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GATE 2024 ME – Question 38

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

A company orders gears in conditions identical to those considered in the economic order quantity (EOQ) model in inventory control. The annual demand is 8000 gears, the cost per order is 300 rupees, and the holding cost is 12 rupees per month per gear. The company uses an order size that is 25% more than the optimal order quantity determined by the EOQ model. The percentage change in the total cost of ordering and holding inventory from that associated with the optimal order quantity is

  1. 2.5
  2. 5
  3. 0
  4. 12.5

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Correct answer: (A) 2.5

Explanation

The total cost is $TC(Q) = \frac{DS}{Q} + \frac{HQ}{2}$. At the optimum $Q^*$ the two terms are equal, so $TC^* = HQ^*$. For $Q = 1.25Q^*$, $\frac{TC}{TC^*} = \frac{1}{2}\left(\frac{Q}{Q^*} + \frac{Q^*}{Q}\right) = \frac{1}{2}(1.25 + 0.8) = 1.025$. The total cost rises by 2.5 %, whatever the values of the demand and the costs.