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GATE 2021 ME (ME2) – Question 46

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

Daily production capacity of a bearing manufacturing company is 30000 bearings. The daily demand of the bearing is 15000. The holding cost per year of keeping a bearing in the inventory is ₹20. The setup cost for the production of a batch is ₹1800. Assuming 300 working days in a year, the economic batch quantity in number of bearings is _____ (in integer).

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Correct answer: 40249

Explanation

Annual demand is D=15000×300=4500000. For finite production rate, $Q^*=\sqrt{2DS/[H(1-d/p)]}$.

Here d/p=0.5, so $Q^*=\sqrt{2(4500000)(1800)/(20\times0.5)}=40249.2236$. **Answer: 40249 bearings**. Ignoring simultaneous consumption would give an undersized batch.