91Ó°ÊÓ

The best order amount for a corporation to acquire for its inventory, given a fixed cost of production, demand rate, and other factors, is known as the economic order quantity (EOQ). This is done to reduce variable inventory costs, and the EOQ equation accounts for storage, ordering, and shortfall costs.

The economic order quantity aids in lowering inventory holding costs. The firm does not have to order surplus inventories that must be held in warehouses, saving money that would otherwise be spent on rent and other storage-related expenditures.

Given,

Daily demand = 60 units

Standard deviation = 10 units

Review period = 10 days

Lead time = 2 days

Inventory stock = 100 units

The formula for calculating optimum order quantity

$\mathrm{q}=\mathrm{d}\left(\mathrm{T}+\mathrm{L}\right)+{\mathrm{³úσ}}_{\left(\mathrm{T}+\mathrm{L}\right)}-1$

Where,

q =order quantity

T= Time of Review

L= lead time

z = number of standard deviation

${\mathrm{σ}}_{\left(\mathrm{T}+\mathrm{L}\right)}$= Standard deviation of demand over the review and lead time

I = Current level inventory

The value of the ${\mathrm{σ}}_{\left(\mathrm{T}+\mathrm{L}\right)}$ will be calculated by the following formula

$$\begin{gathered} {\mathrm{σ}}_{\left(\mathrm{T}+\mathrm{L}\right)}=\sqrt{\left(\mathrm{T}+\mathrm{L}\right){\mathrm{σ}}^2\mathrm{d}} \\ =\sqrt{\left(10+2\right){\left(10\right)}^2} \\ =\sqrt{1200} \\ =34.64 \end{gathered}$$

The z value for the service probability of 98%is obtained by = NORMSINV (0.98) formula in an excel spreadsheet.

The value of z is 2.05.

Now by putting the values in the formula

$$\begin{gathered} \mathrm{q}=\mathrm{d}\left(\mathrm{T}+\mathrm{L}\right)+{\mathrm{³úσ}}_{\left(\mathrm{T}+\mathrm{L}\right)}-\mathrm{I} \\ \mathrm{q}=60\left(10+2\right)+2.05×34.64-100 \\ \mathrm{q}=720+71.012-100 \\ \mathrm{q}=791.012-100 \\ \mathrm{q}=691.012\mathrm{or}691 \end{gathered}$$

So, the 691 units should be ordered to fulfil 98% of the service probability.