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Average inventory is the mean of inventory within a specific fundamental quantity, which can vary from the median of the identical data set, and is computed by averaging the starting and ending inventory values over a specified period.

Economic Order Quantity is the optimal quantity of an item to order at a given moment. The major reason for determining this number is to avoid overspending on an item, as well as to reduce the ordering and holding expenses connected with the item. It assists in determining the frequency and amount of the order by taking into account elements such as demand, holding cost, ordering cost, interest cost, and so on. In other words, the fundamental goal of determining the EOQ is to reduce the overall cost (from ordering to holding) for each order.

Given,

Review period = 14 days

Average daily demand = 2000 capsules

Holding cost (H) = 20% of cost price = $100

Lead time (L) = 5 days

Standard deviation = 800 capsules

Service probability = 99 %

Inventory available at the time of inventory = 25,000 capsules

Calculation of numbers of standard deviation which is denoted by z

By using an excel spreadsheet and function NORMSIV with the probability of 99% as given below:

= NORMSIV (0.99) and this will yield the z value to 2.58

Calculation of the Optimum order quantity by using the following formula as given below:

$$\begin{gathered} \mathrm{Reorder}\mathrm{level}=\mathrm{d}\left(\mathrm{T}+\mathrm{L}\right)+{\mathrm{³úδ}}_{\left(\mathrm{T}+\mathrm{L}\right)}-1 \\ \mathrm{where}, \\ \mathrm{d}\mathrm{is}\mathrm{average}\mathrm{daily}\mathrm{demand} \\ \mathrm{L}\mathrm{is}\mathrm{lead}\mathrm{time} \end{gathered}$$

$$\begin{gathered} \mathrm{z}\mathrm{is}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{standard}\mathrm{deviation}\mathrm{from} \\ \mathrm{a}\mathrm{specified}\mathrm{service}\mathrm{probability} \\ {\mathrm{δ}}_{\mathrm{L}}\mathrm{is}\mathrm{the}\mathrm{standard}\mathrm{deviation}\mathrm{of}\mathrm{usage}\mathrm{in}\mathrm{lead}\mathrm{time} \\ \mathrm{I}\mathrm{is}\mathrm{inventory}\mathrm{available}\mathrm{at}\mathrm{time}\mathrm{of}\mathrm{review} \end{gathered}$$

$\begin{array}{rcl}{\mathrm{δ}}_{\left(T+L\right)}& =& 800\sqrt{\left(14+5\right)}\\ & =& 800\sqrt{19}\\ & =& 3487\mathrm{capsules}\end{array}$

$$\begin{gathered} \mathrm{q}=\overline{\mathrm{d}}\left(\mathrm{T}+\mathrm{L}\right)+{\mathrm{³úδ}}_{\left(\mathrm{T}+\mathrm{L}\right)}-1 \\ =2000×\left(14+5\right)+2.33×\left(3487\right)-25000 \\ =21,125\mathrm{capsules} \end{gathered}$$

So, 21,125 capsules should be ordered