Question

(7) The annual demand for a product is 500,000 units. The inventory carrying cost for this product is 25% per unit per year and the cost of placing one order is $200. The supplier of this product gives quantity discounts outlined in the table below.
							Level 1	Level 2	Level 3	Level 4
If Quantity is:	1 to 1999	2000 to 9999	10000 to 49999	50000 or higher
Price	$     20.00	$            19.80	$     19.75	$     19.70
Provide the following information for the situation above.
	Level 1	Level 2	Level 3	Level 4
Price	$     20.00	$            19.80	$     19.75	$     19.70
Order Quantity
Annual Item Cost
Annual Ordering Cost
Annual Carrying Cost
Annual Total Cost

Answer 1

Given the details as annual demand, D= 500,000 units

Carrying cost, H= 25% of unit cost

Ordering cost, S= $200

Range                        Unit price P                H

1 – 1999                  $20.0                   0.25*20= $5

2000- 9999             $19.8                   0.25*19.8 = $4.95

10000- 49999         $19.75                 0.25*19.75= $4.9375

50000 or higher     $19.7                 0.25*19.70= $4.925

We should find the feasible minimum point starting from the lowest cost.

EOQ= √(2DS/H)

Minimum point19.7 = √(2*500,000*200/4.925)= 6372.5≈ 6373 units

This is not a feasible minimum point as order size of 6273 costs $19.8 rather than $19.7.

Minimum point19.75 = = √(2*500,000*200/4.9375)= 6364.5≈ 6365 units

This is also not a feasible minimum point as order size of 6365 costs $19.8 rather than $19.75.

Minimum point19.8 = √(2*500,000*200/4.95)= 6356.42≈ 6356 units

This is a feasible minimum point as the order size of 6356 units comes within the given range of $19.8.

Now Now we need to calculate the total cost for 6356 units and compare it with the total costs for price breaks of all lower unit costs.

TC= Annual carrying cost+ Annual ordering cost+ Purchase cost

     = (Q/2)H + (D/Q)S + PD

TC6356 = (6356/2)4.95 +(500,000/6356)200 +(19.8*500,000)= $9931464.27

TC10000 = (10000/2)4.9375 +(500,000/10000)200 +(19.75*500,000)= $9909687.5

TC50000 = (50000/2)4.925 +(500,000/50000)200 +(19.7*500,000)= $9975125

We can see that the total cost is the lowest when the quantity is 10,000 units. Hence 10,000 units is the optimal order quantity.

Order quantity = 10,000 units

Annual item cost= PD= 500,000*19.75= 9875000

Annual carrying cost= (Q/2)H = (10000/2)4.9375= $24687.5

Annual ordering cost= (D/Q)S= (500,000/10000)200= 10000

Annual Total cost= 9875000+ 24687.5+ 10000= $9909687.5