Question

Case 2: Lila Battle has determined that the annual demand for number 6 screws is 100,000 screws. Lila, who works in her brother's hardware store, is in charge of purchasing. She estimates that it costs $10 every time an order is placed. This cost includes her wages, the cost of the forms used in placing the order, and so on. Furthermore, she estimates that the cost of carrying one screw in inventory for a year is one-half of 1 cent. Assume that the demand is constant throughout the year. (a) How many number 6 screws should Lila order at a time if she wishes to minimize total inventory cost? (b) How many orders per year would be placed? What would the annual ordering cost be? (c) What would the average inventory be? What would the annual holding cost be?

Answer 1

Details Given:

1. Annual Demand = 100,000 qty;

2. Ordering Cost = $10 per Order

3. Carrying/Holding Cost = $0.005 per Unit (i.e. 1/2 of $1/100)

So, The Economic Order Qty (Q) = Square root {(2*Annual Demand*Ordering Cost per order)/Holding Cost per unit}

Q = sq root {(2*100,000*$10)/$0.005}

Q = 20,000.

Therefore at the level of 20,000 qty, the cost will be at the least level.

Taking reference from the above,

(a) Total of 20,000 units per order will have the minimum inventory cost.

(b) For the annual demand of 100,000 units, a total of 5 orders will fulfill the same.

The total ordering cost is $50, ie, $10 per order and total of 5 order for fulfilling the annual demand.

(c) Avg Inventory = (0+20,000)/2 = 10,000. Holding Cost = $0.005 per unit. Total Holding Cost = $0.005*10,000 = $50.