered}$$

So, the standard deviation during the lead time is 10.58 sets.

Calculation of numbers of standard deviation which is denoted by z

By using an excel spreadsheet and function NORMSIV with the probability of 98% as given below:

=NORMSIV(0.98) and this will yield the z value to 2.05

Calculation of the Reorder point by using the following formula as given below:

$$\begin{gathered} \mathrm{Reorder}\mathrm{level}=\mathrm{dL}+{\mathrm{锄蟽}}_{\mathrm{L}} \\ =\left(7脳7\right)+\left(2.05脳10.58\right) \\ =70.689\mathrm{or}71\mathrm{sets} \end{gathered}$$

So, the reorder point is 71 sets.