GATE 2020 ME (ME1) – Question 58

Production Planning and Control · Inventory control: deterministic models, safety stock, control systems · 2 marks · Numerical answer

Compare two sourcing cases for the same part. Case 1: 1000 pieces/year from X; changeover time 2 hours, price ₹10/piece, holding-cost rate 10%/year. Case 2: 800 pieces/year from X and 200 pieces/year from Y; Y’s changeover is 6 minutes, price ₹5/piece and holding-cost rate 100%/year. Downtime costs ₹200/hour. Find percentage reduction in annual cost for Case 2 relative to Case 1, to two decimals.

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Correct answer: 8.19 to 8.23

Explanation

Case1: D=1000,S=2h×₹200/h=₹400,h=10%×₹10=₹1 per unit-year. EOQ annual cost is $10000+\sqrt{2(1000)(400)(1)}=10894.427$. Case2 uses X:D800,S400,h1 and Y:D200,S20,h5. Total is $9000+\sqrt{640000}+\sqrt{40000}=10000$. Reduction is $(10894.427-10000)/10894.427\times100=\mathbf{8.21\%}$. Include purchase costs and convert percentage holding rates into rupees.