What order quantity will minimize the total inventory cost, Operation Management

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Question:

You are the Operations Manager at Alien University and one of your responsibility is to manage the supplies of the University. One of your supplier has given you quantity discounts for the purchase of marker pens. The normal cost for the marker pen is Rs 5.00. For orders between 1,000 and 1.999 units, the unit cost drops to Rs 4.80; for orders of 2,000 or more units, the unit cost is only Rs 4.75. Furthermore, ordering cost is Rs 49.00 per order and from your records you found that the University uses 5,000 marker pens per year. You have estimated that the inventory carrying charge is 20% of unit cost.

a) What order quantity will minimize the total inventory cost?

b) Since your University is a good customer, the supplier has offered another price break. If you order 2,500 or more marker pens at a time, the unit cost drops to Rs 4.60. What is the optimal order quantity now?

c) Management of the Alien University is seeking your advice to improve inventory management at the University. Could you please suggest the types of inventory counting systems available and new technology for collecting data?

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