Question

Our college purchases sweatshirts from a vendor emblazoned with the college name and logo. The vendor sells the sweatshirts to the college for 45 SAR a piece. The cost to the college for placing an order is 175 SAR and the carrying cost is 20% of the average annual inventory value. The college administration estimates that 2,000 sweatshirts will be sold during the year. The vendor has offered the college the following volume discount schedule:

Quantity	Discount (%)
1 – 299	0%
300 – 499	5%
500 – 799	8%
800+	12%

The college admin staff wants to determine the optimal order quantity, given the foregoing quantity discount information.

Answer 1

Annual Demand ( D) = 2000

Ordering cost ( S) = 175

Holding cost ( I ) = 20% average inventory cost

Discounted price for quantity volumes -

Scenario	Quantity	Discount	Discounted unit price (P)
1	0-299	0%	45.0
2	300-499	5%	42.8
3	500-799	8%	41.4
4	800+	12%	39.6

Calculate EOQ (Optimum order quantity) for each scenario -

Scenario 1

P = 45 with discount of 0 %

=279

Scenario 2

P = 42.8 with discount of 5 %

=286

Scenario 3

P = 41.4 with discount of 8 %

=291

Scenario 4

P = 39.6 with discount of 12 %

=297

Scenario	Quantity	Discount	Discounted unit price (P)	Calculated Optimum Order Qty	Optimum Order Qty with discount
1	0-299	0%	45.0	279	279
2	300-499	5%	42.8	286	300
3	500-799	8%	41.4	291	500
4	800+	12%	39.6	297	800

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