Question

Ergonomics Inc. sells ergonomically designed office chairs. The company has the following information: Average demand = 30 units per day Average lead time = 37 days Item unit cost = $57 for orders of less than 270 units Item unit cost = $56 for orders of 270 units or more Ordering cost = $32 Inventory carrying cost = 20% The business year is 250 days Assume there is no uncertainty at all about the demand or the lead time.

a. Calculate EOQ if unit cost is $57 and $56. (Note: These EOQs do not need to be feasible in their price range.)

b. Calculate annual ordering costs for each alternative?

c. Calculate annual inventory carrying costs for each alternative?

d. Calculate annual product costs for each alternative?

e. What will be the total costs for each alternative? (Round your answers to 2 decimal places.)

f. Based on your analysis, how many chairs should they order at a time?

g. How much the firm can save annually by using the order quantity in Part f. instead of the first EOQ shown in Part a?

Answer 1

Average demand per day = 30 units

The business year = 250 days

Annual Demand, D = 250 *30 = 7500 units

Average lead time = 37 days

Unit cost = $57 for orders of less than 270 units

unit cost = $56 for orders of 270 units or more

Ordering cost, S = $32

Inventory carrying cost = 20%

For orders of less than 270 units, Holding Cost per unit, H = 20% *57

For orders of 270 units or more, Holding Cost per unit, H = 20% *56

@56 unit price, EOQ =  207.0197

@57 unit priceEOQ = 205.1956

	@56	@57
EOQ	270.000	205.196
No.of Orders = 7500/EOQ	27.77778	36.55048
Order Cost = No.of orders*32	888.8889	1169.615
Purchase cost = 7500*unit price	420000	427500
Annual Holding Cost = (EOQ/2)*H	1512	1169.615
	422400.9	429839.2

b)

Annual Ordering Cost @ 56 = $ 888.88

Annual Ordering Cost @ 57 = $ 1169.615

c)

Annual inventory carrying cost @ 56 = $ 1512

Annual inventory carrying cost @ 57 = $ 1169.615

d)

Annual product cost @ 56 = 420000

Annual product cost @ 57 = 427500

e)

Total costs @56 = 422400.9

Total costs @57 = 429839.2

f)

Ordering the chair at the discount price has less total cost. Hence 270 units should be ordered.

g)

	@56	@57	@56
EOQ	270.000	205.196	207.020	Initial EOQ Quantity
No.of Orders = 7500/EOQ	27.77778	36.55048	36.22844
Order Cost = No.of orders*32	888.8889	1169.615	1159.31
Purchase cost = 7500*unit price	420000	427500	420000
Annual Holding Cost = (EOQ/2)*H	1512	1169.615	1159.31
	422400.9	429839.2	422318.6

Saved at discount by ordering 270 units = 429839.2-422400.9 = 7438.342

The EOQ for 56 unit price is 207.02.

By ordering 270 units to avail discount, 429839.2-422318.6 = 82.26 is lost when compared with part a.