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%

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

Answer 1

Scenario 1: Quantity Discount - 0% , Order Qty Range = 0 - 299

Unit Price (P) = 45 SAR

Annual Demand (D) = 2000

Cost of Ordering (S) = 175 SAR

Carrying Cost (H) = 20% of Unit price = 0.20*45 = 9 SAR

Order Quantity (Q)

Q is in the given range of 0% discount

Total Cost = Ordering Cost + Holding Cost + Purchasing Cost

Ordering Cost = (D/Q)* S = (2000/279)*175 = 1254.48 SAR

Holding Cost = (Q/2)*H = (279/2) * 9 = 1255.5 SAR

Purchasing Cost = D*P = 2000*45 = 90000

Total Cost = 1254.48 + 1255.5 + 90000 = 92509.98 ~ 92510 SAR

Scenario 2: Quantity Discount - 10% , Order Qty Range = 300 - 499

Unit Price (P) = 0.95 * 45 = 42.75 SAR

Annual Demand (D) = 2000

Cost of Ordering (S) = 175 SAR

Carrying Cost (H) = 20% of Unit price = 0.20*42.75 =   8.55 SAR

Order Quantity (Q)

Q is not in the given range of 5% discount. So we need to order minimum quantity eligible for discount i.e 300

Q = 300 units

Total Cost = Ordering Cost + Holding Cost + Purchasing Cost

Ordering Cost = (D/Q)* S = (2000/300)*175 = 1166.67 SAR

Holding Cost = (Q/2)*H = (300/2) * 8.55 = 1282.5 SAR

Purchasing Cost = D*P = 2000*42.75 = 85500 SAR

Total Cost = 1166.67 + 1282.5 + 85500 = 87949.17 ~ 87949 SAR

Scenario 3: Quantity Discount - 8% , Order Qty Range = 500-799

Unit Price (P) = 0.92* 45 = 41.4 SAR

Annual Demand (D) = 2000

Cost of Ordering (S) = 175 SAR

Carrying Cost (H) = 20% of Unit price = 0.20*41.4 = 8.28 SAR

Order Quantity (Q)

Q is not in the given range of 8% discount. So we need to order minimum quantity eligible for 8% discount i.e 500

Q = 500 units

Total Cost = Ordering Cost + Holding Cost + Purchasing Cost

Ordering Cost = (D/Q)* S = (2000/500)*175 = 700 SAR

Holding Cost = (Q/2)*H = (500/2) * 8.28 = 2070 SAR

Purchasing Cost = D*P = 2000*41.4 = 82800 SAR

Total Cost = 700 + 2070 + 82800 = 85570 SAR

Scenario 4: Quantity Discount - 10% , Order Qty Range = 800+

Unit Price (P) = 0.90* 45 = 40.5 SAR

Annual Demand (D) = 2000

Cost of Ordering (S) = 175 SAR

Carrying Cost (H) = 20% of Unit price = 0.20*40.5 = 8.10 SAR

Order Quantity (Q)

Q is not in the given range of 10% discount. So we need to order minimum quantity eligible for 10% discount i.e 800

Q = 800 units

Total Cost = Ordering Cost + Holding Cost + Purchasing Cost

Ordering Cost = (D/Q)* S = (2000/800)*175 = 437.5 SAR

Holding Cost = (Q/2)*H = (800/2) * 8.10 = 3240 SAR

Purchasing Cost = D*P = 2000*40.5 = 81000 SAR

Total Cost = 437.5 + 3240 + 81000 = 84667.5 ~ 84668 SAR

Summary

Total Cost for Order Qty 800 is the minimum so the college admin staff should order Qty 800 per order.