Question : A producer distributes 800 packing boxes per month, which he purchased at a cost of Rs. 10 each. The manager has assigned an annual carrying charge of 25 percent of the purchase price per box. Ordering costs are Rs. 28. Currently the manager orders once a month. How much could the firm save annually in ordering and carrying costs using EOQ? Derive the formulae you use from the first principles. (Summer 2005)
Solution : Economic ordering quantity (E.O.Q.) is obtained by the quantity whose procurement cost is equal to inventory carrying cost.
Let,
A = Total items consumed (used) per year
P = Procurement cost per year
C = Annual inventory carrying cost per item of component
Q = Economic ordering quantity
Then, Procurement cost / year
= (Number of orders placed in a year) x (cost per year)
= (AxP)/Q ... (i)
and inventory carrying cost/year
= (Average value of inventory in a year) x (Annual Inventory carrying cost per item component)
= (QxC)/2 ...(ii)
Total Cost = {(AxP)/Q}+{(QxC)/2} ...(iii)
This total cost will be minimum, when
= (AxP)/Q = (QxC)/2
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