GATE ME 2020 Set 1 — Question 58
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Industrial Engineering → Inventory Control → EOQ Model
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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).
Correct answer
8.19 to 8.23
Solution
To find the percentage reduction in annual cost, we calculate the total annual cost for both cases, assuming the company operates at the Economic Order Quantity (EOQ) for each vendor.Case 1:
Demand () = 1000 pieces/year
Price () = Rs. 10/piece
Holding cost rate () = 10% = 0.1
Holding cost () = Rs/piece/year
Ordering cost () = Changeover time Cost of downtime = Rs/order
Total Annual Cost () = Purchase Cost + Ordering Cost + Holding Cost
At EOQ, Ordering Cost + Holding Cost =
RsCase 2:
This case involves splitting the demand between vendor X and vendor Y.
For Vendor X:
pieces/year, , ,
Rs
For Vendor Y:
pieces/year, , Rs/piece/year
Rs/order
Rs
Total Annual Cost for Case 2 () = RsPercentage Reduction:
Reduction = .
Demand () = 1000 pieces/year
Price () = Rs. 10/piece
Holding cost rate () = 10% = 0.1
Holding cost () = Rs/piece/year
Ordering cost () = Changeover time Cost of downtime = Rs/order
Total Annual Cost () = Purchase Cost + Ordering Cost + Holding Cost
At EOQ, Ordering Cost + Holding Cost =
RsCase 2:
This case involves splitting the demand between vendor X and vendor Y.
For Vendor X:
pieces/year, , ,
Rs
For Vendor Y:
pieces/year, , Rs/piece/year
Rs/order
Rs
Total Annual Cost for Case 2 () = RsPercentage Reduction:
Reduction = .
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