Question

Consider two cases as below.
Case 1: A company buys 1000 pieces per year of a certain part from vendor 'X'. The changeover time is 2 hours and the price is Rs. 10 per piece. The holding cost rate per part is 10% per year.

Case 2: For the same part, another vendor 'Y' offers a design where the changeover time is 6 minutes, with a price of Rs. 5 per piece, and a holding cost rate per part of 100% per year. The order size is 800 pieces per year from 'X' and 200 pieces per year from 'Y'.
Assume the cost of downtime as Rs. 200 per hour. The percentage reduction in the annual cost for Case 2, as compared to Case 1 is (round off to 2 decimal places).

• A. 5.32

Answer 1

The correct option is A 5.32
$\text{Given Data :}$

$\text{1000 pieces/year from 'X'.}$

$\text{Changeover time = 2 hrs.}$

$\text{Cost of downtime = Rs. 200/hour}$

$\text{So, Total cost of downtime}$

$\text{2 × 200 = Rs. 400/downtime}$

$\text{C = Rs. 10/piece}$

$\text{Holding cost,}{C}_h=\text{10\% of Rs. 10}$

$C_h=\text{Rs. 1/unit/year}$

$\text{So, total cost for Case I:}$

$\text{= Material Cost + Downtime Cost + Inventory Holding Cost}$

$=1000\times 10+(1\times 400)+\frac{1000}{2}\times 1$

$\text{Total cost for case I = Rs. 10,900/-}$

Case II: Order quantity 800 units from X and 200 units from Y.

$\text{For Y: Change overtime = 6 min. = 0.1 hour}$

$\text{Downtime cost = 0.1 × 200 = Rs. 20/-}$

$\text{Unit cost, C = Rs. 5/piece}$

$\text{Holding cost,}{C}_h=\text{100\% of unit cost = Rs. 5}$

So, total cost for case II:

$\text{Total cost II= Cost for 'X' + Cost for 'Y'}$

$=(800\times 10+400+\frac{800}{2}\times 1)+(200\times 5+20+\frac{200}{2}\times 5)$

$=8000+800+1000+520$

$\text{Total cost for case II = Rs. 10,320/-}$

So, percentage reduction in total cost of case II

$=\frac{10900-10320}{10900}\times 100$

$=\frac{580}{10900}\times 100$

$\text{= 5.32\%}$