Lila Battle has determined that the annual demand for number 6 screws is 100,000

Question

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?

Explanation / Answer

a) let the number of screws to ordered at 1 time = x

number of orders = 100000/x

annual holding cost = 0.5*0.01 * x/2 = x / 400

reordering cost = 10 * 100000/x

total cost = 1000000/x + x/400

we have to minimize total cost

hence x = 20000

b) 5

annual ordering cost = 5 *10 = 50

c) average inventory= x/ 2 = 10000

annual holding cost = x/400 = 10000/200 = 50

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