Question

A particular raw material is available to a company at three different prices, depending on the size of the order:

Less than 100 pounds	$	20	per pound
100 pounds to 999 pounds	$	19	per pound
1,000 pounds or more	$	18	per pound

The cost to place an order is $60. Annual demand is 2,900 units. Holding (or carrying) cost is 20 percent of the material price.

What is the economic order quantity to buy each time, and its total cost? (Round your answers to the nearest whole number.)

Economic order quantity		pounds
Total cost	$

Answer 1

Annual demand = D = 2900

Ordering cost = Co = $60

Since Carrying cost , Ch is proportional to price of the stone, Ch will change depending on respective quantity slab

Accordingly EOQ will also change depending on change in carrying cost

Following table presents different values of EOQ for different price levels and corresponding annual unit inventory carrying cost

Quantity	Price ( $)	Carrying cost- Ch ,$ ( 20% of Price )	EOQ ( rounded to nearest whole number)
1 – 399	20	4	295
400 – 599	19	3.8	303
600 or more	18	3.6	311

Out of the above, it is only order quantity of 295 which matches with order quantity slab of 1- 399. Thus 295 is the optimum order quantity if we have to minimize annual ordering cost plus inventory carrying cost.

However, we will compare total annual cost which is sum of annual purchasing cost , annual ordering cost and annual inventory carrying cost to arrive at economic order quantity.for following quantities :

1. Order quantity = 295
2. Order quantity 400 ( beginning of 2^nd quantity slab)
3. Order Quantity 600 ( beginning of 3^rd quantity slab)

Total cost for order quantity = 295 :

Annual purchasing cost = Price/ unit x annual demand =   $ 20   x 2900 = $58000

Annual ordering cost = Ordering cost x Number of orders = Co x Annual demand/ Order quantity = $60 x 2900/295 = $589.83  

Annual inventory carrying cost = Annual unit inventory carrying cost x Average inventory = Ch x Order quantity/2 = $4x295/2=$590

Total cost = Annual purchasing cost + Annual ordering cost + Annual inventory carrying cost = $59179.83

Total cost for order quantity = 400 :

Annual purchasing cost = Price/ unit x annual demand = $ 19   x 2900 = $55100

Annual ordering cost = Ordering cost x Number of orders = Co x Annual demand/ Order quantity = $60 x 2900/400 = $ 435

Annual inventory carrying cost = Annual unit inventory carrying cost x Average inventory = Ch x Order quantity/2 = $3.8 x400/2=$760

Total cost = Annual purchasing cost + Annual ordering cost + Annual inventory carrying cost = $56295

Total cost for order quantity = 600 :

Annual purchasing cost = Price/ unit x annual demand = $18 x 2900 = $52200

Annual ordering cost = Ordering cost x Number of orders = Co x Annual demand/ Order quantity = $60 x 2900/600= $    290

Annual inventory carrying cost = Annual unit inventory carrying cost x Average inventory = Ch x Order quantity/2 = $3.6x600/2=$1080

Total cost = Annual purchasing cost + Annual ordering cost + Annual inventory carrying cost = $53570

Since total cost works out cheapest for order quantity = 600, the economic order quantity will be 600 units

ECONOMIC ORDER QUANTITY = 600 lb

TOTAL COST = $53750