4. (10 points) The annual demand, ordering cost, and the annual inventory carryi

ID: 412839 • Letter: 4

Question

4. (10 points) The annual demand, ordering cost, and the annual inventory carrying cost rate for a certain item are 600 units, s20 order and 30% of item price, respectively. Price is established by the following quantity discount schedule. The discounts are incremental. uantity rice I to 49 $5,00 per unit $4.50 per unit $4.10 per unit 0 to 249 0 and up (a) What should the order quantity be in order to minimize the average annual cost? (b) S how the minimal average annual cost based on the quantity obtained in (a)

Explanation / Answer

Economic Order Quantity ( EOQ ) is expressed as = Square root ( 2 x Co x D/ Ch)

Where,

Co = Ordering cost = $20

D = Annual demand = 600

Ch = Annual unit holding cost = 30 % of item price.

Since item price is dependent on quantity slabs there will be different Ch and theoretical EOQs for each of the three 3 quantity slabs.

Following table presents corresponding values of Ch and EOQs for each of quantity slab

Quantity slab

EOQ ( rounded to nearest whole number )

1 – 49

30% of $5 = $1.5

126

50 – 249

30% of $4.5 = $1.35

133

250 and above

30% of $4.1 = $1.23

140

The derived EOQ value of the second row matches with its corresponding quantity slab.

Therefore , Economic order quantity which minimizes total annual cost of ordering and inventory holding will be 133

Total annual cost for any order quantity

= Annual product cost + Annual ordering cost + Annual inventory holding cost

= Unit price x annual demand + Ordering cost x Number of orders + Annual unit holding cost x Average inventory

= Unit price x 600 + 20 x Annual demand / Ordering quantity + Annual unit holding cost x Ordering quantity /2

We will calculate total ordering cost for : 1) EOQ of 133 and 2) Minimum order quantity for the next slab i.e. order quantity = 250

Total annual cost for EOQ = 133 :

= 4.5 x 600 + 20 x 600 / 133 + 1.35 x 133 / 2

= 2700 + 90,22 + 89.77

= $2879.99

Total annual cost for order quantity of 250

= 4.1 x 600 + 20 x 600/250 + 1.35 x 250/2

= 2460 + 48 + 168.75

= $2676.75

Thus order quantity that minimizes average annual cost will be 250

ORDER QUANTITY THAT MINIMIZES ANNUAL ORDERING COST = 250

MINIMAL AVERAGE ANNUAL COST = $2676.75