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Inventory Control Model, Operation Research

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1. A local university purchases exercise books to give to their students. Instead of a fixed unit cost, their supplier quotes the following discount pricing:

Order quantity Unit Price
0 – 5000 £3.00
5001 – 10000 £2.96
10001 and over £2.92

An annual holding cost is estimated to be 20% of the purchase price. The university incurs a fixed order placement, transportation and receiving cost of £100 each time an order is placed, regardless of the order quantity. Annual demand for exercise books is 10000.
The discount for the 10001-unit minimum order quantity looks tempting. However, realising that higher order quantities result in higher inventory holding cost, the university should prepare a through cost analysis before making a final ordering recommendation.
Determine the quantity of exercise books the university should order each time it makes an order in such a way as to minimise the total cost incurred.

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