Answer to Question #207644 in Operations Research for Raa

Question

A trading company buys and sells 10000 bottles of pain-balm every year. The company's cost of placing an order of pain-balm is $100. The holding cost per bottle on inventory is $0.30.

To determine the optimum order quantity and inventory cycle time for the pain-balm bottles.

How many orders should be placed each year?

Answer 1

Ans:-

1)

The optimum order quantity $k$ is the ratio between the cost of placing an order $m$ and the holding cost $p,$

$k=\frac mp=\frac{100}{0.3}=333$ bottles;

inventory cycle time $t$ is the ratio between the optimum order quantity $k$ and the quantity of the bottles $n,$

$t=\frac kn=\frac{333}{10000}=\frac{1}{30}$ year (or $12$ days).

2) Number of orders $s$ is the inverse of the inventory cycle time $t,$

$s=\frac 1t=30$ orders per year.