91Ó°ÊÓ

In essence, EOQ is a method for determining the volume and frequency of orders needed to meet a given level of demand while reducing cost per order. The Economic Order Quantity is a fixed point meant to assist businesses in lowering the cost of purchasing and storing inventory.

Thefixed-order quantity model is used by the firm, in which a predetermined amount of buy is made at each order and a purchase is made when the inventory level falls to a specified inventory level. The cost of acquiring inventory decreases as the order volume increases owing to purchasing economies of scale. However, as the amount of the inventory grows, so does the expense of storing the inventory. EOQ is the exact moment at which both of these inversely associated expenses are minimized.

Given,

Annual Demand = 36000 units

Ordering cost per unit = $ 10

Carrying cost per unit = 0.50

$$\begin{gathered} EOQ=\sqrt{\frac{2×A×S}{H}} \\ \text{where,} \\ \text{A = Annual demand} \\ \text{S = Ordering cost per unit} \\ \text{H = Carrying cost per unit} \\ EOQ=\sqrt{\frac{2×A×S}{H}} \\ =\sqrt{\frac{2×36,000×10}{0.50}} \\ =1200units \end{gathered}$$

So, the economic order quantity is 1200 units.

Given,

Lead time (L) = 5 weeks

Standard deviation = 15 units

Weekly demand (d) = 100 units

Calculation of numbers of standard deviation which is denoted by z

By using an excel spreadsheet and function NORMSIV with the probability of 90% as given below:

=NORMSIV(0.90) and this will yield the z value to 1.28

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

$$\begin{gathered} Reorderlevel=dL+z{\mathrm{σ}}_L \\ =(100×5)+(1.28×15) \\ =500+19.2 \\ =519.2 \end{gathered}$$

So, the reorder point is 519 units.