Question

An automobile insurance company uses a lot of expensive multipart paper to process its claims. The printer from whom they receive the paper has informed them of discounts available for quantity orders, but the company doesn't have space to store the entire amount ordered at one time. The company would receive the paper from the printer at the rate of 40 boxes per week, and it uses the paper at the rate of 20 boxes per week. Annual demand is estimated at 1000 boxes. It costs $10 to place and order and it costs 10% of the acquisition cost to store it. The printer is offering the following discounts:

Range of Order Quantities	Acquisition Cost(Price)
0 ‑ 199	$15
200 ‑ 249	$13
251 +	$12

1.What is the optimal order quantity if no discount is available?

2. What is the total stocking cost of ordering EOQ without the discount?

3.Given the discount what will be the order quantity?

Answer 1

1.

optimal order quantity = sqrt((2*annual demand*ordering cost)/holding cost per unit per year) = sqrt((2*1000*10)/(15*10%)) = 115.4700538 (Answer is 115 if rounding is required)

2.

Without the discount, total stocking cost = inventory holding cost + ordering cost + purchase cost
= (1000/115.4700538)*10+(115.4700538/2)*(15*10%)+1000*15 = 15173.20508

3.

If range of order quantity => 0-199, EOQ = sqrt((2*1000*10)/(15*10%)) = 115.4700538 (Answer is 115 if rounding is required)

total stocking cost = inventory holding cost + ordering cost + purchase cost
= (1000/115.4700538)*10+(115.4700538/2)*(15*10%)+1000*15 = 15173.20508

Order quantity 200-249,

EOQ = sqrt((2*1000*10)/(13*10%)) = 124.0347346 (Answer is 124 if rounding is required)

Feasible order quantity is adjusted upwards to 200 to avail discount

total stocking cost = inventory holding cost + ordering cost + purchase cost
= (1000/200)*10+(200/2)*(13*10%)+1000*13 = 13180

Order quantity 251+,

EOQ = sqrt((2*1000*10)/(12*10%)) = 129.0994449 (Answer is 129 if rounding is required)

Feasible order quantity is adjusted upwards to 251 to avail discount

total stocking cost = inventory holding cost + ordering cost + purchase cost
= (1000/251)*10+(251/2)*(12*10%)+1000*12 = 12190.44064

So, we can see total stocking cost is lowest for ordering quantity 251 hence Given the discount , order quantity will be 251