Astockist has to supply 400 units of a product every Monday to his customers. He gets the product at Rs. 50 per unit from the manufacturer. The cost of ordering and transportation from the manufacturer is Rs. 75 per order. The cost of carrying inventory is 7.5% per year of the cost of the product. Find: - 1. The economic lot size - 2. The total optimal cost (including the capital cost) - 3. The total weekly profit if the item is sold for Rs. 55 per unit -

Mumbai University > MECH > Sem 7 > Operations Research

Marks: 10 M

Year: May 2012, May 2013

$\text{Demand} \hspace{4cm} D = 400 \ \text{units/week} = 400×52 = 20800 \ \text{units/year} \\ \text{Unit cost} \hspace{3.9cm} Cp = Rs. 50 \\ \text{Inventory holding costs} \hspace{1.4cm} Ch = 7.5 \ \% \ of \ Cp \\ \text{Cost of each order} \hspace{2.3cm} Co = Rs. 75$

1. Economic Lot Size:

   $Q*$ $= \sqrt{\bigg(\dfrac{2.D.Co}{Ch}\bigg)} \\ = \sqrt{\bigg(\dfrac{2.D.Co}{Cp.I} \bigg)} \\ = \sqrt{\bigg(\dfrac{2×20800×75}{50×0.075} \bigg)} \\ = 912 \ units$

2. Total optimal cost (including capital cost):

   Cost $= D×Cp + \sqrt{(2.D.Ch.Co)} \\ = 20800×50 + \sqrt{(2×20800×50×0.075×75)} \\ = Rs. 1043420.526 \ \text{per year} \\ = Rs. 20065.78 \ \text{per week}$

3. Weekly profit:

   $\text{Profit}$ $= \text{selling price × unites sold – cost price per week} \\ = 55×400 – 20065.78 \\ = Rs. 1934.22 \ \text{per week}$