It takes approximately 8 working days for an order of number 6 screws to arrive once the order has been placed. (Refer to Problem 6-20.) The demand for number 6 screws is fairly constant, and on the average, Lila has observed that her brother’s hardware store sells 500 of these screws each day. Because the demand is fairly constant, Lila believes that she can avoid stockouts completely if she only orders the number 6 screws at the correct time. What is the ROP?

Problem 6-20

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?

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