Answer to Question #174304 in Operations Research for deepak

Question

A trading company buys and sells 10,000 bottles of pain-balm every year. The 

company’s cost of placing an order of pain-balm is Rs. 100. The holding cost per 

bottle on inventory is Rs. 0.3. (5) 

 (i) Determine the optimum order quantity and inventory cycle time for the pain-balm, 

bottles. 

 (ii) How many orders should be placed each year?

Answer 1

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.