### Distributed with a standard deviation

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##### Reference no: EM13905456

Suppose that you are the manager of a production department that uses 400 boxes of rivets per year. The supplier quotes you a price of \$8.50 per box for an order size of 199 boxes or less, a price of \$8.00 per box for orders of 200 to 999 boxes, and a price of \$7.50 per box for an order of 1,000 or more boxes. You assign a holding cost of 20 percent of the price to this inventory. What order quantity would you use if the objective is to minimize total annual costs of holding, purchasing, and ordering?

a. Assume ordering cost is \$80/order.

b. At Q=200, what is the carrying cost?

The manager of the Quick Stop convenience store (which never closes) sells 24 six packs of Fizzy soda each day. Order costs are \$8.00 per order, and Fizzy soda costs \$4.00 per six-pack. Holding costs are \$1 per six pack. Orders arrive five days from the time they are placed.

If lead time is constant and demand is normally distributed with a standard deviation of 5 six packs, what safety stock should Quick Stop carry for a 99% service level (round to nearest whole number)? Round to the nearest whole number.

a. If demand is constant and lead time is normally distributed with a standard deviation of 2 days, what safety stock should Quick Stop carry for a 95% service level (round to the nearest whole number)?

b. If demand varies with a standard deviation of 5 six packs and lead time varies with a standard deviation of 2 days and the Quick Stop carries safety stock for a 98% service level, what is the reorder point (round to the nearest whole number)?

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