Question

Ergonomics Inc. sells ergonomically designed office chairs. The company has the following information:

Average demand = 29 units per day

Average lead time = 30 days

Item unit cost = $56 for orders of less than 260 units

Item unit cost = $54 for orders of 260 units or more

Ordering cost = $31

Inventory carrying cost = 25%

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 $60 and $58.

Unit cost at 56 (           ).

Unit cost at 54 (           ).

____________________________________________________

b. Calculate annual ordering costs for each alternative?

Unit cost at 56 (             ).

Unit cost at 54 (             ).

_____________________________________________________

c. Calculate annual inventory carrying costs for each alternative?

Unit cost at 56 (              ).

Unit cost at 54 (              ).

______________________________________________________

d. Calculate annual product costs for each alternative?

Unit cost at 56 (               ).

Unit cost at 54 (               ).

_______________________________________________________

e. What will be the total costs for each alternative?

Unit cost at 56 (               ).

Unit cost at 54 (               ).

________________________________________________________

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

Order quantity of (                          ) chairs.

_________________________________________________________

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?

Amount saved (             ).

Answer 1

Given

Average demand d= 29 units per day

Number of business days in a year is 250 days

Annual demand D = 29 * 250 = 7250 units

lead time (L)= 30 days

Item unit cost = $56 for orders of less than 260 units

Item unit cost = $54 for orders of 260 units or more

Ordering cost = $31

Inventory carrying cost = 25%

Therefore, holding cost

Number of Units               Holding Cost

Less than 260 units          =0.25 * 56 = $ 14

More than 260 Units             = 0.25 * 54 =$ 13.5

Holding Cost at unit price of 60 and 58 is 0.25 *60 = $ 15 and 0.25 * 58 = 14.5

EOQ at different Units Costs are

Part a)

EOQ =

Q(60) =sqrt ( 2* 7520 * 31 / 15) = 173 Units

Q(58) = sqrt(2* 7520 * 31 / 14.5 )= 176 Units

Q(56) = sqrt(2* 7520 * 31 / 14 )= 179 Units

Q(54) = sqrt(2* 7520 * 31 / 13.5) = 182 Units

Part b)

The annual ordering cost is given by = (D/Q) * S

Since at different unit price of $ 56 and $ 54 are calculated below.

For unit cost to be $56, The EOQ will be 179 units as there will be no discount at this price

So, Ordering Cost = (7250/179 )* 31 = $1255.5

For unit cost to be $58, The minimum quantity to be ordered should be 260 units

So, Ordering Cost = (7250/260 )* 31 = $864.42

Hence , Annual ordering cost at the different prices are

Unit cost at $60 =  $1255.5

Unit cost at $58 = $864.42

Part c) Inventory carrying cost = (Q/2)*H

For unit cost at $56, Quantity = 180 Units

H = $ 14 As calculated earlier

So, ICC = (180/2)* 14 = $ 1260

For unit cost at $54, Quantity = 260 Units

H = $ 13.5 As calculated earlier

So, ICC = (260/2)* 13.5 = $ 1755

Part d)

Annual Product cost at differenet prices are:

At unit price of $58, = 58*7250 = $ 420500

At unit price of $56, = 56*7250 =$ 406000