Question

Ivonne Callen sells beauty supplies. Her annual demand for a particular skin lotion is 1,000 units. The cost of placing an order is $100, while the holding cost per unit per year is 20% of the cost. This item currently cost $50 if the order quantity is less than 100. For orders between 100 and 399 units, the unit cost falls to $49. For orders of 400 units or more, the unit cost falls to $48. To minimize total Inventory cost: (1) How many units should Ivonne order each time she places an order? (2) What is the minimum annual total cost? Show work.

Answer 1

(1) Annual demand, D = 1000 units

Ordering cost, S = $ 100

Considering unit price, C = $ 50

Holding cost, H = 50*0.2 = $ 10

EOQ = SQRT(2*DS/H) = SQRT(2*1000*100/10) = 141.42

This is more than 100, therefore, applicable price is $ 49

Recalculate H = 49*0.2 = 9.8

EOQ = SQRT(2*1000*100/9.8) = 142.86 ~ 143

Total annual cost of EOQ policy = Ordering cost + Holding cost + Product cost = (D/Q)*S+(Q/2)*H+D*P

= (1000/143)*100+(143/2)*9.8+1000*49

= $ 50,400

For Q=400, P = $ 48 , H = 48*0.2 = $ 9.6

Total annual cost of Q=400 policy = Ordering cost + Holding cost + Product cost = (D/Q)*S+(Q/2)*H+D*P

= (1000/400)*100+(400/2)*9.6+1000*48

= $ 50,170

Total cost of 400 units order policy is lower. Therefore, Ivonne should order 400 units each time she places an order.

(2) Minimum annual total cost = $ 50,170   (as calculated in part 1)