written 5.3 years ago by
sayalibagwe
♦ 8.1k

•
modified 5.3 years ago

$\text{Demand} \hspace{3.1cm} D = 10,000 \ \text{units} \\
\text{Unit cost} \hspace{3cm} Cp = Rs. 100 \ \text{(orders below 200 units)} \\
\hspace{4.6cm} Cp = Rs. 95 \ \text{(orders of 200 and above)} \\
\text{Inventory holding costs} \hspace{0.5cm} Ch = 10 \% \ of \ Cp \\
\text{Cost of each order} \hspace{1.6cm} Co = Rs. 5$
Case 1:
Finding EOQ (i.e. Q*) when Cp = Rs. 100
$Q*$ $= \sqrt{(2.D.CoCh)} \\
= \sqrt{(2.D.CoCp.I )} \\
= \sqrt{(2×10000×5100×0.1 )} \\
= 100 \ units$
Total minimum cost $= \sqrt{(2.D.Ch.Co) + Cp.D} \\
= \sqrt{(2×10000×100×0.1×5) + 100×10000} \\
= Rs. 10,01,000$
Case 2:
Finding EOQ (i.e. Q*) when Cp = Rs. 95
$Q*$ $= \sqrt{(2.D.CoCh)} \\
= \sqrt{(2.D.CoCp.I )} \\
= \sqrt{(2×10000×595×0.1 )} \\
= 102.6 \ units$
But we cannot use this, since Cp = 95 is allowed only for orders for 200 and above.
Case 3:
Cp = Rs. 95 and Q = 200 units
Total minimum cost $= \sqrt{(2.D.Ch.Co) + Cp.D} \\
= \sqrt{(2×10000×95×0.1×5) + 95×10000} \\
= Rs. 9,50,974.7$
So the economic lot size should be 200 units, and (10,000÷200) 50 orders need to be placed each year.